Asymptotic Behavior and Symmetry of Internal Waves in Two-Layer Fluids of Great Depth

✍ Scribed by S.M. Sun

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 740 KB
• Volume: 129
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0110

✦ Synopsis

This paper studies certain asymptotic and geometric properties of internal waves at the interface of a two-layer fluid flow of infinite depth bounded below by a rigid bottom under influence of gravity. It is shown that if the governing equations of the flow have a nontrivial solution which approaches to a supercritical equilibrium state at infinity, then the solution decays to the equilibrium exactly with an order O(1Âx 2 ) for large x where x is the horizontal variable. Furthermore, the solution is symmetric. The interface is always above the equilibrium state and monotonically decreasing for positive x and increasing for negative x. The exact decay estimates are obtained using the properties of Green's function for an integro-differential equation and some tools from harmonic analysis. The proof of symmetry is similar to the one given by Craig and Sternberg for a two-fluid flow of finite depth using the Alexandrov method of moving planes.