Related papers: Three-dimensional solutions for the geostrophic fl…
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing…
Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event…
The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak…
Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…
We analyze a class of physical properties, forming the content of the so-called von Zeipel theorem, which characterizes stationary, axisymmetric, non-selfgravitating perfect fluids in circular motion in the gravitational field of a compact…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow v.s. convection) to compute the torque in Taylor-Couette…
This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In this third paper we elevate the Newtonian theory of the…
We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…
We show that the intrinsic diameter of mean curvature flow in $\mathbb{R}^3$ is uniformly bounded as one approaches the first singular time $T$. This confirms the bounded diameter conjecture of Haslhofer. In addition, we establish several…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
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…
Starting from the Navier--Stokes equations in rotating spherical coordinates with constant density and eddy viscosity varying only with depth, and appropriate, physically motivated boundary conditions, we derive an asymptotic model for the…
Landau's criterion for superfluidity is a special case of a broader principle: A moving fluid cannot be stopped by frictional forces if its state of motion is a local minimum of the grand potential. We employ this general thermodynamic…
We consider the inhomogeneous incompressible Euler equations including their local energy inequality as a differential inclusion. Providing a corresponding convex integration theorem and constructing subsolutions, we show the existence of…
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing…
A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is…
The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method, when the latter is hard to apply. Fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of…
Models and simulations of the flow of thin films of fluids have many important applications in industrial and natural processes. We consider the motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary solid,…