Related papers: Remarks on Sedov-type Solution of Isotropic Turbul…
We prove the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier-Stokes equations. Our result solves a long-standing…
Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders…
This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to…
We study the three dimensional Navier-Stokes equation with a random Gaussian force acting on large wavelengths. Our work has been inspired by Polyakov's analysis of steady states of two dimensional turbulence. We investigate the time…
One of the main benchmarks in direct numerical simulations of three-dimensional turbulence is the Kolmogorov 1941 prediction for third-order structure functions with homogeneous and isotropic statistics in the infinite-Reynolds number…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow…
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that…
Motivated by Kolmogorov's theory of turbulence we present a unified approach to the regularity problems for the 3D Navier-Stokes and Euler equations. We introduce a dissipation wavenumber $\Lambda (t)$ that separates low modes where the…
How predictable are turbulent flows? Here we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the non-uniqueness of the solutions to the Euler equation that is…
We prove that every solution of a KdV-Burgers-Sivashinsky type equation blows up in the energy space, backward in time, provided the solution does not belong to the global attractor. This is a phenomenon contrast to the backward behavior of…
The energy dissipation in the inviscid limit is a central problem in turbulence theory. Kolmogorov's K41 theory predicts a positive dissipation rate independent of viscosity -- a phenomenon known as anomalous dissipation. Bru\'e and De…
A recent Letter by Oberlack et al. [Phys. Rev. Lett. 128, 024502 (2022)] claims to have derived new symmetry-induced solutions of the non-modelled statistical Navier-Stokes equations of turbulent channel flow. A high accuracy match to DNS…
A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3-D Euler equation with high-wavenumber spectral truncation is characterized. Large-scale dissipative effects, caused by the…
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small…
In practically all turbulent flows, turbulent energy decay is present and competes with numerous other phenomena. In Kolmogorov's theory, decay proceeds by transfer from large energy-containing scales towards small viscous scales through…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
We prove a mathematical theorem that solution for all $t > 0$ of the two-dimensional (2D) Kolmogorov flow governed by Navier-Stokes (NS) equations with periodic boundary condition keeps the same spatial symmetry as its smooth initial…
By direct numerical simulation to the two-dimensional Navier-Stokes equations with small-scale forcing and large-scale damping, Xiao-Wan-Chen-Eyink (2009) found an evidence that inverse energy cascade may proceed with the vortex thinning…
The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model. This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the…