2015/02/26 by Robin Ming Chen, Chen, Robin Ming, Samuel Walsh +1
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35J60 #35R35 #76B15 #76B55 #76B70 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geological formations and processes #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #math-ph #math.AP #math.MP #msc:35J60 #msc:35R35 #msc:76B15 #msc:76B55 #msc:76B70 #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1502.07775
33 pages, 1 figure
arxiv created 2015/02/26 · openalex publication_date 2015/02/26 · arxiv updated 2015/03/02 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28
Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed, upstream and downstream density profile, and the trace of the pressure on the bed. First, we prove that this data uniquely determines the wave, both in the (real) analytic and Sobolev regimes. Second, for waves that consist of multiple layers of constant density immiscible fluids, we provide an exact formula describing each of the interfaces in terms of the data. Finally, for continuously stratified fluids, we detail a reconstruction scheme based on approximation by layer-wise constant density flows.