Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

作     者：Korekazu Ueyama Korekazu Ueyama

作者机构：Graduate School of Engineering Science Osaka University Toyonaka Japan 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2024年第12卷第1期

页      面：16-33页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Boundary Condition for Vorticity Surface Layer Interface Momentum Flux Vorticity Flux 

摘      要：Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.