Inviscid incompressible limits of strongly stratified fluids
نویسندگان
چکیده
We consider the motion of a compressible viscous fluid in the asymptotic regime of low Mach and high Reynolds numbers under strong stratification imposed by a conservative external force. Assuming a bi-dimensional character of the flow, we identify the limit system represented by the so-called lake equation the Euler system supplemented by an anelastic type constraint imposed by the limit density profile.
منابع مشابه
The Poincaré Recurrence Problem of Inviscid Incompressible Fluids
Nadirashvili presented a beautiful example showing that the Poincaré recurrence does not occur near a particular solution to the 2D Euler equation of inviscid incompressible fluids. Unfortunately, Nadirashvili’s setup of the phase space is not appropriate, and details of the proof are missing. This note fixes that.
متن کاملExamples of singular limits in hydrodynamics
This chapter is devoted to the study of some asymptotic problems in hydrodynamics. In particular, we will review results about the inviscid limit, the compressible-incompressible limit, the study of rotating fluids at high frequency, the hydrodynamic limit of the Boltzmann equation as well as some homogenization problems in fluid mechanics.
متن کاملTransport and Instability for Incompressible and Inviscid Fluids
Incompressible perfect fluids are described by the Euler equations. We provide a new simple proof for well-posedness for velocities in C1;α and linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of C1;α is too fine for interesting questions about large time behavior.
متن کاملStatement of problem on vortical inviscid flow of barotropic and incompressible fluids
Statement of problem on vortical inviscid flow of barotropic and incompressible fluids. Abstract The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the f...
متن کاملNon-linear asymptotic stability for the through-passing flows of inviscid incompressible fluid
The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Asymptotic Analysis
دوره 89 شماره
صفحات -
تاریخ انتشار 2014