Search results for "Primitive equations"

showing 3 items of 3 documents

Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

2016

The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\). The main assumption is spatial analyticity of the initial datum.

Analysis; Mathematics (miscellaneous); Mechanical EngineeringMechanical Engineering010102 general mathematicsMathematical analysisZero (complex analysis)Analysi01 natural scienceslaw.inventionEuler equations010101 applied mathematicsViscositysymbols.namesakeBoundary layerMathematics (miscellaneous)lawPrimitive equationssymbolsLimit (mathematics)0101 mathematicsHydrostatic equilibriumAsymptotic expansionAnalysisMathematics
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Numerical study of the primitive equations in the small viscosity regime

2018

In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.

PhysicsSingularity tracking methodApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsPrimitive equationMechanicsSlip (materials science)Vorticity01 natural sciences010305 fluids & plasmasPhysics::Fluid DynamicsBoundary layerDipole0103 physical sciencesPrimitive equationsGravitational singularity0101 mathematicsZero viscosity limitPressure gradient
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A Unified Perspective on the Dynamics of Axisymmetric Hurricanes and Monsoons

2006

Abstract This paper provides a unified perspective on the dynamics of hurricane- and monsoonlike vortices by identifying them as specific limiting cases of a more general flow system. This more general system is defined as stationary axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the f plane. The model is based on the primitive equations assuming gradient wind balance in the radial momentum equation. The flow is forced by heating in the vortex center, which is implemented as relaxation toward a specified equilibrium temperature Te. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. The heating is assumed …

Thermal equilibriumPhysicsAtmospheric ScienceWind gradientFlow (mathematics)Inviscid flowSecondary circulationPrimitive equationsF-planeThermodynamicsMechanicsPhysics::Atmospheric and Oceanic PhysicsVortexJournal of the Atmospheric Sciences
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