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Journal articles on the topic 'Eulerian perturbation theory'
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1
Almeida, Juan P. Beltrán, Josué Motoa-Manzano, Jorge Noreña, Thiago S. Pereira, and César A. Valenzuela-Toledo. "Structure formation in an anisotropic universe: Eulerian perturbation theory." Journal of Cosmology and Astroparticle Physics 2022, no. 02 (February 1, 2022): 018. http://dx.doi.org/10.1088/1475-7516/2022/02/018.
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Abstract We present an effective Eulerian description, in the non-relativistic regime, of the growth of cosmological perturbations around a homogeneous but anisotropic Bianchi I spacetime background. We assume a small deviation from isotropy, sourced at late times for example by dark energy anisotropic stress. We thus derive an analytic solution for the linear dark matter density contrast, and use it in a formal perturbative approach which allows us to derive a second order (non-linear) solution. As an application of the procedure followed here we derive analytic expressions for the power spectrum and the bispectrum of the dark matter density contrast. The power spectrum receives a quadrupolar correction as expected, and the bispectrum receives several angle-dependent corrections. Quite generally, we find that the contribution of a late-time phase of anisotropic expansion to the growth of structure peaks at a finite redshift between CMB decoupling and today, tough the exact redshift value is model-dependent.
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Aviles, Alejandro, Arka Banerjee, Gustavo Niz, and Zachary Slepian. "Clustering in massive neutrino cosmologies via Eulerian Perturbation Theory." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (November 1, 2021): 028. http://dx.doi.org/10.1088/1475-7516/2021/11/028.
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Abstract We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the QUIJOTE simulations, finding excellent agreement on scales k ≲ 0.25 h Mpc-1. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels.
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Kozlikin, Elena, Robert Lilow, Felix Fabis, and Matthias Bartelmann. "A first comparison of Kinetic Field Theory with Eulerian Standard Perturbation Theory." Journal of Cosmology and Astroparticle Physics 2021, no. 06 (June 1, 2021): 035. http://dx.doi.org/10.1088/1475-7516/2021/06/035.
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NANDY, MALAY K., and JAYANTA K. BHATTACHARJEE. "MODE-COUPLING THEORY, DYNAMIC SCALING, AND TWO-DIMENSIONAL TURBULENCE." International Journal of Modern Physics B 09, no. 09 (April 20, 1995): 1081–97. http://dx.doi.org/10.1142/s0217979295000446.
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A self-consistent mode-coupling scheme, along with dynamic scaling ideas, is used to obtain a renormalized perturbation theory in the Eulerian framework from Wyld’s perturbation theory of the forced Navier-Stokes equation. For the force-correlation behaving as k−(d−4+y), the Kolmogorov and Kraichnan-Batchelor scaling spectra of two-dimensional turbulence for the inverse energy cascade, [Formula: see text] and the direct entropy cascade, [Formula: see text], are obtained for y=4 and y=6 respectively, including the logarithmic correction for the latter. Unlike the usual Eulerian formulations (e.g. the direct-interaction approximation), the theory is finite in the energy regime, while it becomes marginal in the enstrophy regime, leading to the logarithmic correction. Calculations yield C=6.447 and C′=1.923 at one-loop order, which are in exact agreement with those of field-theoretic renormalization group calculations [P. Olla, Phys. Rev. Lett. 67, 2465 (1991)]. However, a self-consistent treatment of the logarithmic scalings in E(k) and the inverse response-time yields a different value: C′=2.201. The theory is free of any external parameter; the choice of y(=4 or 6) is dictated by the condition of conserved transfer of energy or enstrophy.
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Roth, Nina, and Cristiano Porciani. "Testing standard perturbation theory and the Eulerian local biasing scheme against N-body simulations." Monthly Notices of the Royal Astronomical Society 415, no. 1 (May 13, 2011): 829–44. http://dx.doi.org/10.1111/j.1365-2966.2011.18768.x.
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Roycroft, R., J. P. Sauppe, and P. A. Bradley. "Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF." Physics of Plasmas 29, no. 3 (March 2022): 032704. http://dx.doi.org/10.1063/5.0083190.
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Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.
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Arico', Giovanni, Raul Angulo, and Matteo Zennaro. "Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory." Open Research Europe 1 (June 15, 2022): 152. http://dx.doi.org/10.12688/openreseurope.14310.2.
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The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum, the analysis of data usually requires 104-106 evaluations, which means this task can be the most computationally expensive aspect of data analysis. Here, we address this problem by building a neural network emulator that provides the linear theory (total and cold) matter power spectrum in about one millisecond with ≈0.2%(0.5%) accuracy over redshifts z ≤ 3 (z ≤ 9), and scales10-4 ≤ k [h Mpc-1] < 50. We train this emulator with more than 200,000 measurements, spanning a broad cosmological parameter space that includes massive neutrinos and dynamical dark energy. We show that the parameter range and accuracy of our emulator is enough to get unbiased cosmological constraints in the analysis of a Euclid-like weak lensing survey. Complementing this emulator, we train 15 other emulators for the cross-spectra of various linear fields in Eulerian space, as predicted by 2nd-order Lagrangian Perturbation theory, which can be used to accelerate perturbative bias descriptions of galaxy clustering. Our emulators are specially designed to be used in combination with emulators for the nonlinear matter power spectrum and for baryonic effects, all of which are publicly available at http://www.dipc.org/bacco.
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Arico', Giovanni, Raul Angulo, and Matteo Zennaro. "Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory." Open Research Europe 1 (December 16, 2021): 152. http://dx.doi.org/10.12688/openreseurope.14310.1.
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The linear matter power spectrum is an essential ingredient in all theoretical models for interpreting large-scale-structure observables. Although Boltzmann codes such as CLASS or CAMB are very efficient at computing the linear spectrum, the analysis of data usually requires 104-106 evaluations, which means this task can be the most computationally expensive aspect of data analysis. Here, we address this problem by building a neural network emulator that provides the linear theory (total and cold) matter power spectrum in about one millisecond with ≈0.2%(0.5%) accuracy over redshifts z ≤ 3 (z ≤ 9), and scales10-4 ≤ k [h Mpc-1] < 50. We train this emulator with more than 200,000 measurements, spanning a broad cosmological parameter space that includes massive neutrinos and dynamical dark energy. We show that the parameter range and accuracy of our emulator is enough to get unbiased cosmological constraints in the analysis of a Euclid-like weak lensing survey. Complementing this emulator, we train 15 other emulators for the cross-spectra of various linear fields in Eulerian space, as predicted by 2nd-order Lagrangian Perturbation theory, which can be used to accelerate perturbative bias descriptions of galaxy clustering. Our emulators are specially designed to be used in combination with emulators for the nonlinear matter power spectrum and for baryonic effects, all of which are publicly available at http://www.dipc.org/bacco.
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Larsson, Jonas. "A new Hamiltonian formulation for fluids and plasmas. Part 1. The perfect fluid." Journal of Plasma Physics 55, no. 2 (April 1996): 235–59. http://dx.doi.org/10.1017/s002237780001881x.
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A new formulation of the Hamiltonian structure underlying the perfect fluid equations is presented. Besides time, a parameter c is also used. Correspondingly, there are two interdependent systems of equations expressing time evolution and e evolution respectively. The accessibility equations define the e dynamics and give the variation in the usual Eulerian fluid variables as determined by the generating functions. The time evolutions of both the Eulerian fluid variables and the generating functions are obtained from an action principle. The consistency of the e and the time dynamics is crucial for this formulation, i.e. the accessibility equations must be propagated in time by the Euler–Lagrange equations. The reason for introducing this new formulation is its power in certain applications where the existing Hamiltonian alternatives seem less convenient to use. In particular, it is a promising tool for Hamiltonian perturbation theory. We consider the small-amplitude expansion, and find, very simply and naturally, the Hermitian structure of the linearized ideal fluid equations as well as coupling coefficients for resonant three-wave interaction exhibiting the Manley–Rowe relations.
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ZHAO, MING, and MOHAMED S. GHIDAOUI. "TRANSIENT DYNAMICS OF STREAK AND LONGITUDINAL VORTICES IN SHEAR FLOW WITH WAVE." International Journal of Modern Physics: Conference Series 19 (January 2012): 139–53. http://dx.doi.org/10.1142/s2010194512008689.
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Langmuir circulations are alternating right and left helical vortices in the ocean having horizontal axes parallel to the wind. They are manifested by floating material on the ocean surface as streaks. The laboratory wind driven shear flow demonstrate streak feature with/without wave condition. When the wave is present the explanation of results with Craik-Leibovich instability mechanism, originally proposed for weak current shear in ocean, is not appropriate for some problem as in the laboratory the current shear is strong. The existing normal mode analysis based on the generalized Lagrangian mean formulation for wave with strong shear is not able to capture the fully dynamics of streak and longitudinal vortices. We extend Craik-Leibovich theory to strong shear in Eulerian framework but focusing on the fully perturbation evolution dynamics. Transient dynamics of perturbation is studied with an initial value problem. In this approach the effect of shear and wave and its interaction are made clear. The transient growth in the time period without wave is significant and is crucial to the initial preferred wave number observed in the experiments. The optimal longitudinal vortex form perturbation is searched and the preferred spanwise wave number predicted is well consistent with experimental data of wind shear and wave.
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Umeyama, Motohiko, Tetsuya Shintani, and Shinya Watanabe. "MEASUREMENTS OF PARTICLE VELOCITIES AND TRAJECTORIES IN A WAVE-CURRENT MOTION USING PARTICLE IMAGE VELOCIMETRY." Coastal Engineering Proceedings 1, no. 32 (January 17, 2011): 2. http://dx.doi.org/10.9753/icce.v32.waves.2.
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This article deals with some physical aspects of a water particle under surface waves, which propagate with or without a current in a constant water depth, using an imaging technique. The use of particle image velocimetry (PIV) made it possible to investigate the velocity and trajectory of each individual water particle. The velocity vector fields and its vertical distributions were estimated at several phases in one wave cycle. The theory of progressive waves based on finite-amplitude approximation was adapted to express the velocity potential, surface displacement and angular frequency. The PIV result showed suitable agreement with a solution solved to the third order by a perturbation method. In addition, the distributions of horizontal and vertical velocity components by the PIV measurement were compared with those by an EC meter. These attempts proved the ability of the PIV technique to accurately measure both temporal and spatial variations of the velocity. This technique was applied to the prediction of particle trajectory in a Eulerian scheme. In the method, the surrounding grid velocities were used to identify a Lagrangian velocity. The measured particle path was compared with the positions found theoretically by integrating the Eulerian velocity to the second order of a Taylor series expansion.
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Famaey, B., G. Monari, A. Siebert, J. B. Fouvry, and J. Binney. "Distribution functions for Galactic disc stellar populations in the presence of non-axisymmetric perturbations." Proceedings of the International Astronomical Union 13, S334 (July 2017): 195–98. http://dx.doi.org/10.1017/s174392131700672x.
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AbstractThe present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential, in the form of a bar or spiral arms, can be treated, away from the main resonances, through perturbation theory within the action-angle coordinates of the unperturbed axisymmetric system. The first order moments of such a perturbed distribution function (DF) in the presence of spiral arms give rise to non-zero radial and vertical mean stellar velocities, called breathing modes. Such an Eulerian linearized treatment however diverges at resonances. The Lagrangian approach to the impact of non-axisymmetries at resonances avoids this problem. It is based on the construction of new orbital tori in the resonant trapping region, which come complete with a new system of angle-action variables. These new tori can be populated by phase-averaging the unperturbed DF over the new tori. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits only depends on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data with an action-based DF.
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BALLAI, I., R. ERDÉLYI, and M. GOOSSENS. "Nonlinear theory of non-axisymmetric resonant slow waves in straight magnetic flux tubes." Journal of Plasma Physics 64, no. 5 (November 2000): 579–99. http://dx.doi.org/10.1017/s0022377800008965.
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Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer.
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Radko, Timour, and John Marshall. "The Antarctic Circumpolar Current in Three Dimensions." Journal of Physical Oceanography 36, no. 4 (April 1, 2006): 651–69. http://dx.doi.org/10.1175/jpo2893.1.
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Abstract A simple theory is developed for the large-scale three-dimensional structure of the Antarctic Circumpolar Current and the upper cell of its overturning circulation. The model is based on a perturbation expansion about the zonal-average residual-mean model developed previously by Marshall and Radko. The problem is solved using the method of characteristics for idealized patterns of wind and buoyancy forcing constructed from observations. The equilibrium solutions found represent a balance between the Eulerian meridional overturning, eddy-induced circulation, and downstream advection by the mean flow. Depth and stratification of the model thermocline increase in the Atlantic–Indian Oceans sector where the mean wind stress is large. Residual circulation in the model is characterized by intensification of the overturning circulation in the Atlantic–Indian sector and reduction in strength in the Pacific Ocean region. Predicted three-dimensional patterns of stratification and residual circulation in the interior of the ACC are compared with observations.
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Valášek, Jan, and Petr Sváček. "Aeroacoustic computation of fluid-structure interaction problems with low Mach numbers." EPJ Web of Conferences 180 (2018): 02113. http://dx.doi.org/10.1051/epjconf/201818002113.
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This contribution deals with the acoustic simulation of aerodynamical noise generated by a flow over an airfoil or by flow in a flexible channel. Since the considered flow has low Mach number the hybrid approach of acoustic analogies can be applied here with benefits. The fluid-structure-acoustic interaction problem is generally described as a quite complicated problem comprising of three different physical fields - the vibration of the elastic body, the unsteady fluid flow and the acoustics together with mutual couplings. The fluid flow in time dependent domain is governed by the incompressible Navier-Stokes equations in arbitrary Langrangian-Eulerian formulation and the elastic structure is modelled by the means of linear elasticity theory. The Lighthill analogy and acoustic perturbation equation (APE) is considered to describe the sound propagation. The simulation of fluid-structure (FSI) interaction and acoustic field is implemented using the FEM in an in-house solver. The sound sources computed from FSI results are analyzed and within sound propagation simulation the perfectly matched layer technique is used. In the end the results of Lighthill and APE analogy are compared.
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WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave." Journal of Fluid Mechanics 659 (July 27, 2010): 191–224. http://dx.doi.org/10.1017/s0022112010002430.
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Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described by the linear wave equation, also for the first and second orders. Matching between the two expansions provides the model for the non-spherical bubble behaviour in a compressible fluid. A numerical model using the mixed Eulerian–Lagrangian method and a modified boundary integral method is used to obtain the evolving bubble shapes. The primary advantage of this method is its computational efficiency over using the wave equation throughout the fluid domain. The numerical model is validated against the Keller–Herring equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the fourth oscillation. Numerical analyses are further performed for non-spherical oscillating acoustic bubbles. Bubble evolution and jet formation are simulated. Outputs also include the bubble volume, bubble displacement, Kelvin impulse and liquid jet tip velocity. Bubble behaviour is studied in terms of the wave frequency and amplitude. Particular attention is paid to the conditions if/when the bubble jet is formed and when the bubble becomes multiply connected, often forming a toroidal bubble. When subjected to a weak acoustic wave, bubble jets may develop at the two poles of the bubble surface after several cycles of oscillations. A resonant phenomenon occurs when the wave frequency is equal to the natural oscillation frequency of the bubble. When subjected to a strong acoustic wave, a vigorous liquid jet develops along the direction of wave propagation in only a few cycles of the acoustic wave.
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Chen, Yang-Yih, Meng-Syue Li, Hung-Chu Hsu, and Ying-Pin Lin. "LAGRANGIAN BREAKER CHARACTERISTICS FOR NONLINEAR WATER WAVES PROPAGATING ON SLOPING BOTTOMS." Coastal Engineering Proceedings 1, no. 32 (January 29, 2011): 15. http://dx.doi.org/10.9753/icce.v32.posters.15.
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In this paper, a new third-order Lagrangian asymptotic solution describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. The model is formulated in the Lagrangian variables and we use a two-parameter perturbation method to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness and the bottom slope perturbed to third order. The analytical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. The proposed model has proved to be capable of a better description of non-linear wave effects than the corresponding approximation of the same order derived by using the Eulerian description.
The proposed solution has also been used to determine the wave shoaling process, and the comparisons between the experimental and theoretical results are presented in Fig.1a~1b. In addition, the basic wave-breaking criterion, namely the kinematical Stokes stability condition, has been investigated. The comparisons between the present theory, empirical formula of Goda (2004) and the experiments made by Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005) for the breaking index(Hb/L0) versus the relative water depth(d0/L0) under two different bottom slopes are depicted in Figs 2a~2b. It is found that the theoretical breaking index is well agreement with the experimental results for three bottom slopes. However,for steep slope of 1/3 shown in Fig 2b, the result of Goda‘s empirical formula gives a larger value in comparison with the experimental data and the present theory. Some of empirical formulas presented the breaking wave height in terms of deepwater wave condition, such as in Sunamura (1983) and in Rattanapitikon and Shibayama(2000). Base on the results depicted in Fig. 3a~3b, it showed that the theoretical results are in good agreement with the experimental data (Iwagali et al. 1974, Deo et al.2003 and Tsai et al. 2005) than the empirical formulas. The empirical formula of Sunamura (1983) always predicts an overestimation value.
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Chizhonkov, Eugene V., and Alexander A. Frolov. "Influence of electron temperature on breaking of plasma oscillations." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 2 (April 24, 2019): 71–84. http://dx.doi.org/10.1515/rnam-2019-0006.
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Abstract The influence of thermal motion of electrons on the processes of relativistic plasma oscillations is studied analytically and numerically. It is shown that if the temperature of electrons grows and exceeds a certain critical level, then the breaking effect vanishes due to transformation of plasma oscillations into travelling waves. Analytical conclusions are made in the framework of the theory of small perturbations based on Lagrangian variables. Numerical simulation of the transformation is performed using three different algorithms constructed on the basis of the method of finite differences in Eulerian variables. The analytical results are in good agreement with numerical experiments.
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Aiki, H., and T. Yamagata. "Energetics of the layer-thickness form drag based on an integral identity." Ocean Science 2, no. 2 (October 12, 2006): 161–71. http://dx.doi.org/10.5194/os-2-161-2006.
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Abstract. The vertical redistribution of the geostrophic momentum by the residual effects of pressure perturbations (called the layer-thickness form drag) is investigated using thickness-weighted temporal-averaged mean primitive equations for a continuously stratified fluid in an adiabatic formulation. A four-box energy diagram, in which the mean and eddy kinetic energies are defined by the thickness-weighted mean velocity and the deviation from it, respectively, shows that the layer-thickness form drag reduces the mean kinetic energy and endows the eddy field with an energy cascade. The energy equations are derived using an identity (called the "pile-up rule") between cumulative sums of the Eulerian mean quantity and the thickness-weighted mean quantity in each vertical column. The pile-up rule shows that the thickness-weighted mean velocity satisfies a no-normal-flow boundary condition at the top and bottom of the ocean, which enables the volume budget of pressure flux divergence in the energy diagram to be determined. With the pile-up rule, the total kinetic energy based on the Eulerian mean can be rewritten in a thickness-weighted form. The four-box energy diagram in the present study should be consistent with energy diagrams of layer models, the temporal-residual-mean theory, and Iwasaki's atmospheric theory. Under certain assumptions, the work of the layer-thickness form drag in the global ocean circulation is suggested to be comparable to the work done by the wind forcing.
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Aiki, H., and T. Yamagata. "Energetics of the layer-thickness form drag based on an integral identity." Ocean Science Discussions 3, no. 3 (June 20, 2006): 541–68. http://dx.doi.org/10.5194/osd-3-541-2006.
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Abstract. The vertical redistribution of the geostrophic momentum by the residual effects of pressure perturbations (called the layer-thickness form drag) is investigated using thickness-weighted temporal-averaged mean primitive equations for a continuously stratified fluid in an adiabatic formulation. A four-box energy diagram, in which the mean and eddy kinetic energies are defined by the thickness-weighted mean velocity and the deviation from it, respectively, shows that the layer-thickness form drag reduces the mean kinetic energy and endows the eddy field with an energy cascade. The energy equations are derived using an identity (called the "pile-up rule'') between cumulative sums of the Eulerian mean quantity and the thickness-weighted mean quantity in each vertical column. The pile-up rule shows that the thickness-weighted mean velocity satisfies a no-normal-flow boundary condition at the top and bottom of the ocean, which enables the volume budget of pressure flux divergence in the energy diagram to be determined. With the pile-up rule, the total kinetic energy based on the Eulerian mean can be rewritten in a thickness-weighted form. The four-box energy diagram in the present study should be consistent with energy diagrams of layer models, the temporal-residual-mean theory, and Iwasaki's atmospheric theory. Under certain assumptions, the work of the layer-thickness form drag in the global ocean circulation is suggested to be comparable to the work done by the wind forcing.
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Bates, J. W. "On the theory of a shock wave driven by a corrugated piston in a non-ideal fluid." Journal of Fluid Mechanics 691 (December 5, 2011): 146–64. http://dx.doi.org/10.1017/jfm.2011.463.
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AbstractIn the context of an Eulerian fluid description, we investigate the dynamics of a shock wave that is driven by the steady impulsively initiated motion of a two-dimensional planar piston with small corrugations superimposed on its surface. This problem was originally solved by Freeman (Proc. Royal Soc. A, vol. 228, 1955, pp. 341–362), who showed that piston-driven shocks are unconditionally stable when the fluid medium through which they propagate is an ideal gas. Here, we generalize Freeman’s mathematical framework to account for a fluid characterized by an arbitrary equation of state. We find that a sufficient condition for shock stability is $\ensuremath{-} 1\lt h\lt {h}_{c} $, where $h$ is the D’yakov parameter and ${h}_{c} $ is a critical value less than unity. For values of $h$ within this range, linear perturbations imparted to the front by the piston at time $t= 0$ attenuate asymptotically as ${t}^{\ensuremath{-} 3/ 2} $. Outside of this range, the temporal behaviour of perturbations is more difficult to determine and further analysis is required to assess the stability of a shock front under such circumstances. As a benchmark of the main conclusions of this paper, we compare our generalized expression for the linearized shock-ripple amplitude with an independent Bessel-series solution derived by Zaidel’ (J. Appl. Math. Mech., vol. 24, 1960, pp. 316–327) and find excellent agreement.
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Manucharyan, Georgy E., Michael A. Spall, and Andrew F. Thompson. "A Theory of the Wind-Driven Beaufort Gyre Variability." Journal of Physical Oceanography 46, no. 11 (November 2016): 3263–78. http://dx.doi.org/10.1175/jpo-d-16-0091.1.
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AbstractThe halocline of the Beaufort Gyre varies significantly on interannual to decadal time scales, affecting the freshwater content (FWC) of the Arctic Ocean. This study explores the role of eddies in the Ekman-driven gyre variability. Following the transformed Eulerian-mean paradigm, the authors develop a theory that links the FWC variability to the stability of the large-scale gyre, defined as the inverse of its equilibration time. The theory, verified with eddy-resolving numerical simulations, demonstrates that the gyre stability is explicitly controlled by the mesoscale eddy diffusivity. An accurate representation of the halocline dynamics requires the eddy diffusivity of 300 ± 200 m2 s−1, which is lower than what is used in most low-resolution climate models. In particular, on interannual and longer time scales the eddy fluxes and the Ekman pumping provide equally important contributions to the FWC variability. However, only large-scale Ekman pumping patterns can significantly alter the FWC, with spatially localized perturbations being an order of magnitude less efficient. Lastly, the authors introduce a novel FWC tendency diagnostic—the Gyre Index—that can be conveniently calculated using observations located only along the gyre boundaries. Its strong predictive capabilities, assessed in the eddy-resolving model forced by stochastic winds, suggest that the Gyre Index would be of use in interpreting FWC evolution in observations as well as in numerical models.
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Chakraborty, Rishiraj, Aaron Coutino, and Marek Stastna. "Particle clustering and subclustering as a proxy for mixing in geophysical flows." Nonlinear Processes in Geophysics 26, no. 3 (September 16, 2019): 307–24. http://dx.doi.org/10.5194/npg-26-307-2019.
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Abstract. The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating a Lagrangian description of the flow. The existence and persistence of Lagrangian coherent structures in fluid flow has been a topic of considerable study. Here we focus on the ability of Lagrangian methods to characterize mixing in geophysical flows. We study the instability of a strongly non-linear double-jet flow, initially in geostrophic balance, which forms quasi-coherent vortices when subjected to ageostrophic perturbations. Particle clustering techniques are applied to study the behavior of the particles in the vicinity of coherent vortices. Changes in inter-particle distance play a key role in establishing the patterns in particle trajectories. This paper exploits graph theory in finding particle clusters and regions of dense interactions (also known as subclusters). The methods discussed and results presented in this paper can be used to identify mixing in a flow and extract information about particle behavior in coherent structures from a Lagrangian point of view.
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Maeder, Marcus, Gwénaël Gabard, and Steffen Marburg. "90 Years of Galbrun’s Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement." Journal of Theoretical and Computational Acoustics 28, no. 04 (October 13, 2020): 2050017. http://dx.doi.org/10.1142/s2591728520500176.
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The field of aeroacoustics has gained much attention since the well-known acoustic analogies were first published in the 1950s. In parallel, the continuous growth of computational resources has enabled researchers and engineers to investigate phenomena involving flow-induced noise or sound propagation effects related to arbitrary velocity fields. To describe the latter mentioned physical processes, Galbrun utilized a mixed Eulerian–Lagrangian framework to describe perturbations of the underlying fluid dynamics. While less known compared to the more common linearized Euler equations, Galbrun’s equation provides an original framework. Since its publication in 1931, a number of scholars have further developed the approach first proposed by Galbrun. This paper provides a review of the existing literature dedicated to the use of Galbrun’s equation by highlighting possible advantages of the underlying theory as well as difficulties when utilizing numerical methods for solving problems in time or frequency domain. Furthermore, this work intents to serve as a companion for researchers interested in the field of aeroacoustics and hydroacoustics associated with Galbrun’s equation.
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Bose, Benjamin, Alkistis Pourtsidou, Katarina Markovič, and Florian Beutler. "Assessing non-linear models for galaxy clustering – II. Model validation and forecasts for Stage IV surveys." Monthly Notices of the Royal Astronomical Society 493, no. 4 (February 19, 2020): 5301–22. http://dx.doi.org/10.1093/mnras/staa502.
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ABSTRACT Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large-scale structure (EFTofLSS) inspired model. Using simulation data and a least-χ2 analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilizing the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, f, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalized constraints on f at z = 0.5 and z = 1 than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.
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Kleinert, Andreas. "Leonhardi Euleri Opera omnia: Editing the works and correspondence of Leonhard Euler." Studia Historiae Scientiarum 14 (May 27, 2015): 13–35. http://dx.doi.org/10.4467/23921749pkhn_pau.16.002.5258.
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The paper gives an overview on the history and present state of the edition of the complete works of Leonhard Euler (1707–1783). After several failed initiatives in the 19th century, the project began in 1907 with the edition of Euler’s printed works. The works were divided into three series: I. Mathematics (29 volumes); II. Mechanics and Astronomy (31 volumes); and III. Physics and Miscellaneous (12 volumes). After several ups and downs due to two World Wars and economic problems, the publication of the printed works with a total of 72 volumes is nearly finished. Only two volumes on perturbation theory in astronomy are still missing. The publication of series IV (manuscripts and correspondence) started in 1967 as a joint project of the Swiss and the Soviet academies of sciences. The manuscript edition was postponed, and the project focussed on Euler’s correspondence which contains approximately 3000 letters, 1000 of them written by Euler. The correspondents include famous mathematicians of the 18th century like d’Alembert, Clairaut and the Bernoullis, but also many less-known people with whom Euler corresponded on a great variety of subjects. A major problem is to find and to finance appropriate editors who are able to read French, Latin, and the old German handwriting, and who are acquainted with history, culture and science of the 18th century. During the last 50 years, the editors gathered copies or scans of most of the preserved Euler’s letters. The original letters addressed to Euler were made available to the editorial group in Switzerland by the Russian Academy of Sciences before World War I, and before their restitution in 1947 the editors made fairly good photographs that are now an important part of the material basis of the edition. Each volume of the letter series (VIA) contains Euler’s correspondence with one or more of his contemporaries, presented in a chronological order. Up to the present day, four volumes of the correspondence have been published, in addition to an inventory of all known letters to and from Euler, including short summaries and useful information about the date, language and location of the existing copies, and former publication. Four more volumes are in progress and will be published in 2016 or 2017. The remaining letters that are not intended for publication in the printed volumes are planned to be made available in an online edition.
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Hahn, Oliver, Cornelius Rampf, and Cora Uhlemann. "Higher-order initial conditions for mixed baryon-CDM simulations." Monthly Notices of the Royal Astronomical Society, December 11, 2020. http://dx.doi.org/10.1093/mnras/staa3773.
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Abstract We present a novel approach to generate higher-order initial conditions (ICs) for cosmological simulations that take into account the distinct evolution of baryons and dark matter. We focus on the numerical implementation and the validation of its performance, based on both collisionless N-body simulations and full hydrodynamic Eulerian and Lagrangian simulations. We improve in various ways over previous approaches that were limited to first-order Lagrangian perturbation theory (LPT). Specifically, we (1) generalize nth-order LPT to multi-fluid systems, allowing 2LPT or 3LPT ICs for two-fluid simulations, (2) employ a novel propagator perturbation theory to set up ICs for Eulerian codes that are fully consistent with 1LPT or 2LPT, (3) demonstrate that our ICs resolve previous problems of two-fluid simulations by using variations in particle masses that eliminate spurious deviations from expected perturbative results, (4) show that the improvements achieved by going to higher-order PT are comparable to those seen for single-fluid ICs, and (5) demonstrate the excellent (i.e., few per cent level) agreement between Eulerian and Lagrangian simulations, once high-quality initial conditions are used. The rigorous development of the underlying perturbation theory is presented in a companion paper. All presented algorithms are implemented in the Monofonic Music-2 package that we make publicly available.
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"Eulerian perturbation theory in non-flat universes: second-order approximation." Monthly Notices of the Royal Astronomical Society, September 1, 1995. http://dx.doi.org/10.1093/mnras/276.1.39.
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Gomez-Navarro, D. V., A. J. Mead, A. Aviles, and A. de la Macorra. "Impact of cosmological signatures in two-point statistics beyond the linear regime." Monthly Notices of the Royal Astronomical Society, November 4, 2020. http://dx.doi.org/10.1093/mnras/staa3393.
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Abstract Some beyond ΛCDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and hmcode- a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard ΛCDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations.
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Kitaura, Francisco-Shu, Metin Ata, Sergio A. Rodríguez-Torres, Mónica Hernández-Sánchez, A. Balaguera-Antolínez, and Gustavo Yepes. "COSMIC BIRTH: Efficient Bayesian Inference of the Evolving Cosmic Web from Galaxy Surveys." Monthly Notices of the Royal Astronomical Society, December 15, 2020. http://dx.doi.org/10.1093/mnras/staa3774.
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Abstract We present COSMIC BIRTH: COSMological Initial Conditions from Bayesian Inference Reconstructions with THeoretical models: an algorithm to reconstruct the primordial and evolved cosmic density fields from galaxy surveys on the light-cone. The displacement and peculiar velocity fields are obtained from forward modelling at different redshift snapshots given some initial cosmic density field within a Gibbs-sampling scheme. This allows us to map galaxies, observed in a light-cone, to a single high redshift and hereby provide tracers and the corresponding survey completeness in Lagrangian space including tetrahedral tessellation mapping. These Lagrangian tracers in turn permit us to efficiently obtain the primordial density field, making the COSMIC BIRTH code general to any structure formation model. Our tests are restricted for the time being to Augmented Lagrangian Perturbation theory. We show how to robustly compute the non-linear Lagrangian bias from clustering measurements in a numerical way, enabling us to get unbiased dark matter field reconstructions at initial cosmic times. We also show that we can accurately recover the information of the dark matter field from the galaxy distribution based on a detailed simulation. Novel key ingredients to this approach are a higher-order Hamiltonian sampling technique and a non-diagonal Hamiltonian mass-matrix. This technique could be used to study the Eulerian galaxy bias from galaxy surveys and could become an ideal baryon acoustic reconstruction technique. In summary, this method represents a general reconstruction technique, including in a self-consistent way a survey mask, non-linear and non-local bias and redshift space distortions, with an efficiency about 10 times superior to previous comparable methods.
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Mohaghar, Mohammad, and Donald R. Webster. "Characterization of Non-linear Internal Waves Using PIV/PLIF Techniques." 14th International Symposium on Particle Image Velocimetry 1, no. 1 (August 1, 2021). http://dx.doi.org/10.18409/ispiv.v1i1.84.
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Internal waves are ubiquitous in the ocean. They often form in regions of high temperature or salinity variability as the pycnocline oscillates to form the wave (Phillips, 1966). They can be generated either from the interaction of tidal currents with submarine bathymetry (Garrett and Kunze, 2007) or by wind stress at the ocean surface (Munk and Wunsch, 1998). The current study addresses non-linear internal waves due to their importance in the mixing and dynamics of both atmospheric and oceanographic flows. Due to the significance of this phenomena, numerous investigations have been conducted to obtain satisfactory theoretical solutions for internal waves in several types of fluid systems. The verification of these models requires precise and accurate experimental data. It should be noted that such models generally assume simple two-layer stratified system separated by a sharp interface. In reality, there is a gradient of density at the interface of the two layers, which can make both experimental and theoretical analysis more challenging. To date, most experimental studies for several types of internal waves have been performed using ultrasonic probes, conductivity probes, resistance-type wave gauges, or salinity-sensor-type wave gauges, as given by Davis and Acrivos (1967),Koop and Butler (1981),Michallet and Barthelemy (1998) and Umeyama (2002). There is one recent study that used the particle image velocimetry (PIV) technique to determine the Eulerian velocity field of internal waves, but it lacks the detailed density measurements necessary to fully understand the flow (Umeyama and Matsuki, 2011). The current work aims to fully understand the dynamics of internal waves by measuring the density and velocity fields, and then comparing the experimental results with the theoretical non-linear wave solution. A laboratory-scale apparatus was created to replicate the flow characteristics of internal waves in a twolayer stratified system. An experimental configuration is presented with a density jump of 1.1 and 1.5 σt separately. Experiments are conducted in the tank (2.438 m × 50 cm × 50 cm), which was constructed from clear acrylic sheets with thickness of 1.905 cm. The schematic of the internal wavemaker apparatus is shown in Fig. 1(a) (Mohaghar et al., 2020). A line diffuser (PVC) was installed along the middle of the tank floor to be used to fill the tank. A half-cylinder plunger-type wavemaker was used to create a perturbation at the pycnocline represented by the interface between the density layers. On each revolution of the drive mechanism, the switch sent a voltage signal to the external trigger port of a pulse generator. By precisely controlling the delay following the external trigger signal, the pulse generator sent a signal to the Nd:YAG laser and the camera to capture an image at a targeted phase of the wave cycle. Images are recorded with a high resolution 29 MP CCD camera, (14-bits, 6600 × 4400 pixels). PIV was used to measure the velocity field, and the fluids in both layers were seeded with neutrallybuoyant particles. The seeded particles were illuminated using a dual-cavity New Wave Research Gemini PIV laser at wavelength of 532 nm, which is diverged into a sheet. Light entering the PIV camera passed through a 532 nm bandpass filter. The image pairs were processed with Insight 4GTM software using a 32 × 32 pixel final spot size with 50% overlap. A sample of PIV vector field for the case of ∆ρ = 1.5σt is shown in Fig. 1(b). In order to measure the density fields, the flow is visualized using the planar laser-induced fluorescence (PLIF) method for scalar visualization. A laser-fluorescing dye, Rhodamine 6G, is mixed into the heavier layer and the light sheet is used to fluoresce the dye. Following the procedures outlined by Mohaghar (2019), the dye concentration is then inferred from the digital images. In order to capture only fluorescence emitted by Rhodamine 6G, the camera is equipped with a notch filter blocking the 532 nm wavelength of light. A sample of a final processed PLIF image for the case of ∆ρ = 1.5σt is shown in Fig. 1(c). The interface location, density gradient, wave amplitude and period, velocity and vorticity fields, kinetic energy and shear strain rate are quantified by several phases in one wave cycle and subsequently compared with the corresponding predictions based on third-order Stokes internal-wave theory.
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Canet, Léonie. "Functional renormalisation group for turbulence." Journal of Fluid Mechanics 950 (October 24, 2022). http://dx.doi.org/10.1017/jfm.2022.808.
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Turbulence is a complex nonlinear and multi-scale phenomenon. Although the fundamental underlying equations, the Navier–Stokes equations, have been known for two centuries, it remains extremely challenging to extract from them the statistical properties of turbulence. Therefore, for practical purposes, a sustained effort has been devoted to obtaining an effective description of turbulence, that we may call turbulence modelling, or statistical theory of turbulence. In this respect, the renormalisation group (RG) appears as a tool of choice, since it is precisely designed to provide effective theories from fundamental equations by performing in a systematic way the average over fluctuations. However, for Navier–Stokes turbulence, a suitable framework for the RG, allowing in particular for non-perturbative approximations, has been missing, which has thwarted RG applications for a long time. This framework is provided by the modern formulation of the RG called the functional renormalisation group (FRG). The use of the FRG has enabled important progress in the theoretical understanding of homogeneous and isotropic turbulence. The major one is the rigorous derivation, from the Navier–Stokes equations, of an analytical expression for any Eulerian multi-point multi-time correlation function, which is exact in the limit of large wavenumbers. We propose in this JFM Perspectives article a survey of the FRG method for turbulence. We provide a basic introduction to the FRG and emphasise how the field-theoretical framework allows one to systematically and profoundly exploit the symmetries. We stress that the FRG enables one to describe fully developed turbulence forced at large scales, which was not accessible by perturbative means. We show that it yields the energy spectrum and second-order structure function with accurate estimates of the related constants, and also the behaviour of the spectrum in the near-dissipative range. Finally, we expound the derivation of the spatio-temporal behaviour of $n$ -point correlation functions, and largely illustrate these results through the analysis of data from experiments and direct numerical simulations.