Related papers: Chaotic mixing in plane Couette turbulence
The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to…
We consider a fluid-structure interaction problem in the Eulerian, phase-field formulation. The problem is described using the Navier--Stokes equations for a viscous, incompressible fluid, coupled with the incompressible hyperelasticity…
Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model streamfunction, Hamiltonian…
We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fourier system. The shell constitutes an unknown part of the…
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…
A finite-volume method for the steady, compressible, reacting, turbulent Navier-Stokes equations is developed by using a steady-state preserving splitting scheme for the stiff source terms in chemical reaction. Laminar and turbulent…
We investigate the effects of bacterial activity on the mixing and transport properties of a passive scalar in time-periodic flows in experiments and in a simple model. We focus on the interactions between swimming E. coli and the…
Fractional Navier-Stokes equations -- featuring a fractional Laplacian -- provide a `bridge' between the Euler equations (zero diffusion) and the Navier-Stokes equations (full diffusion). The problem of whether an initially smooth flow can…
In plane Couette flow, the incompressible fluid between two plane parallel walls is driven by the motion of those walls. The laminar solution, in which the streamwise velocity varies linearly in the wall-normal direction, is known to be…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
We report experimental measurements of Lagrangian accelerations in the bulk of intense turbulent flows of dilute polymer solutions by following tracer particles with a high-speed optical tracking system. We observed a significant decrease…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
Incompressible Navier-Stokes equations in the spherical coordinates are solved using a pseudo-spectral method to simulate the problem of spherical Couette flow. The flow is investigated for a narrow gap ratio with only the inner sphere…
This work presents a stabilized finite element formulation of the arbitrary Lagrangian-Eulerian (ALE) surface theory for Navier-Stokes flow on self-evolving manifolds developed in Sauer (2025). The formulation is physically frame-invariant,…
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…
Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this…
We show a case of steady flow in a granular gas that, for small shear rates, is accurately described by Navier-Stokes hydrodynamics, even for high inelasticity. The (low density) granular gas is composed of identical inelastic spheres and…
We study the lagrangian structure for weak solutions of two dimensional Navier-Stokes equations for a non-barotropic compressible fluid, i.e. we show the uniqueness of particle trajectories for two dimensional compressible fluids including…
In this paper we derive a representation of the deterministic 3-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for…