Classification of Casimirs in 2D hydrodynamics
نویسنده
چکیده
We describe a complete list of Casimirs for 2D Euler hydrodynamics on a surface without boundary: we define generalized enstrophies which, along with circulations, form a complete set of invariants for coadjoint orbits of area-preserving diffeomorphisms on a surface. We also outline a possible extension of main notions to the boundary case and formulate several open questions in that setting.
منابع مشابه
Investigation on the sloshing effect in a 2D tank under harmonic excitation using Smoothed Particle Hydrodynamics (SPH) and Finite Volume method (FVM)
Abstract Sloshing describes liquids motion in the semi-filled tanks, and exerts dynamic loading on its walls. This effect is of great importance in a number of dynamic systems e.g. aerospace vehicles, road tankers, liquefied natural gas carriers, elevated water towers and petroleum cylindrical tanks. Pressures insert impacts which are important for structural strength evaluation and its co...
متن کاملCharacterization of steady solutions to the 2D Euler equation
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among isovorticed fields. For this we introduce the notion of an antiderivative (or circulation function) on a measured graph, the Reeb graph associated to the vortici...
متن کاملCerebrospinal Pulsation Hydrodynamics in a 2D Simulation of Brain Ventricles
In this article, dynamics of the cerebrospinal fluid (CSF) was studied, using computational fluid dynamics. Using MRI images of two special cases, a 2-dimensional model of the ventricular system was made. CSF velocity and pressure distribution in ventricular system have high importance since the flow pattern of this liquid has an important effect on intracranial pressure, i.e., ICP, which has a...
متن کاملIntegrable Structures for 2D Euler Equations of Incompressible Inviscid Fluids
The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...
متن کامل2D Computational Fluid Dynamic Modeling of Human Ventricle System Based on Fluid-Solid Interaction and Pulsatile Flow
Many diseases are related to cerebrospinal .uid (CSF) hydrodynamics. Therefore, understanding the hydrodynamics of CSF .ow and intracranial pressure is helpful for obtaining deeper knowledge of pathological processes and providing better treatments. Furthermore, engineering a reliable computational method is promising approach for fabricating in vitro models which is essential for inventing gen...
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 2017