相关论文: Nonsingular Surface-Quasi-Geostrophic Flow

The classic evolution equations for potential flow on the free surface of a fluid flow are not closed because the pressure and the vertical velocity dynamics are not specified on the free surface. Moreover, their wave dynamics does not…

We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for atmospheric and oceanic motions near a horizontal boundary. The cascade involves geometrically shrinking…

In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty…

We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…

We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal…

We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus $T^3$ and, in this class, we solve the singular initial value problem for the Einstein-Euler system of general relativity, when an initial data…

A scale invariant, selfsimilar atmospheric eddy continuum exists in the planetary atmospheric boundary layer spanning several orders of magnitude in scales and gives rise to the observed fractal geometry for the global cloud cover pattern.…

We consider a quasilinear system of hyperbolic equations that describes plane one-dimensional non-relativistic oscillations of electrons in a cold plasma with allowance for electron-ion collisions. Accounting for collisions leads to the…

At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from…

In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW front, which is a nonlinear, nonlocal dispersive equation, and…

Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be…

Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…

Physical systems made of many interacting quantum particles can often be described by Euler hydrodynamic equations in the limit of long wavelengths and low frequencies. Recently such a classical hydrodynamic framework, now dubbed…

Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces…

Ultra-hot Jupiters, an extreme class of planets not found in our solar system, provide a unique window into atmospheric processes. The extreme temperature contrasts between their day- and night-sides pose a fundamental climate puzzle: how…

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…

This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…

One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a…

In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…