Related papers: Dynamic Phase Alignment in Navier-Stokes Turbulenc…
We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction…
An enstrophy cascade is exhibited for the Navier-Stokes equations in physical scales independently of boundary conditions under physically reasonable assumptions on the flow.
This article presents a theoretical study of the scaling properties of the kinetic energy spectrum in compressible turbulence. From the fundamental symmetries and linear transformations of the microscopic action, we derive exact relations…
Perturbed, helical trefoil vortex knots and a set of anti-parallel vortices are examined numerically to identify the scaling of their helicity and vorticity norms during reconnection. For the volume-integrated enstrophy $Z=\int\omega^2 dV$,…
Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three dimensional Navier-Stokes equations that shares exactly the same ideal…
We review the properties of the nonlinearly dispersive Navier-Stokes-alpha (NS-alpha) model of incompressible fluid turbulence -- also called the viscous Camassa-Holm equations and the LANS equations in the literature. We first re-derive…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
We investigate the energy cascade in wall-bounded turbulence by analysing the interscale transfer between streamwise and spanwise length scales in periodic channels. This transfer originates from the nonlinear interactions in the advective…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
We provide a convergence analysis for a new fractional time-stepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent,…
We explore the utility of the recently proposed alpha equations in providing a subgrid model for fluid turbulence. Our principal results are comparisons of direct numerical simulations of fluid turbulence using several values of the…
We investigate the process of formation of large-scale structures in a turbulent flow confined in a thin layer. By means of direct numerical simulations of the Navier-Stokes equations, forced at an intermediate scale, we obtain a split of…
Spectral analysis for a class of Lagrangian-averaged Navier--Stokes (LANS) equations on the sphere is carried out. The equations arise from the Navier--Stokes equations by applying a Helmholtz filter of width $\alpha$ to the advecting…
For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…
We inquire the scaling properties of the 2d Navier-Stokes equation sustained by a forcing field with Gaussian statistics, white-noise in time and with power-law correlation in momentum space of degree $2-2 \eps$. This is at variance with…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…
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…