Stratified steady inviscid water flows with effects of surface tension and constant non-zero vorticity

IF 0.9 3区 数学 Q1 MATHEMATICS
Nataliia Kolun
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引用次数: 0

Abstract

In this paper we consider steady inviscid three-dimensional stratified water flows of finite depth with a free surface and an interface. The interface plays the role of an internal wave that separates two layers of constant and different density. We study two cases separately: when the free surface and the interface are functions of one variable and when the free surface and the interface are functions of two variables. In both cases, considering effects of surface tension, we prove that the bounded solutions to the three-dimensional equations are essentially two-dimensional. More specifically, assuming that the vorticity vectors in the two layers are constant, non-vanishing and parallel to each other we prove that their third coordinate vanishes in both layers. Also we prove that the free surface, the interface, the pressure and the velocity field present no variations in the direction orthogonal to the direction of motion.

具有表面张力和恒定非零涡度效应的分层稳定不粘性水流
本文考虑具有自由表面和界面的有限深度的稳定无粘三维分层水流。界面起着内波的作用,将密度恒定和密度不同的两层分开。我们分别研究了自由曲面和界面为单变量函数和自由曲面和界面为双变量函数的两种情况。在这两种情况下,考虑表面张力的影响,我们证明了三维方程的有界解本质上是二维的。更具体地说,假设两层的涡度矢量是恒定的、不消失的、彼此平行的,我们证明了它们的第三坐标在两层中都消失了。我们还证明了自由表面、界面、压力场和速度场在与运动方向正交的方向上没有变化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
99
审稿时长
>12 weeks
期刊介绍: This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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