Repository: Freie Universität Berlin, Math Department

On the boundary layer arising from fast internal waves dynamics

Liu, X. and Klein, R. (2024) On the boundary layer arising from fast internal waves dynamics. (Submitted)

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In this paper, we investigate the boundary layer arising from the fast internal waves in the Boussinesq equations with the Brunt-Vaisälä frequency of order O(1/ε). For the homogeneous-in-height stratification, previous work by \emph{Desjardins, Lannes, Saut, 3(1):153--192, Water Waves, 2021} establishes uniform-in-ϵ estimates locally in time, with additional constraints on the boundary data initially, which essentially restricts the dynamics in the spatially periodic domain. Removing such constraints, our goal is to investigate the general near-boundary behavior. We observe that the fast internal waves will give rise to large growth of the spatial derivatives in the normal direction of the solutions in the vicinity of the boundary. To capture this phenomenon, we introduce an inviscid boundary layer using a natural scaling. In addition, we investigate the well-posedness of such a boundary layer system in the space of analytic functions.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:3091
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 10:34
Last Modified:19 Feb 2024 10:34

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