Search results for "Barotropic fluid"

Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere

2006

We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15

A multiscale approach to liquid flows in pipes I: The single pipe

2012

Abstract In the present paper we study the propagation of pressure waves in a barotropic flow through a pipe, with a possibly varying cross-sectional area. The basic model is the Saint–Venant system. We derive two multiscale models for the cases of weak and strong damping, respectively, which describe the time evolution of the piezometric head and the velocity. If the damping is weak, then the corresponding first-order hyperbolic system is linear but contains an additional integro-differential equation that takes into account the damping. In the case of strong damping, the system is nonlinear. The full and multiscale models are compared numerically; we also discuss results obtained by a lar…

Convergence of a finite volume scheme for the compressible Navier–Stokes system

2019

We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.

On numerical relativistic hydrodynamics and barotropic equations of state

2012

The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.

High-resolution numerical modelling of the barotropic tides in the Gulf of Gabes, eastern Mediterranean Sea (Tunisia)

2017

International audience; A high-resolution 2D barotropic tidal model was developed for the Gulf of Gabes and used to characterise hydrodynamic processes and tidal dynamics. The model is based on the Regional Ocean Modelling System. It is forced at the open boundaries by the semidiurnal M2 and S2 astronomical components while meteorological forcing has been neglected. The model results show good agreement with observations confirming that it reproduces the gulf's main tidal characteristics reasonably well. In fact, the simulated semidiurnal tidal components M2 and S2 generate important sea level variations and coastal currents. Tidal propagation is directed to the gulf's western sector while …

Nonlinear Critical Layers in Barotropic Stability

1991

Abstract Applying the method of matched asymptotic expansions (MAE) to the shallow water equations on a rotating sphere, the structure of critical layers that occur in the linear and inviscid analysis of neutral disturbances of barotropic zonal flows is investigated, assuming that the critical layers are controlled by nonlinearity rather than viscosity or nonparallel flow effects. It turns out that nonlinearity is insufficient to resolve the critical layer singularity completely. It suffices however to connect linear and nondissipative solutions across critical latitudes.

The barotropic model

2003

Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory

2020

Abstract. Ray paths of stationary Rossby waves emanating from a local midlatitude source are usually refracted equatorward. However, this general tendency for equatorward propagation is mitigated by the presence of a midlatitude jet that acts as a zonal waveguide. This opens up the possibility of circum-global teleconnections and quasi-resonance, which suggests that the ability to guide a wave in the zonal direction is an important jet property. This paper investigates waveguidability of idealized midlatitude jets in a barotropic model on the sphere. A forced-dissipative model configuration with a local source for Rossby waves is used in order to quantify waveguidability by diagnosing the l…

Potential-vorticity dynamics of troughs and ridges within Rossby wave packets during a 40-year reanalysis period

2020

Rossby wave packets (RWPs) are fundamental to midlatitude dynamics and govern weather systems from their individual life cycles to their climatological distributions. Renewed interest in RWPs as precursors to high-impact weather events and in the context of atmospheric predictability motivates this study to revisit the dynamics of RWPs. A quantitative potential vorticity (PV) framework is employed. Based on the well established PV-thinking of midlatitude dynamics, the processes governing RWP amplitude evolution comprise group propagation of Rossby waves, baroclinic interaction, the impact of upper-tropospheric divergent flow, and direct diabatic PV modification by nonconservative processes.…