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Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…

Statistical Mechanics · Physics 2012-06-01 Corentin Herbert , Bérengère Dubrulle , Pierre-Henri Chavanis , Didier Paillard

It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…

Chaotic Dynamics · Physics 2016-12-07 Vishwanath Shukla , Stephan Fauve , Marc Brachet

In this study, we propose a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on the extended Navier-Stokes (N-S) equations. With some phenomenological observations and H. J. Kreuer's…

Fluid Dynamics · Physics 2023-06-21 Shanwen Tan , Zhengui Li , Wangxu Li

Swimming involves a body's capability to navigate through a fluid by undergoing self-deformations. Typically, fluid dynamics are described by the Navier-Stokes equations, and when integrated with a swimming body, it results in a highly…

Analysis of PDEs · Mathematics 2024-08-27 Céline Van Landeghem , Luca Berti , Laëtitia Giraldi , Christophe Prud'Homme

Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp. 499-505, Podvigina et al., J. Comput. Phys.,…

Fluid Dynamics · Physics 2017-08-01 Nicolas Besse , Uriel Frisch

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations,…

Fluid Dynamics · Physics 2021-07-07 Stéphane Perrard , Aliénor Rivière , Wouter Mostert , Luc Deike

We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We…

Fluid Dynamics · Physics 2019-05-22 Richard Ho , Arjun Berera , Daniel Clark

The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…

Chaotic Dynamics · Physics 2020-11-16 Alexis Tantet , Valerio Lucarini , Frank Lunkeit , Henk A. Dijkstra

Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on…

Fluid Dynamics · Physics 2026-03-25 Alejandro Sevilla

Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…

Mathematical Physics · Physics 2009-06-02 S. G. Rajeev

Visual manifestations of intermittency in computations of three dimensional Navier-Stokes fluid turbulence appear as the low-dimensional or `thin' filamentary sets on which vorticity and strain accumulate as energy cascades down to small…

Chaotic Dynamics · Physics 2020-12-02 John D. Gibbon

Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…

Analysis of PDEs · Mathematics 2023-06-14 Dennis Gallenmüller , Raphael Wagner , Emil Wiedemann

We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is…

Fluid Dynamics · Physics 2020-03-10 Luca Galantucci , Andrew W. Baggaley , Carlo F. Barenghi , Giorgio Krstulovic

Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…

Chaotic Dynamics · Physics 2025-11-19 Arkady Pikovsky

Decoherence in quantum systems which are classically chaotic is studied. The Arnold cat map and the quantum kicked rotor are chosen as examples of linear and nonlinear chaotic systems. The Feynman-Vernon influence functional formalism is…

chao-dyn · Physics 2009-10-28 K. Shiokawa , B. L. Hu

Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence…

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory…

Computational Physics · Physics 2021-08-17 Yifei Guan , Steven L. Brunton , Igor Novosselov

The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…

Analysis of PDEs · Mathematics 2025-05-21 Filippo Gazzola , Mikhail V. Korobkov , Xiao Ren , Gianmarco Sperone

The concept of a fluid algebra was introduced by Sullivan over a decade ago as an algebraic construct which contains everything necessary in order to write down a form of the Euler equation, as an ODE whose solutions have invariant…

Analysis of PDEs · Mathematics 2025-04-09 Ofir Aharoni , Daniel An , Alice Kwon , Ruth Lawrence , Dennis Sullivan

This paper compares three different types of ``onset of chaos'' in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three…

Statistical Mechanics · Physics 2009-11-11 R. Tonelli , M. Coraddu