Nonlinear stability of two-layer shallow water flows with a free surface
نویسندگان
چکیده
منابع مشابه
Nonlinear Stability of Two – Layer Flows ∗
We study the dynamics of two–layer, stratified shallow water flows. This is a model in which two scenarios for eventual mixing of stratified flows (shear-instability and internal breaking waves) are, in principle, possible. We find that unforced flows cannot reach the threshold of shearinstability, at least without breaking first. This is a fully nonlinear stability result for a model of strati...
متن کاملLocal Well-Posedness of the Two-Layer Shallow Water Model with Free Surface
In this paper, we address the question of the hyperbolicity and the local wellposedness of the two-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model ...
متن کاملAnalysis of a double layer shallow water model with free surface
A double layer shallow water model is established, departing from 3D Euler incompressible equations with free surface. On the one hand, the model is augmented with curl, as a new unknown. A result of existence and uniqueness is proved for a smooth initial condition (i.e. in Sobolev spaces) using criteria from [2]. On the other hand, the system without curl is considered. In order to treat more ...
متن کاملLocal Well-posedness of the Multi-layer Shallow Water Model with Free Surface∗
In this paper, we address the question of the hyperbolicity and the local wellposedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this mode...
متن کاملHyperbolicity of the multi-layer shallow-water model with free surface
Considering n fluids, which are homogeneous, inviscid, incompressible and without surface tension, the 3D Euler equations with long wave assumptions provide the multi-layer shallow-water model with free surface. Since salinity is assumed discontinuous, these equations can be used to describe the oceans. The study of the hyperbolicity of this quasi-linear PDEs system is divided in two parts. Fir...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2020
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2019.0594