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Journal articles on the topic 'Fluid dynamical problems'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Nobumasa, Sugimoto. "IL12 THERMOACOUSTIC INSTABILITY AND ITS RELATED FLUID DYNAMICAL PROBLEMS." Proceedings of the International Conference on Jets, Wakes and Separated Flows (ICJWSF) 2013.4 (2013): _IL12–1_—_IL12–12_. http://dx.doi.org/10.1299/jsmeicjwsf.2013.4._il12-1_.

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Lim, H. A. "Lattice-gas automaton simulations of simple fluid dynamical problems." Mathematical and Computer Modelling 14 (1990): 720–27. http://dx.doi.org/10.1016/0895-7177(90)90276-s.

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3

Zeytounian, R. Kh. "Well-posedness of problems in fluid dynamics (a fluid-dynamical point of view)." Russian Mathematical Surveys 54, no. 3 (1999): 479–564. http://dx.doi.org/10.1070/rm1999v054n03abeh000152.

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Koumboulis, F. N., M. G. Skarpetis, and B. G. Mertzios. "Numerical integration of fluid dynamics problems by discrete dynamical systems." Chaos, Solitons & Fractals 11, no. 1-3 (2000): 193–206. http://dx.doi.org/10.1016/s0960-0779(98)00284-7.

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Zarnescu, Arghir. "Mathematical problems of nematic liquid crystals: between dynamical and stationary problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2201 (2021): 20200432. http://dx.doi.org/10.1098/rsta.2020.0432.

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Mathematical studies of nematic liquid crystals address in general two rather different perspectives: that of fluid mechanics and that of calculus of variations. The former focuses on dynamical problems while the latter focuses on stationary ones. The two are usually studied with different mathematical tools and address different questions. The aim of this brief review is to give the practitioners in each area an introduction to some of the results and problems in the other area. Also, aiming to bridge the gap between the two communities, we will present a couple of research topics that genera

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Rahman, Aminur, and Denis Blackmore. "Walking droplets through the lens of dynamical systems." Modern Physics Letters B 34, no. 34 (2020): 2030009. http://dx.doi.org/10.1142/s0217984920300094.

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Over the past decade the study of fluidic droplets bouncing and skipping (or “walking”) on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems, potential connections with quantum mechanics, and complex nonlinear dynamics. We detail advancements in the field of walking droplets through the lens of Dynamical Systems Theory, and outline questions that can be answered using dynamical systems analysis. The paper begins by discussing the history of the fluidic experiments and their resemblance to quantum experimen

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Geiser, Jürgen. "Modelling and analysis of multiscale systems related to fluid dynamical problems." Mathematical and Computer Modelling of Dynamical Systems 24, no. 4 (2018): 315–18. http://dx.doi.org/10.1080/13873954.2018.1488743.

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8

Wang, Hao Cheng, and Jian Liu. "On Dynamical Simulations in Abrasive Flow Finishing." Advanced Materials Research 320 (August 2011): 75–80. http://dx.doi.org/10.4028/www.scientific.net/amr.320.75.

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In this paper, we point out several problems on fluid mechanics existing in the abrasive flow finishing, and study the dynamic simulations methods in the area. A case study is conducted on the process of free abrasive flow finishing, where we complete the dynamic simulations on the kinematic characteristics by a model of two-phase fluid. It is shown that the theory of two-phase fluid can practically direct the design of polishing machine, and the selection as well as the optimization of parameters for polishing technique.

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9

Moon, F. C. "Nonlinear Dynamical Systems." Applied Mechanics Reviews 38, no. 10 (1985): 1284–86. http://dx.doi.org/10.1115/1.3143693.

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New discoveries have been made recently about the nature of complex motions in nonlinear dynamics. These new concepts are changing many of the ideas about dynamical systems in physics and in particular fluid and solid mechanics. One new phenomenon is the apparently random or chaotic output of deterministic systems with no random inputs. Another is the sensitivity of the long time dynamic history of many systems to initial starting conditions even when the motion is not chaotic. New mathematical ideas to describe this phenomenon are entering the field of nonlinear vibrations and include ideas f

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Salmon, John K., and Michael S. Warren. "Fast Parallel Tree Codes for Gravitational and Fluid Dynamical N-Body Problems." International Journal of Supercomputer Applications and High Performance Computing 8, no. 2 (1994): 129–42. http://dx.doi.org/10.1177/109434209400800205.

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Dijkstra, Henk A., Fred W. Wubs, Andrew K. Cliffe, et al. "Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation." Communications in Computational Physics 15, no. 1 (2014): 1–45. http://dx.doi.org/10.4208/cicp.240912.180613a.

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AbstractWe provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly referred to as ‘tipping points’, is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix

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Bellomo, N., P. LeTallec, and B. Perthame. "Nonlinear Boltzmann Equation Solutions and Applications to Fluid Dynamics." Applied Mechanics Reviews 48, no. 12 (1995): 777–94. http://dx.doi.org/10.1115/1.3005093.

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This paper provides a review of the mathematical results on the solution of the nonlinear Boltzmann equation. The survey deals both with analytical and computational aspects: Mathematical formulation of problems, initial and/or boundary value problems, a survey of the qualitative analysis of solutions, and computational treatment of fluid dynamical problems. A discussion of some problems deserving further study concludes this work.

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SCHMID, PETER J. "Dynamic mode decomposition of numerical and experimental data." Journal of Fluid Mechanics 656 (July 1, 2010): 5–28. http://dx.doi.org/10.1017/s0022112010001217.

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The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degre

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Hasslacher, Brosl, and David A. Meyer. "Modeling Dynamical Geometry with Lattice-Gas Automata." International Journal of Modern Physics C 09, no. 08 (1998): 1597–605. http://dx.doi.org/10.1142/s0129183198001448.

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Conventional lattice-gas automata consist of particles moving discretely on a fixed lattice. While such models have been quite successful for a variety of fluid flow problems, there are other systems, e.g., flow in a flexible membrane or chemical self-assembly, in which the geometry is dynamical and coupled to the particle flow. Systems of this type seem to call for lattice gas models with dynamical geometry. We construct such a model on one-dimensional (periodic) lattices and describe some simulations illustrating its nonequilibrium dynamics.

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15

VLADIMIROV, V. A., and K. I. ILIN. "On the stability of the dynamical system ‘rigid body + inviscid fluid’." Journal of Fluid Mechanics 386 (May 10, 1999): 43–75. http://dx.doi.org/10.1017/s0022112099004267.

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In this paper we study a dynamical system consisting of a rigid body and an inviscid incompressible fluid. Two general configurations of the system are considered: (a) a rigid body with a cavity completely filled with a fluid and (b) a rigid body surrounded by a fluid. In the first case the fluid is confined to an interior (for the body) domain and in the second case it occupies an exterior domain, which may, in turn, be bounded by some fixed rigid boundary or may extend to infinity. The aim of the paper is twofold: (i) to develop Arnold's technique for the system ‘body + fluid’ and (ii) to ob

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Shao, Mingyu, Chicheng Ma, Shuaizhao Hu, Chuansong Sun, and Dong Jing. "Effects of Time-Varying Fluid on Dynamical Characteristics of Cantilever Beams: Numerical Simulations and Experimental Measurements." Mathematical Problems in Engineering 2020 (December 21, 2020): 1–18. http://dx.doi.org/10.1155/2020/6679443.

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In order to obtain the effects of time-varying fluid on dynamical characteristics of cantilever beams, this paper gives a comprehensive study of cantilever beams vibrating in a fluid with variable depth. The mathematical model of the cantilever beams in time-varying fluid is derived by combining Euler–Bernoulli beam theory and velocity potential theory, and the influence of the time-varying fluid is discussed. Then, a two-way fluid-structure interaction (FSI) numerical simulation procedure is proposed to calculate the transient responses of the beam. The validity and accuracy are verified acco

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Griffith, Boyce E., and Sookkyung Lim. "Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method." Communications in Computational Physics 12, no. 2 (2012): 433–61. http://dx.doi.org/10.4208/cicp.190211.060811s.

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AbstractMany problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary (IB) method. In the IB approach to such problems, the elastic forces generated by the immersed structure are applied to the surrounding fluid, and the motion of the immersed structure is determined by the local motion of the fluid. Recently, the IB method has been extended to treat more general elasticity models that include both positional and rotational degrees of freedom. For such models, force and torque must both be applied to the fluid. The positional degrees

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Cheemaa, N., S. Chen, and A. R. Seadawy. "Chiral soliton solutions of perturbed chiral nonlinear Schrödinger equation with its applications in mathematical physics." International Journal of Modern Physics B 34, no. 31 (2020): 2050301. http://dx.doi.org/10.1142/s0217979220503014.

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In this article, we have discussed the analytical treatment of perturbed chiral nonlinear Schrödinger equation with the help of our newly developed method extended modified auxiliary equation mapping method (EMAEMM). By using this newly proposed technique we have found some quite general and new variety of exact traveling wave solutions, which are collecting some kind of semi half bright, dark, bright, semi half dark, doubly periodic, combined, periodic, half hark, and half bright via three parametric values, which is the primary key point of difference of our technique. These results are high

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Goldstein, Raymond E. "Batchelor Prize Lecture Fluid dynamics at the scale of the cell." Journal of Fluid Mechanics 807 (October 17, 2016): 1–39. http://dx.doi.org/10.1017/jfm.2016.586.

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The world of cellular biology provides us with many fascinating fluid dynamical phenomena that lie at the heart of physiology, development, evolution and ecology. Advances in imaging, micromanipulation and microfluidics over the past decade have made possible high-precision measurements of such flows, providing tests of microhydrodynamic theories and revealing a wealth of new phenomena calling out for explanation. Here I summarize progress in four areas within the field of ‘active matter’: cytoplasmic streaming in plant cells, synchronization of eukaryotic flagella, interactions between swimmi

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HENNINGSON, DAN S. "Description of complex flow behaviour using global dynamic modes." Journal of Fluid Mechanics 656 (July 20, 2010): 1–4. http://dx.doi.org/10.1017/s0022112010002776.

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A novel method for performing spectral analysis of a fluid flow solely based on snapshot sequences from numerical simulations or experimental data is presented by Schmid (J. Fluid Mech., 2010, this issue, vol. 656, pp. 5–28). Dominant frequencies and wavenumbers are extracted together with dynamic modes which represent the associated flow structures. The mathematics underlying this decomposition is related to the Koopman operator which provides a linear representation of a nonlinear dynamical system. The procedure to calculate the spectra and dynamic modes is based on Krylov subspace methods;

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Brunton, Steven L., Joshua L. Proctor, and J. Nathan Kutz. "Discovering governing equations from data by sparse identification of nonlinear dynamical systems." Proceedings of the National Academy of Sciences 113, no. 15 (2016): 3932–37. http://dx.doi.org/10.1073/pnas.1517384113.

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Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in

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22

Amabili, Marco, and Michael P. Paı¨doussis. "Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction." Applied Mechanics Reviews 56, no. 4 (2003): 349–81. http://dx.doi.org/10.1115/1.1565084.

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This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear

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23

Wang, Lihua, and Zheng Zhong. "Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid." International Journal of Applied Mechanics 07, no. 03 (2015): 1550045. http://dx.doi.org/10.1142/s1758825115500453.

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A Meshfree Radial Basis Collocation Method (RBCM) associated with explicit and implicit time integration scheme is formulated to study the coupling dynamics of a rotating flexible tube conveying fluid, which involves a partial differential equation (PDE) with variable coefficients. Dispersion studies are performed and they indicate that the proposed RBCM has a very small dispersion error compared with conventional FEM and Galerkin-based meshfree methods. Numerical examples are conducted for the influence of initial flow rate of the fluid, discretization and shape parameter on the dispersion er

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D'yachenko, A. I., and G. A. Lyubimov. "System of equations for describing dynamical problems associated with the mechanics of lung parenchyma." Fluid Dynamics 23, no. 3 (1988): 340–47. http://dx.doi.org/10.1007/bf01054738.

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25

Xie, Xuping, Guannan Zhang, and Clayton G. Webster. "Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network." Mathematics 7, no. 8 (2019): 757. http://dx.doi.org/10.3390/math7080757.

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In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In co

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Drapaca, C. S., S. Sivaloganathan, G. Tenti, and J. M. Drake. "Dynamical Morphology of the Brain's Ventricular Cavities in Hydrocephalus." Journal of Theoretical Medicine 6, no. 3 (2005): 151–60. http://dx.doi.org/10.1080/10273660500143631.

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Although interest in the biomechanics of the brain goes back over centuries, mathematical models of hydrocephalus and other brain abnormalities are still in their infancy and a much more recent phenomenon. This is rather surprising, since hydrocephalus is still an endemic condition in the pediatric population with an incidence of approximately 1–3 per 1000 births. Treatment has dramatically improved over the last three decades, thanks to the introduction of cerebrospinal fluid (CSF) shunts. Their use, however, is not without problems and the shunt failure at two years remains unacceptably high

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Keskinen, R. P. "Transient Hydroelastic Vibration of Piping With Local Nonlinearities." Journal of Pressure Vessel Technology 107, no. 4 (1985): 350–55. http://dx.doi.org/10.1115/1.3264463.

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A mode superposition algorithm is presented to solve fluid and structural dynamics problems in piping systems with a local cross-sectional material nonlinearity, such as cavitation of fluid or circumferential cracking of the pipe material. Two families of eigenmodes are used to decompose the total response into so-called compatibility-controlling and resistance-controlling responses which satisfy the governing partial differential equations. The responses are simultaneously solved in time by means of convolution integral techniques. Either response is always predicting for the other an additio

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Paidoussis, Michael P. "Flow-induced Instabilities of Cylindrical Structures." Applied Mechanics Reviews 40, no. 2 (1987): 163–75. http://dx.doi.org/10.1115/1.3149530.

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A kaleidoscopic view of the many diverse and interesting instabilities are presented, to which cylindrical structures are susceptible when in contact with flowing fluids. The physical mechanisms involved are discussed in each case, to the extent that they are understood, and the degree of success of available mathematical models is assessed. Four classes of problems are dealt with, according to the disposition of the flow vis-a`-vis the cylindrical structures: (a) instabilities induced by internal flows in tubular structures; (b) instabilities of solitary or clustered cylinders due to external

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Gomoyunov, M. I., and D. A. Serkov. "Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 4 (2020): 553–71. http://dx.doi.org/10.35634/vm200402.

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For a dynamical system controlled under conditions of disturbances, a problem of optimizing the guaranteed result is considered. A feature of the problem is the presence of functional constraints on disturbances, under which, in general, the set of admissible disturbances is not closed with respect to the operation of “gluing up” of two of its elements. This circumstance does not allow to apply directly the methods developed within the differential games theory for studying the problem and, thus, leads to the necessity of modifying them appropriately. The paper provides a new notion of a non-a

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Blizorukova, M. S., and V. I. Maksimov. "Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 4 (2020): 533–52. http://dx.doi.org/10.35634/vm200401.

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In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the in

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Godoy-Diana, R., and B. Thiria. "On the diverse roles of fluid dynamic drag in animal swimming and flying." Journal of The Royal Society Interface 15, no. 139 (2018): 20170715. http://dx.doi.org/10.1098/rsif.2017.0715.

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Questions of energy dissipation or friction appear immediately when addressing the problem of a body moving in a fluid. For the most simple problems, involving a constant steady propulsive force on the body, a straightforward relation can be established balancing this driving force with a skin friction or form drag, depending on the Reynolds number and body geometry. This elementary relation closes the full dynamical problem and sets, for instance, average cruising velocity or energy cost. In the case of finite-sized and time-deformable bodies though, such as flapping flyers or undulatory swim

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HOLMES, PHILIP. "NINETY PLUS THIRTY YEARS OF NONLINEAR DYNAMICS: LESS IS MORE AND MORE IS DIFFERENT." International Journal of Bifurcation and Chaos 15, no. 09 (2005): 2703–16. http://dx.doi.org/10.1142/s0218127405013678.

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I review the early (1885–1975) and more recent history of dynamical systems theory, identifying key principles and themes, including those of dimension reduction, normal form transformation and unfolding of degenerate cases. I end by briefly noting recent extensions and applications in nonlinear fluid and solid mechanics, with a nod toward mathematical biology. I argue throughout that this essentially mathematical theory was largely motivated by nonlinear scientific problems, and that after a long gestation it is propagating throughout the sciences and technology.

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Koshel, Konstantin, Eugene Ryzhov, and Xavier Carton. "Vortex Interactions Subjected to Deformation Flows: A Review." Fluids 4, no. 1 (2019): 14. http://dx.doi.org/10.3390/fluids4010014.

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Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices

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Davey, A., and H. Salwen. "On the stability of flow in an elliptic pipe which is nearly circular." Journal of Fluid Mechanics 281 (December 25, 1994): 357–69. http://dx.doi.org/10.1017/s0022112094003149.

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In an earlier paper (Davey 1978) the first author investigated the linear stability of flow in a straight pipe whose cross-section was an ellipse, of small ellipticity e, by regarding the flow as a perturbation of Poiseuille flow in a circular pipe. That paper contained some serious errors which we correct herein. We show analytically that for the most important mode n = 1, for which the circular problem has a double eigenvalue c0 as the ‘swirl’ can be in either direction, the ellipticity splits the double eigenvalue into two separate eigenvalues c0 ± e2c12, to leading order, when the cross-se

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Gu, Yaqing, and Dean S. Oliver. "An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation." SPE Journal 12, no. 04 (2007): 438–46. http://dx.doi.org/10.2118/108438-pa.

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Summary The dynamical equations for multiphase flow in porous media are highly nonlinear and the number of variables required to characterize the medium is usually large, often two or more variables per simulator gridblock. Neither the extended Kalman filter nor the ensemble Kalman filter is suitable for assimilating data or for characterizing uncertainty for this type of problem. Although the ensemble Kalman filter handles the nonlinear dynamics correctly during the forecast step, it sometimes fails badly in the analysis (or updating) of saturations. This paper focuses on the use of an iterat

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Chinyoka, Tirivanhu, and Daniel Oluwole Makinde. "Unsteady and porous media flow of reactive non-Newtonian fluids subjected to buoyancy and suction/injection." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 7 (2015): 1682–704. http://dx.doi.org/10.1108/hff-10-2014-0329.

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Purpose – The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions. Design/methodology/approach – The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the c

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Wiggins, S., and A. M. Mancho. "Barriers to transport in aperiodically time-dependent two-dimensional velocity fields: Nekhoroshev's theorem and "Nearly Invariant" tori." Nonlinear Processes in Geophysics 21, no. 1 (2014): 165–85. http://dx.doi.org/10.5194/npg-21-165-2014.

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Abstract. In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov–Arnold–Moser (KAM) theorem and the Nekhoroshev theorem. While there is no f

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Li, Haijing, and Federico Toschi. "Plasma-induced catalysis: towards a numerical approach." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2175 (2020): 20190396. http://dx.doi.org/10.1098/rsta.2019.0396.

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A lattice Boltzmann (LB) model is developed, validated and used to study simplified plasma/flow problems in complex geometries. This approach solves a combined set of equations, namely the Navier–Stokes equations for the momentum field, the advection–diffusion and the Nernst–Planck equations for electrokinetic and the Poisson equation for the electric field. This model allows us to study the dynamical interaction of the fluid/plasma density, velocity, concentration and electric field. In this work, we discuss several test cases for our numerical model and use it to study a simplified plasma fl

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Grafke, Tobias, Rainer Grauer, and Stephan Schindel. "Efficient Computation of Instantons for Multi-Dimensional Turbulent Flows with Large Scale Forcing." Communications in Computational Physics 18, no. 3 (2015): 577–92. http://dx.doi.org/10.4208/cicp.031214.200415a.

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AbstractExtreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action functional. Due to the high number of degrees of freedom in multi-dimensional fluid flows, traditional global minimization techniques quickly become prohibitive in their memory requirements. We outline a novel method for finding the minimizing trajectory in a wide class of problems that typically occurs in turbulence setups, where the underlying dynamic

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Momen, Mostafa, Zhong Zheng, Elie Bou-Zeid, and Howard A. Stone. "Inertial gravity currents produced by fluid drainage from an edge." Journal of Fluid Mechanics 827 (August 29, 2017): 640–63. http://dx.doi.org/10.1017/jfm.2017.480.

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We present theoretical, numerical and experimental studies of the release of a finite volume of fluid instantaneously from an edge of a rectangular domain for high Reynolds number flows. For the cases we considered, the results indicate that approximately half of the initial volume exits during an early adjustment period. Then, the inertial gravity current reaches a self-similar phase during which approximately 40 % of its volume drains and its height decreases as $\unicode[STIX]{x1D70F}^{-2}$, where $\unicode[STIX]{x1D70F}$ is a dimensionless time that is derived with the typical gravity wave

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ROBINSON, JAMES C. "Parametrization of global attractors, experimental observations, and turbulence." Journal of Fluid Mechanics 578 (April 26, 2007): 495–507. http://dx.doi.org/10.1017/s0022112007005137.

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This paper is concerned with rigorous results in the theory of turbulence and fluid flow. While derived from the abstract theory of attractors in infinite-dimensional dynamical systems, they shed some light on the conventional heuristic theories of turbulence, and can be used to justify a well-known experimental method.Two results are discussed here in detail, both based on parametrization of the attractor. The first shows that any two fluid flows can be distinguished by a sufficient number of point observations of the velocity. This allows one to connect rigorously the dimension of the attrac

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Derfoufi, Soufiane, Fayçal Moufekkir, and Ahmed Mezrhab. "Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 3 (2018): 745–62. http://dx.doi.org/10.1108/hff-04-2017-0161.

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Purpose The paper aims to focus on modeling of combined mixed convection and volumetric radiation within a vertical channel using a hybrid thermal lattice Boltzmann method (LBM). The multiple relaxation time LBM (MRT-LBM) is used to compute the dynamical field. The thermal field is determined by a finite difference method (FDM), and the simple relaxation time-LBM (SRT-LBM) serves to calculate the radiative part. The geometry considered concerns a vertical channel defined by two diffuse and isothermal walls. The active fluid represents a gray gas participating in absorption, emission and isotro

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Boldrini, José Luiz, Exequiel Mallea-Zepeda, and Marko Antonio Rojas-Medar. "Optimal boundary control for the stationary Boussinesq equations with variable density." Communications in Contemporary Mathematics 22, no. 05 (2019): 1950031. http://dx.doi.org/10.1142/s0219199719500317.

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Certain classes of optimal boundary control problems for the Boussinesq equations with variable density are studied. Controls for the velocity vector and temperature are applied on parts of the boundary of the domain, while Dirichlet and Navier friction boundary conditions for the velocity and Dirichlet and Robin boundary conditions for the temperature are assumed on the remaining parts of the boundary. As a first step, we prove a result on the existence of weak solution of the dynamical equations; this is done by first expressing the fluid density in terms of the stream-function. Then, the bo

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Maksimov, V. I. "On the application of regularized extremal shift to the investigation of some problems of dynamical identification and robust control for systems with delay." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, no. 2 (April 2008): 83–86. http://dx.doi.org/10.20537/vm080230.

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Sánchez-Martín, P., J. J. Masdemont, and M. Romero-Gómez. "From manifolds to Lagrangian coherent structures in galactic bar models." Astronomy & Astrophysics 618 (October 2018): A72. http://dx.doi.org/10.1051/0004-6361/201833451.

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We study the dynamics near the unstable Lagrangian points in galactic bar models using dynamical system tools in order to determine the global morphology of a barred galaxy. We aim at the case of non-autonomous models, in particular with secular evolution, by allowing the bar pattern speed to decrease with time. We have extended the concept of manifolds widely used in the autonomous problem to the Lagrangian coherent structures (LCS), widely used in fluid dynamics, which behave similar to the invariant manifolds driving the motion. After adapting the LCS computation code to the galactic dynami

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Eke, F. O., and Song-Min Wang. "Equations of Motion of Two-Phase Variable Mass Systems With Solid Base." Journal of Applied Mechanics 61, no. 4 (1994): 855–60. http://dx.doi.org/10.1115/1.2901568.

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This paper develops dynamical equations for variable mass systems that can be viewed, at any given instant, as comprising a solid phase and a fluid phase. The equations of translational and rotational motion are presented, and several versions of each are given. It is shown that some versions have major advantages over others because they involve parameters that are relatively easy to estimate in practical problems, and make close-form solutions possible without the usual penalty of drastic simplifying assumptions. A simple rocket example is presented, and shows that instability cannot be rule

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HANSRAJ, SUDAN, and DANIEL KRUPANANDAN. "ALGORITHMIC CONSTRUCTION OF EXACT SOLUTIONS FOR NEUTRAL STATIC PERFECT FLUID SPHERES." International Journal of Modern Physics D 22, no. 09 (2013): 1350052. http://dx.doi.org/10.1142/s0218271813500521.

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Although it ranks amongst the oldest of problems in classical general relativity, the challenge of finding new exact solutions for spherically symmetric perfect fluid spacetimes is still ongoing because of a paucity of solutions which exhibit the necessary qualitative features compatible with observational evidence. The problem amounts to solving a system of three partial differential equations in four variables, which means that any one of four geometric or dynamical quantities must be specified at the outset and the others should follow by integration. The condition of pressure isotropy yiel

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BIELLO, JOSEPH A., KENNETH I. SALDANHA, and NORMAN R. LEBOVITZ. "Instabilities of exact, time-periodic solutions of the incompressible Euler equations." Journal of Fluid Mechanics 404 (February 10, 2000): 269–87. http://dx.doi.org/10.1017/s0022112099007089.

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We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows rep

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Epifanio, C. C., and R. Rotunno. "The Dynamics of Orographic Wake Formation in Flows with Upstream Blocking." Journal of the Atmospheric Sciences 62, no. 9 (2005): 3127–50. http://dx.doi.org/10.1175/jas3523.1.

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Abstract The development of orographic wakes and vortices is revisited from the dynamical perspective of a three-dimensional (3D) vorticity-vector potential formulation. Particular emphasis is given to the role of upstream blocking in the formation of the wake. Scaling arguments are first presented to explore the limiting form of the 3D vorticity inversion for the case of flow at small dynamical aspect ratio δ. It is shown that in the limit of small δ the inversion is determined completely by the two horizontal vorticity components—that is, the part of the velocity induced by the vertical comp

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Chapman, C. J. "The asymptotic theory of dispersion relations containing Bessel functions of imaginary order." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (2012): 4008–23. http://dx.doi.org/10.1098/rspa.2012.0459.

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This paper presents a method of analysing wave-field dispersion relations in which Bessel functions of imaginary order occur. Such dispersion relations arise in applied studies in oceanography and astronomy, for example. The method involves the asymptotic theory developed by Dunster in 1990, and leads to simple analytical approximations containing only trigonometric and exponential functions. Comparisons with accurate numerical calculations show that the resulting approximations to the dispersion relation are highly accurate. In particular, the approximations are powerful enough to reveal the

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