Related papers: Canonical scale separation in two-dimensional inco…
The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the…
We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the…
The temporal evolution of a dilute granular gas, both in a compressible flow (uniform longitudinal flow) and in an incompressible flow (uniform shear flow), is investigated by means of the direct simulation Monte Carlo method to solve the…
Turbulent flows are observed in low-Reynolds active fluids. They are intrinsically different from the classical inertial turbulence and behave distinctively in two- and three-dimensions. Understanding the behaviors of this new type of…
In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids,…
The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analogue, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D…
The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…
We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
We consider a system of two incompressible fluids separated by a free interface. The first fluid is inviscid, governed by the Euler system, while the second fluid has positive viscosity and is governed by the Navier-Stokes system. We…
The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model…
We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes…
In Part II of the paper, we prove linear instability of a certain class of radially symmetric flows of an ideal incompressible fluid in dimension two used in Part I
The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial separation (the stirring scale) at a constant rate.…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…
It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian…
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated…