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Journal articles on the topic 'Cascade of turbulent cells'

Author: Grafiati

Published: 28 June 2021

Last updated: 1 February 2022

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1

Medina, Socorro, Ellen Sukovich, and Robert A. Houze. "Vertical Structures of Precipitation in Cyclones Crossing the Oregon Cascades." Monthly Weather Review 135, no. 10 (October 1, 2007): 3565–86. http://dx.doi.org/10.1175/mwr3470.1.

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Abstract The vertical structure of radar echoes in extratropical cyclones moving over the Oregon Cascade Mountains from the Pacific Ocean indicates characteristic precipitation processes in three basic storm sectors. In the early sector of a cyclone, a leading edge echo (LEE) appears aloft and descends toward the surface. Updraft cells inferred from the vertically pointing Doppler radial velocity are often absent or weak. In the middle sector the radar echo consists of a thick, vertically continuous layer extending from the mountainside up to a height of approximately 5–6 km that lasts for several hours. When the middle sector passes over the windward slope of the Cascades, the vertical structure of the precipitation exhibits a double maximum echo (DME). One maximum is associated with the radar reflectivity bright band. The second reflectivity maximum is located approximately 1–2.5 km above the bright band. The secondary reflectivity maximum aloft does not appear until the middle sector passes over the windward slope of the Cascades, suggesting that this feature results from or is enhanced by the interaction of the baroclinic system with the terrain. In the intervening region between the two reflectivity maxima there is a turbulent layer with updraft cells (>0.5 m s−1), spaced 1–3 km apart. This turbulent layer is thought to be crucial for enhancing the growth of precipitation particles and thus speeding up their fallout over the windward slope of the Cascades. In the late sector of the storm, the precipitation consists of generally isolated shallow convection echoes (SCEs), with low echo tops and, in some cases, upward motion near the tops of the cells. The SCEs become broader upon interacting with the windward slope of the Cascade Range, suggesting that orographic uplift enhances the convective cells. In the SCE period the precipitation decreases very sharply on the lee slope of the Cascades.

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2

Budiarso, Ahmad Indra Siswantara, Steven Darmawan, and Harto Tanujaya. "Inverse-Turbulent Prandtl Number Effects on Reynolds Numbers of RNG k-ε Turbulence Model on Cylindrical-Curved Pipe." Applied Mechanics and Materials 758 (April 2015): 35–44. http://dx.doi.org/10.4028/www.scientific.net/amm.758.35.

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Inverse-turbulent Prandtl number (α) is one of important parameters on RNG k-ε turbulence model which represent the cascade energy of the flow, which occur in cylindrical curved-pipe. Although many research has been done, turbulent flow in curved pipe is still a challanging problem. The range of α of the basic RNG k-ε turbulence model described by Yakhot and Orszag (1986) with range 1-1.3929 has to be more specific on Reynolds number (Re) and geometry. However, since the viscosity is sensitive to velocity and temperature, the reference of α is needed on specific range of Reynolds number. This paper is aimed to gain optimum inverse-turbulent Prandtl number of the flow in curved pipe with upper and lower Re which simulated numerically with CFD. The Re at the inlet side were; Re = 13000 and Re = 63800 on cylindrical curved-pipe with r/D of 1.607.The inverse-turbulent Prandtl number (α) were varied to 1, 1.1, 1.2, 1.3. The curved pipe was an cylindrical air pipe with 43mm inlet diameter. The computational grid that is used for CFD numerical simulation with CFDSOF®, hexagonal-surface fitted consist of 139440 cells. CFD simulation done with inverse-turbulent Prandtl number α varies by 1, 1.1, 1.2, dan 1.3. The wall is assumed to zero-roughness. The CFD simulation generated several results; at Re 13000, the value of α did not affect the turbulent parameter which also confirmed the basic therory of RNG k-ε turbulence model that the minimum Re of α is 2.5 x 104. At Re = 63800, the use of α of 1.1 shows more turbulent flow domination on molecular flow. Lower eddy dissipation by 1.67%, increasing turbulent kinetic energy by 2.2%, and Effective viscosity increase by 4.7% compared to α = 1. Therefore, the use of α 1.1 is the most suitable value to be used to represent turbulent flow in curved pipe with RNG k-ε turbulence model with Re 63800 and r/D 1.607 among others value that have discussed in this paper.

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3

Houze, Robert A., and Socorro Medina. "Turbulence as a Mechanism for Orographic Precipitation Enhancement." Journal of the Atmospheric Sciences 62, no. 10 (October 1, 2005): 3599–623. http://dx.doi.org/10.1175/jas3555.1.

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Abstract This study examines the dynamical and microphysical mechanisms that enhance precipitation during the passage of winter midlatitude systems over mountain ranges. The study uses data obtained over the Oregon Cascade Mountains during the Improvement of Microphysical Parameterization through Observational Verification Experiment 2 (IMPROVE-2; November–December 2001) and over the Alps in the Mesoscale Alpine Program (MAP; September–November 1999). Polarimetric scanning and vertically pointing S-band Doppler radar data suggest that turbulence contributed to the orographic enhancement of the precipitation associated with fronts passing over the mountain barriers. Cells of strong upward air motion (>2 m s−1) occurred in a layer just above the melting layer while the frontal precipitation systems passed over the mountain ranges. Upstream flow appeared to be generally stable except for some weak conditional instability at low levels in the two IMPROVE-2 cases. The cells occurred in a layer of strong shear at the top of a low-level layer of apparently retarded or blocked flow (shown by Doppler radial velocity data). The shear apparently provided a favorable environment for the turbulent cells to develop. The updraft cells appeared at the times and locations where the shear was strongest (>∼10 m s−1 km−1). The Richardson number was slightly less than 0.25 at the level where the cells were observed, suggesting shear-generated turbulence could have been the origin of the updraft cells. Another possibility is that the rough mountainous lower boundary could have triggered buoyancy oscillations within the stable, sheared flow. The existence of turbulent cells made possible a precipitation growth mechanism that would not have been present in a laminar upslope flow. The turbulent cells appeared to facilitate the rapid growth and fallout of condensate generated over the lower windward slopes of the mountains. In a laminar flow over terrain, upward motions would be unlikely to produce liquid water contents adequate to increase the density (and hence the fall speed) of precipitating ice particles by riming. The turbulent updraft cells apparently create pockets of higher values of liquid water content embedded in the widespread frontal cloud system, and snow particles falling from the parent cloud systems can then rapidly rime within the cells and fall out. Observations by polarimetric radar and direct aircraft sampling indicate the occurrence of rimed aggregate snowflakes and/or graupel in the turbulent layer. Inasmuch as the shear layer is the consequence of retardation or blocking of the low-level cross-barrier flow, and the turbulence is a response to the shear, the shear-induced cellularity is an indirect response of the flow to the topography. The turbulence embodied in this orographically induced cellularity allows a quick response of the precipitation fallout to the orography since aggregation and riming of ice particles in the turbulent layer produce heavier, more rapidly falling precipitation particles. Without the turbulent cells, condensate would more likely be advected farther up and perhaps even over the mountain range. Small-scale cellularity has traditionally been associated with the release of buoyant instability by the upslope flow. Our results suggest that cellularity may be achieved even if buoyant instability is weak or nonexistent, so that even a stable flow has the capacity to form cells that will enhance the precipitation fallout over the windward slopes.

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4

Petukhov, E. P., Y. B. Galerkin, and A. F. Rekstin. "A Study of Testing Procedures of Vaned Diffusers of a Centrifugal Compressor Stage in a Virtual Wind Tunnel." Proceedings of Higher Educational Institutions. Маchine Building, no. 8 (713) (August 2019): 51–64. http://dx.doi.org/10.18698/0536-1044-2019-8-51-64.

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A mathematical model of a vaned diffuser of a centrifugal compressor stage can be constructed based on the results of mass CFD-calculations, similar to that of vaneless diffusors. The methods for calculating the annular cascade and the straight cascade differ due to the existence of vaneless diffusor sections in front of the cascade and behind it. The rational dimensions of these sections are determined. The calculations of two-dimensional cascades without restricting walls appear to be irrational. The calculation is effective for a sector with one vane channel, a moderate number of cells, and the turbulence model k–ε. Averaging the flow parameters at the blade cascade exit leads to ambiguous results. To calculate the characteristics of the blade cascade, the parameters in a section with a diameter equal to 1.85 of the diameter of the blade cascade exit should be used. In domestic and foreign literature, it is customary to emphasize the effectiveness of the CFD methods that replace physical experiments. Calculations of the compressor stages are called virtual rig testing, while those of the blade cascade are known as virtual wind tunnel testing. To study stationary flow, as a virtual wind tunnel, it suffices to consider the blade cascade itself, the preceding and the subsequent vaneless spaces.

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5

Hwang, C. J., and J. L. Liu. "Inviscid and Viscous Solutions for Airfoil/Cascade Flows Using a Locally Implicit Algorithm on Adaptive Meshes." Journal of Turbomachinery 113, no. 4 (October 1, 1991): 553–60. http://dx.doi.org/10.1115/1.2929114.

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A numerical solution procedure, which includes a locally implicit finite volume scheme and an adaptive mesh generation technique, has been developed to study airfoil and cascade flows. The Euler/Navier–Stokes, continuity, and energy equations, in conjunction with Baldwin-Lomax model for turbulent flow, are solved in the Cartesian coordinate system. To simulate physical phenomena efficiently and correctly, a mixed type of mesh, with unstructured triangular cells for the inviscid region and structured quadrilateral cells for the viscous, boundary layer, and wake regions, is introduced in this work. The inviscid flow passing through a channel with circular arc bump and the laminar flows over a flat plate with/without shock interaction are investigated to confirm the accuracy, convergence, and solution-adaptibility of the numerical approach. To prove the reliability and capability of the present solution procedure further, the inviscid/viscous results for flows over the NACA 0012 airfoil, NACA 65-(12)10 compressor, and one advanced transonic turbine cascade are compared to the numerical and experimental data given in related papers and reports.

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6

Yang, Yan-Tao, and Jie-Zhi Wu. "Channel turbulence with spanwise rotation studied using helical wave decomposition." Journal of Fluid Mechanics 692 (December 16, 2011): 137–52. http://dx.doi.org/10.1017/jfm.2011.500.

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AbstractTurbulent channel flow with spanwise rotation is studied by direct numerical simulation (DNS) and the so-called helical wave decomposition (HWD). For a wall-bounded channel domain, HWD decomposes the flow fields into helical modes with different scales and opposite polarities, which allows us to investigate the energy distribution and nonlinear transfer among various scales. Our numerical results reveal that for slow rotation, the fluctuating energy concentrates into large-scale modes. The flow visualizations show that the fine vortices at the unstable side of the channel form long columns, which are basically along the streamwise direction and may be related to the roll cells reported in previous studies. As the rotation rate increases, the concentration of the fluctuating energy shifts towards smaller scales. For strong rotation, an inverse energy cascade occurs due to the nonlinear interaction of the fluctuating modes. A possible mechanism for this inverse cascade is then proposed and attributed to the Coriolis effect. That is, under strong rotation the fluctuating Coriolis force tends to be parallel to the fluctuating vorticity in the region where the streamwise mean velocity has linear profile. Thus the force can induce strong axial stretching/shrinking of the vortices and change the scales of the vortical structures significantly.

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7

Day, Steven W., and James C. McDaniel. "PIV Measurements of Flow in a Centrifugal Blood Pump: Steady Flow." Journal of Biomechanical Engineering 127, no. 2 (November 18, 2004): 244–53. http://dx.doi.org/10.1115/1.1865189.

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Magnetically suspended left ventricular assist devices have only one moving part, the impeller. The impeller has absolutely no contact with any of the fixed parts, thus greatly reducing the regions of stagnant or high shear stress that surround a mechanical or fluid bearing. Measurements of the mean flow patterns as well as viscous and turbulent (Reynolds) stresses were made in a shaft-driven prototype of a magnetically suspended centrifugal blood pump at several constant flow rates (3–9L∕min) using particle image velocimetry (PIV). The chosen range of flow rates is representative of the range over which the pump may operate while implanted. Measurements on a three-dimensional measurement grid within several regions of the pump, including the inlet, blade passage, exit volute, and diffuser are reported. The measurements are used to identify regions of potential blood damage due to high shear stress and∕or stagnation of the blood, both of which have been associated with blood damage within artificial heart valves and diaphragm-type pumps. Levels of turbulence intensity and Reynolds stresses that are comparable to those in artificial heart valves are reported. At the design flow rate (6L∕min), the flow is generally well behaved (no recirculation or stagnant flow) and stress levels are below levels that would be expected to contribute to hemolysis or thrombosis. The flow at both high (9L∕min) and low (3L∕min) flow rates introduces anomalies into the flow, such as recirculation, stagnation, and high stress regions. Levels of viscous and Reynolds shear stresses everywhere within the pump are below reported threshold values for damage to red cells over the entire range of flow rates investigated; however, at both high and low flow rate conditions, the flow field may promote activation of the clotting cascade due to regions of elevated shear stress adjacent to separated or stagnant flow.

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8

Abhari, R. S., and M. Giles. "A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping." Journal of Turbomachinery 119, no. 1 (January 1, 1997): 77–84. http://dx.doi.org/10.1115/1.2841013.

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An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct interblade phase angles. The validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), and the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the nondimensional aerodynamic damping was influenced by the amplitude of the oscillation.

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9

Düben, Peter D., and Peter Korn. "Atmosphere and Ocean Modeling on Grids of Variable Resolution—A 2D Case Study." Monthly Weather Review 142, no. 5 (April 30, 2014): 1997–2017. http://dx.doi.org/10.1175/mwr-d-13-00217.1.

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Abstract Grids of variable resolution are of great interest in atmosphere and ocean modeling as they offer a route to higher local resolution and improved solutions. On the other hand there are changes in grid resolution considered to be problematic because of the errors they create between coarse and fine parts of a grid due to reflection and scattering of waves. On complex multidimensional domains these errors resist theoretical investigation and demand numerical experiments. With a low-order hybrid continuous/discontinuous finite-element model of the inviscid and viscous shallow-water equations a numerical study is carried out that investigates the influence of grid refinement on critical features such as wave propagation, turbulent cascades, and the representation of geostrophic balance. The refinement technique the authors use is static h refinement, where additional grid cells are inserted in regions of interest known a priori. The numerical tests include planar and spherical geometry as well as flows with boundaries and are chosen to address the impact of abrupt changes in resolution or the influence of the shape of the transition zone. For the specific finite-element model under investigation, the simulations suggest that grid refinement does not deteriorate geostrophic balance and turbulent cascades and the shape of mesh transition zones appears to be less important than expected. However, the results show that the static local refinement is able to reduce the local error, but not necessarily the global error and convergence properties with resolution are changed. The relatively simple tests already illustrate that grid refinement has to go along with a simultaneous change of the parameterization schemes.

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10

He, W., R. S. Gioria, J. M. Pérez, and V. Theofilis. "Linear instability of low Reynolds number massively separated flow around three NACA airfoils." Journal of Fluid Mechanics 811 (December 15, 2016): 701–41. http://dx.doi.org/10.1017/jfm.2016.778.

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Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar–turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien–Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin–Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin–Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin–Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin–Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained.

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11

Eyink, Gregory L. "Turbulent cascade of circulations." Comptes Rendus Physique 7, no. 3-4 (April 2006): 449–55. http://dx.doi.org/10.1016/j.crhy.2006.01.008.

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12

Cheverry, Christophe. "Cascade of phases in turbulent flows." Bulletin de la Société mathématique de France 134, no. 1 (2006): 33–82. http://dx.doi.org/10.24033/bsmf.2501.

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13

CHEN, SHIYI, and ROBERT H. KRAICHNAN. "Inhibition of turbulent cascade by sweep." Journal of Plasma Physics 57, no. 1 (January 1997): 187–93. http://dx.doi.org/10.1017/s0022377896005326.

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The effects of large-scale sweeping velocity on the turbulent cascade to small scales are examined for two problems: the advection of a passive scalar by a multivariate-Gaussian velocity field and incompressible Alfvén-wave turbulence. In both cases, the sweeping produces anisotropy and reduces the strength of cascade. If the direction of the sweep velocity varies with time, a balance is reached between this anisotropy and isotropizing effects associated with the change of direction.

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14

Friedrich, R., and J. Peinke. "Statistical properties of a turbulent cascade." Physica D: Nonlinear Phenomena 102, no. 1-2 (March 1997): 147–55. http://dx.doi.org/10.1016/s0167-2789(96)00235-7.

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15

Schertzer, D., S. Lovejoy, F. Schmitt, Y. Chigirinskaya, and D. Marsan. "Multifractal Cascade Dynamics and Turbulent Intermittency." Fractals 05, no. 03 (September 1997): 427–71. http://dx.doi.org/10.1142/s0218348x97000371.

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Turbulent intermittency plays a fundamental role in fields ranging from combustion physics and chemical engineering to meteorology. There is a rather general agreement that multifractals are being very successful at quantifying this intermittency. However, we argue that cascade processes are the appropriate and necessary physical models to achieve dynamical modeling of turbulent intermittency. We first review some recent developments and point out new directions which overcome either completely or partially the limitations of current cascade models which are static, discrete in scale, acausal, purely phenomenological and lacking in universal features. We review the debate about universality classes for multifractal processes. Using both turbulent velocity and temperature data, we show that the latter are very well fitted by the (strong) universality, and that the recent (weak, log-Poisson) alternative is untenable for both strong and weak events. Using a continuous, space-time anisotropic framework, we then show how to produce a causal stochastic model of intermittent fields and use it to study the predictability of these fields. Finally, by returning to the origins of the turbulent "shell models" and restoring a large number of degrees of freedom (the Scaling Gyroscope Cascade, SGC models) we partially close the gap between the cascades and the dynamical Navier–Stokes equations. Furthermore, we point out that beyond a close agreement between universal parameters of the different modeling approaches and the empirical estimates in turbulence, there is a rather common structure involving both a "renormalized viscosity" and a "renormalized forcing". We conclude that this gives credence to the possibility of deriving analytical/renormalized models of intermittency built on this structure.

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16

Foias, Ciprian, Oscar P. Manley, Ricardo M. S. Rosa, and Roger Temam. "Cascade of energy in turbulent flows." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, no. 6 (March 2001): 509–14. http://dx.doi.org/10.1016/s0764-4442(01)01831-6.

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17

Ballouz, Joseph G., and Nicholas T. Ouellette. "Tensor geometry in the turbulent cascade." Journal of Fluid Mechanics 835 (November 29, 2017): 1048–64. http://dx.doi.org/10.1017/jfm.2017.802.

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The defining characteristic of highly turbulent flows is the net directed transport of energy from the injection scales to the dissipation scales. This cascade is typically described in Fourier space, obscuring its connection to the mechanics of the flow. Here, we recast the energy cascade in mechanical terms, noting that for some scales to transfer energy to others, they must do mechanical work on them. This work can be expressed as the inner product of a turbulent stress and a rate of strain. But, as with all inner products, the relative alignment of these two tensors matters, and determines how strong the energy transfer will be. We show that this tensor alignment behaves very differently in two and three dimensions; in particular, the tensor eigenvalues affect the inner product in very different ways. By comparing the observed energy flux to the maximum possible if the tensors were in perfect alignment, we define an efficiency for the energy cascade. Using data from a direct numerical simulation of isotropic turbulence, we show that this efficiency is perhaps surprisingly low, with an average value of approximately 25 % in the inertial range, although it is spatially heterogeneous. Our results have implications for how the stress and strain-rate magnitudes influence the flux of energy between scales, and may help to explain why the energy cascades in two and three dimensions are different.

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18

Greiner, Martin, Jens Giesemann, and Peter Lipa. "Translational invariance in turbulent cascade models." Physical Review E 56, no. 4 (October 1, 1997): 4263–74. http://dx.doi.org/10.1103/physreve.56.4263.

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19

Cardesa, José I., Alberto Vela-Martín, and Javier Jiménez. "The turbulent cascade in five dimensions." Science 357, no. 6353 (August 17, 2017): 782–84. http://dx.doi.org/10.1126/science.aan7933.

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20

de Divitiis, Nicola. "Bifurcations analysis of turbulent energy cascade." Annals of Physics 354 (March 2015): 604–17. http://dx.doi.org/10.1016/j.aop.2015.01.017.

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21

HIJIKATA, Kunio, and Motohisa YOKOI. "Turbulent structure in a pipe flow with inclined cascade turbulent promoters." Transactions of the Japan Society of Mechanical Engineers Series B 53, no. 488 (1987): 1176–82. http://dx.doi.org/10.1299/kikaib.53.1176.

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22

Bolotnov, Igor A., Richard T. Lahey, Donald A. Drew, and Kenneth E. Jansen. "Turbulent cascade modeling of single and bubbly two-phase turbulent flows." International Journal of Multiphase Flow 34, no. 12 (December 2008): 1142–51. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2008.06.006.

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23

SMITH, K. S., G. BOCCALETTI, C. C. HENNING, I. MARINOV, C. Y. TAM, I. M. HELD, and G. K. VALLIS. "Turbulent diffusion in the geostrophic inverse cascade." Journal of Fluid Mechanics 469 (October 15, 2002): 13–48. http://dx.doi.org/10.1017/s0022112002001763.

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Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earth's atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes.When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When β is significant, we find a clear distinction between the tracer mixing scale, which depends on β but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and β. Our predictions are tested via high- resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.

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24

She, Zhen-Su. "Universal Law of Cascade of Turbulent Fluctuations." Progress of Theoretical Physics Supplement 130 (1998): 87–102. http://dx.doi.org/10.1143/ptps.130.87.

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25

Badii, R., and P. Talkner. "Biasymptotic formula for the turbulent energy cascade." Physical Review E 60, no. 4 (October 1, 1999): 4138–42. http://dx.doi.org/10.1103/physreve.60.4138.

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26

Beck, Christian. "Chaotic cascade model for turbulent velocity distributions." Physical Review E 49, no. 5 (May 1, 1994): 3641–52. http://dx.doi.org/10.1103/physreve.49.3641.

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27

Qiu, Xin, San-Qiu Liu, and Ming-Yang Yu. "Turbulent cascade in a two-ion plasma." Physics of Plasmas 21, no. 11 (November 2014): 112304. http://dx.doi.org/10.1063/1.4901592.

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28

Drivas, Theodore D. "Turbulent Cascade Direction and Lagrangian Time-Asymmetry." Journal of Nonlinear Science 29, no. 1 (June 20, 2018): 65–88. http://dx.doi.org/10.1007/s00332-018-9476-8.

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29

SIVASHINSKY, GREGORY I. "Cascade-Renormalization Theory of Turbulent Flame Speed." Combustion Science and Technology 62, no. 1-3 (November 1988): 77–96. http://dx.doi.org/10.1080/00102208808924003.

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30

Friedrich, R. "Ratchet effect in the inverse turbulent cascade." Chemical Physics 375, no. 2-3 (October 2010): 587–90. http://dx.doi.org/10.1016/j.chemphys.2010.07.027.

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31

Gürcan, Ö. D. "Dynamical network models of the turbulent cascade." Physica D: Nonlinear Phenomena 426 (November 2021): 132983. http://dx.doi.org/10.1016/j.physd.2021.132983.

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32

Hartlep, Thomas, and Jeffrey N. Cuzzi. "Cascade Model for Planetesimal Formation by Turbulent Clustering." Astrophysical Journal 892, no. 2 (April 3, 2020): 120. http://dx.doi.org/10.3847/1538-4357/ab76c3.

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Yasuda, T., and J. C. Vassilicos. "Spatio-temporal intermittency of the turbulent energy cascade." Journal of Fluid Mechanics 853 (August 23, 2018): 235–52. http://dx.doi.org/10.1017/jfm.2018.584.

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In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative term, the spatial turbulent transport of fluctuating energy and the pressure–velocity term. These fluctuations are correlated with each other and with the intense intermittent fluctuations of the interscale energy transfer rate. These correlations are caused by the sweeping effect, the link between nonlinearity and non-locality, and also relate to geometrical alignments between the two-point fluctuating pressure force difference and the two-point fluctuating velocity difference in the case of the correlation between the interscale transfer rate and the pressure–velocity term. All these processes are absent from the spatio-temporal-average picture of the turbulence cascade in statistically stationary and homogeneous turbulence.

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34

Baggaley, Andrew W., and Carlo F. Barenghi. "Turbulent cascade of Kelvin waves on vortex filaments." Journal of Physics: Conference Series 318, no. 6 (December 22, 2011): 062001. http://dx.doi.org/10.1088/1742-6596/318/6/062001.

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35

Xu, Shaokang, P. Morel, and Ö. D. Gürcan. "A turbulent cascade model of bounce averaged gyrokinetics." Physics of Plasmas 25, no. 2 (February 2018): 022304. http://dx.doi.org/10.1063/1.5020145.

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36

Bourgoin, Mickaël. "Turbulent pair dispersion as a ballistic cascade phenomenology." Journal of Fluid Mechanics 772 (May 8, 2015): 678–704. http://dx.doi.org/10.1017/jfm.2015.206.

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Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows ballistically first (Batchelor regime), before undergoing a transition towards a super-diffusive regime where the mean-square separation grows as $t^{3}$ (Richardson regime). Richardson empirically interpreted this super-diffusive regime in terms of a non-Fickian process with a scale-dependent diffusion coefficient (the celebrated Richardson’s ‘$4/3$rd’ law). However, the actual physical mechanism at the origin of such a scale dependent diffusion coefficient remains unclear. The present article proposes a simple physical phenomenology for the time evolution of the mean-square relative separation in turbulent flows, based on a scale-dependent ballistic scenario rather than a scale-dependent diffusive. It is shown that this phenomenology accurately retrieves most of the known features of relative dispersion for particles mean-square separation, among others: (i) it is quantitatively consistent with most recent numerical simulations and experiments for mean-square separation between particles (both for the short-term Batchelor regime and the long-term Richardson regime, and for all initial separations at inertial scales); (ii) it gives a simple physical explanation of the origin of the super-diffusive $t^{3}$ Richardson regime which naturally builds itself as an iterative process of elementary short-term scale-dependent ballistic steps; (iii) it shows that the Richardson constant is directly related to the Kolmogorov constant (and eventually to a ballistic persistence parameter); and (iv) in a further extension of the phenomenology, taking into account third-order corrections, it robustly describes the temporal asymmetry between forward and backward dispersion, with an explicit connection to the cascade of energy flux across scales. An important aspect of this phenomenology is that it simply and robustly connects long-term super-diffusive features to elementary short-term mechanisms, and at the same time it connects basic Lagrangian features of turbulent relative dispersion (both at short and long times) to basic Eulerian features of the turbulent field: second-order Eulerian statistics control the growth of separation (both at short and long times) while third-order Eulerian statistics control the temporal asymmetry of the dispersion process, which can then be directly identified as the signature of the energy cascade and associated to well-known exact results as the Karman–Howarth–Monin relation.

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Lewalle, Jacques, and Lawrence L. Tavlarides. "A cascade‐transport model for turbulent shear flows." Physics of Fluids 6, no. 9 (September 1994): 3109–15. http://dx.doi.org/10.1063/1.868135.

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Musacchio, Stefano, and Guido Boffetta. "Split energy cascade in turbulent thin fluid layers." Physics of Fluids 29, no. 11 (November 2017): 111106. http://dx.doi.org/10.1063/1.4986001.

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KLIMENKO, A. Y. "Examining the Cascade Hypothesis for Turbulent Premixed Combustion." Combustion Science and Technology 139, no. 1 (October 1998): 15–40. http://dx.doi.org/10.1080/00102209808952079.

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40

Yoo, J. Y., and J. W. Yun. "Calculation of a three-dimensional turbulent cascade flow." Computational Mechanics 14, no. 2 (May 1994): 101–15. http://dx.doi.org/10.1007/bf00350278.

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41

Surkov, S. V. "Cascade character of the growth of turbulent eddies." Journal of Engineering Physics 48, no. 4 (April 1985): 409–15. http://dx.doi.org/10.1007/bf00872063.

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Frik, P. G. "Modeling cascade processes in two-dimensional turbulent convection." Journal of Applied Mechanics and Technical Physics 27, no. 2 (1986): 221–28. http://dx.doi.org/10.1007/bf00914733.

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Huang, Mei-Jiau. "Enstrophy Cascade and Smagorinsky Model of 2D Turbulent Flows." Journal of Mechanics 17, no. 3 (September 2001): 121–29. http://dx.doi.org/10.1017/s1727719100004482.

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ABSTRACTDirect numerical simulations of 2D turbulent flows, freely decaying as well as forced, are performed to examine the mechanism of the enstrophy cascade and serve as a template of developing LES models. The stretching effect on the 2D vorticity gradients is emphasized on the analogy of the stretching effect on 3D vorticity. The enstrophy cascade rate, the Reynolds stresses and the associated eddy viscosity for 2D turbulence are correspondingly derived and investigated. Proposed herein is that the enstrophy cascade rate to be modeled in a large-eddy simulation can be and should be calculated using the only available large-eddy information, especially when the Reynolds number is not very large or when the flow is not stationary.The simulation results suggest all Kolmogorov's, Kraichnan's, and Saffman's similarity spectra. The Kolmogorov's spectrum appears in front of forced wave numbers and creates a subrange of a zero enstrophy cascade rate and a constant energy cascade rate. The Saffman's spectrum is the dissipation spectrum at large wave numbers. Kraichnan's spectrum shows up at intermediate wave numbers when the Reynolds number is sufficiently high. When the Smagorinsky model is employed for a large eddy simulation, its inability of capturing the significant reverse cascade phenomenon as observed in the DNS data becomes a fatal defect. Nonetheless, if only the mean cascade rate is concerned, the required Smagorinsky constant is evaluated using the DNS data and compared with the theoretical prediction of the Kraichnan's spectrum.

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44

Reinke, Nico, André Fuchs, Daniel Nickelsen, and Joachim Peinke. "On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics." Journal of Fluid Mechanics 848 (June 5, 2018): 117–53. http://dx.doi.org/10.1017/jfm.2018.360.

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Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small-scale features. Two approaches are used to answer this question. First, two-point statistics, namely structure functions of longitudinal velocity increments, and, second, joint multiscale statistics of these velocity increments are analysed. The joint multiscale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three-point closure that reduces the joint multiscale statistics to simple conditional probability density functions (cPDFs). The cPDFs are described by the Fokker–Planck equation in scale and its Kramers–Moyal coefficients (KMCs). The KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker–Planck equation for each dataset. Knowledge of these stochastic cascade equations enables one to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus, the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. The IFT is taken as a new tool to prove the optimal functional form of the Fokker–Planck equations and subsequently to investigate the question of universality of small-scale turbulence in the datasets. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small-scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multiscale cascades, in other words, their own stochastic fingerprints.

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Valente, P. C., C. B. da Silva, and F. T. Pinho. "The effect of viscoelasticity on the turbulent kinetic energy cascade." Journal of Fluid Mechanics 760 (October 31, 2014): 39–62. http://dx.doi.org/10.1017/jfm.2014.585.

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AbstractDirect numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model, such as those laden with polymers, are presented. It is shown that the strong depletion of the turbulence dissipation reported by previous authors does not necessarily imply a depletion of the nonlinear energy cascade. However, for large relaxation times, of the order of the eddy turnover time, the polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the turbulent dissipative scales. This is effectively a polymer-induced kinetic energy cascade which competes with the nonlinear energy cascade of the turbulence leading to its depletion. It is also shown that the total energy flux to the small scales from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the nonlinear energy cascade flux in Newtonian turbulence.

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46

Louda, Petr, Jaromír Příhoda, and Karel Kozel. "Numerical modelling of turbulent transition in complex geometries." EPJ Web of Conferences 180 (2018): 02057. http://dx.doi.org/10.1051/epjconf/201818002057.

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The work deals with numerical simulation of laminar-turbulent transition in transonic flows in turbine cas-cades. The 3D cascade geometry as well as 2D model cascade in a wind tunnel is simulated. The γ-ζ transition model is based on empirical criteria for start of the transition. The implementation of the model is discussed including re-formulation of the criterion for transition on separation bubble.

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Cimarelli, A., E. De Angelis, J. Jiménez, and C. M. Casciola. "Cascades and wall-normal fluxes in turbulent channel flows." Journal of Fluid Mechanics 796 (May 4, 2016): 417–36. http://dx.doi.org/10.1017/jfm.2016.275.

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The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.

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Horbury, T. S., and A. Balogh. "Structure function measurements of the intermittent MHD turbulent cascade." Nonlinear Processes in Geophysics 4, no. 3 (September 30, 1997): 185–99. http://dx.doi.org/10.5194/npg-4-185-1997.

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Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.

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Bolotnov, Igor A., Richard T. Lahey, Jr., Donald A. Drew, Kenneth E. Jansen, and Assad A. Oberai. "Spectral Cascade Modeling of Turbulent Flow in a Channel." JAPANESE JOURNAL OF MULTIPHASE FLOW 23, no. 2 (2009): 190–204. http://dx.doi.org/10.3811/jjmf.23.190.

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Smith, Charles W., Bernard J. Vasquez, Jesse T. Coburn, Miriam A. Forman, and Julia E. Stawarz. "Correlation Scales of the Turbulent Cascade at 1 au." Astrophysical Journal 858, no. 1 (April 27, 2018): 21. http://dx.doi.org/10.3847/1538-4357/aabb00.

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