Two-dimensionality of gravity water flows governed by the equatorial \(f\)-plane approximation
type: Item
instance of: scholarly article
title: Two-dimensionality of gravity water flows governed by the equatorial \(f\)-plane approximation
zbMATH Open document ID: 1382.35202
author: Calin Iulian Martin
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2017-11-24T00:00:00Z
review text: The purpose of this paper is to study the system of governing equations for gravity wave trains at the free surface, governed by the equatorial \(f\)-plane approximation. This system consists of seven equations. Choose a rotating coordinate system with origin at a point on the Earth's surface, with the \(x\)-axis pointing to the east, the \(y\)-axis pointing to the north, and the \(z\)-axis pointing upward. The main theorem states that the water flow over this flat bed governed by the first five equations has a constant vorticity only if the flow is two-dimensional. The proof by contradiction, which uses the Phragmen-Lindelöf method, is made by showing a lack of \(y\)-dependence for the velocity field.
reviewed by: Thomas Ernst
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q86
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 6812673
zbMATH Keywords: \(f\)-plane approximation
zbMATH Keywords: vorticity
zbMATH Keywords: gravity wave trains
MaRDI profile type: Publication
full work available at URL: s10231-017-0663-2
OpenAlex ID: W2607188340
Wikidata QID: Q59607338
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DOI: 10.1007/S10231-017-0663-2
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description: scientific article; zbMATH DE number 6812673