Related papers: The Equatorial Ekman Layer
We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and…
The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the…
Starting from the Navier-Stokes equation in the $f$-plane approximation, we provide an exact and explicit solution of the governing equations at leading order for fluid flows in the upper layer of the ocean at mid-latitudes, driven by a…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena…
The semi-geostrophic equations have attracted the attention of the physical and mathematical communities since the work of Hoskins in the 1970s owing to their ability to model the formation of fronts in rotation-dominated flows, and also to…
We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If…
In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P.,…
In this paper we study the motion of a finite composite cylindrical annulus made of generalized neo-Hookean solids that is subject to periodic shear loading on the inner boundary. Such a problem has relevance to several problems of…
The near-bottom mixing that allows abyssal waters to upwell tilts isopycnals and spins up flow over the flanks of mid-ocean ridges. Meso- and large-scale currents along sloping topography are subjected to a delicate balance of Ekman arrest…
The response of amorphous solids to an applied shear deformation is an important problem, both in fundamental and applied research. To tackle this problem, we focus on a system of hard spheres in infinite dimensions as a solvable model for…
This paper is concerned with a complete asymptoticanalysis as $\mathfrak{E} \to 0$ of the stationary Munk equation $\partial\_x\psi-\mathfrak{E} \Delta^2 \psi=\tau$ in a domain $\Omega\subset \mathbf{R}^2$, supplemented with…
Motivated by recent studies in geophysical and planetary sciences, we investigate the PDE-analytical aspects of time-averages for barotropic, inviscid flows on a fast rotating sphere $S^2$. Of particular interests are the incompressible…
It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. In this work, this oscillatory boundary layer theory is generalized to the case of linear viscoelastic(LVE) flow. We…
This paper deals with the convergence/divergence issue of the Chapman-Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform…
We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a {three dimensional} domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a…
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied by the authors in [LT]. In this paper, we will show that all these solutions are ancient solutions. We also discuss rigidity of ancient mean…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…