Singular front formation in a model for quasigeostrophic flow
نویسندگان
چکیده
A two-dimensional model for quasigeostrophic flow which exhibits an analogy with the three-dimensional incompressible Euler equations is considered. Numerical experiments show that this model develops sharp fronts without the need to explicitly incorporate any ageostrophic effect. Furthermore, these fronts appear to become singular in finite time. The numerical evidence for singular behavior survives the tests of rigorous mathematical criteria.
منابع مشابه
A two-dimensional model for quasigeostrophic flow: comparison with the two-dimensional Euler flow
A simple two-dimensional model for quasigeostrophic flow is contrasted with the two-dimensional incompressible Euler equations. The model arises under the assumptions of fast rotation, uniform stratification and uniform potential vorticity. It is found that the more local feed-back of the quasigeostrophic model gives rise to strongly nonlinear front formation, as opposed to two-dimensional Eule...
متن کاملNumerical simulation of a self-similar cascade of filament instabilities in the surface quasigeostrophic system.
We provide numerical evidence for the existence of a cascade of filament instabilities in the surface quasigeostrophic system for rotating, stratified flow near a horizontal boundary. The cascade involves geometrically shrinking spatial and temporal scales and implies the singular collapse of the filament width to zero in a finite time. The numerical method is both spatially and temporally adap...
متن کاملExponential Stability of the Quasigeostrophic Equation under Random Perturbations
Progress in Probability 49(2001), 241-256. The quasigeostrophic model describes large scale and relatively slow fluid motion in geophysical flows. We investigate the quasigeostrophic model under random forcing and random boundary conditions. We first transform the model into a partial differential equation with random coefficients. Then we show that, under suitable conditions on the random forc...
متن کاملNonlinear Generalization of Singular Vectors: Behavior in a Baroclinic Unstable Flow
Singular vector (SV) analysis has proved to be helpful in understanding the linear instability properties of various types of flows. SVs are the perturbations with the largest amplification rate over a given time interval when linearizing the equations of a model along a particular solution. However, the linear approximation necessary to derive SVs has strong limitations and does not take into ...
متن کاملThe predictability of large-scale wind-driven flows
The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving exa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999