Related papers: An existence result for the steady rotating Prandt…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
The flow through a porous medium strongly depends on the boundary conditions, very often assumed to be static. Here, we consider changes in the medium due to swelling and erosion and extend existing Lattice-Boltzmann models to include both.…
We consider the area-preserving Willmore evolution of surfaces that are close to a half-sphere with a small radius, sliding on the boundary S of a domain while meeting it orthogonally. We prove that the flow exists for all times and keeps a…
One approach to reduce the cost to simulate transitional compressible boundary layer flow is to adopt a near body reduced domain with boundary conditions enforced to be compatible with a computationally cheaper 3D RANS simulation. In such…
A thermal convection fluid motion in the three-dimensional domain exterior to a sphere is considered. A purely conductive steady state arises due to the fluid heated from the sphere. A fractional equation system is introduced by using…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient…
This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…
We obtained steady solutions to the two-dimensional Boussinesq approximation equations without mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function…
In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$…
Pipe flow often traverses a regime where laminar and turbulent flow co-exist. Prandtl and Tietjens explained this intermittency as a feedback between the fluctuations of the internal flow resistance and the constant pressure drop driving…
Though highly impacting our lives, rotating turbulent flows are not well understood. These anisotropic three-dimensional disordered flows are governed by different nonlinear processes, each of which can be dominant in a different range of…
In this paper, we consider steady Euler flows in two-dimensional bounded annuli, as well as in exterior circular domains, in punctured disks and in the punctured plane. We always assume rigid wall boundary conditions. We prove that, if the…
The baroclinic instability problem is considered in the framework of Laplacian tidal theory. The Hilbert space of the quasigeostrophic vorticity budget is spanned by spheroidal functions. The fluid is linearly stable against…
In this paper we present a new kind of boundary layer flow produced by an electromagnetic Lorentz force which acts parallel to the plate in an electrically conductive fluid. The plate is motionless and the ambient fluid stagnant. This flow…
We propose a novel method to find local plane-wave solutions of the linearized equations of motion of relativistic hydrodynamics in inhomogeneous equilibrium configurations, i.e., when a fluid in equilibrium is rigidly moving with nonzero…
We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference…
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important…
There are two distinct regimes commonly used to model traveling waves in stratified water: continuous stratification, where the density is smooth throughout the fluid, and layer-wise continuous stratification, where the fluid consists of…