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Initialization of the shallow water equations with open boundaries by the bounded derivative method

Browning, G. and Kreiss, H.-O. (1982) Initialization of the shallow water equations with open boundaries by the bounded derivative method. Tellus, 34 (4). pp. 334-351. ISSN 0040-2826. https://resolver.caltech.edu/CaltechAUTHORS:20150810-093141406

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Abstract

The shallow water equations are a symmetric hyperbolic system with two time scales. In meteorological terms, slow and fast scale motions are referred to as Rossby and inertial/gravity waves, respectively. We prove the existence of smooth solutions (solutions with a number of space and time derivatives on the order of the slow time scale) of the open boundary problem for the shallow water equations by the bounded derivative method. The proof requires that a number of initial time derivatives be of the order of the slow time scale and that the boundary data be smooth. If the boundary data are smooth and only have small errors, then we show that the solution of the open boundary problem is smooth and that only small errors are produced in the interior. If the boundary data are smooth but have large errors, then we show that the solution of the open boundary problem is still smooth. Unfortunately the boundary error propagates into the interior at the speed associated with the fast time scale and destroys the solution in a short time. Thus it is necessary to keep the boundary error small if the solution is to be computed correctly. We show that this restriction can be relaxed so that only the large-scale boundary data need be correct. We demonstrate the importance of these conclusions in several numerical experiments.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1111/j.2153-3490.1982.tb01823.xDOIArticle
http://tellusa.net/index.php/tellusa/article/view/10820PublisherArticle
Additional Information:This journal is published under the terms of the Creative Commons Attribution 4.0 International (CC-BY 4.0) License. (Manuscript received June 10; in final form December 14, 1981) Sponsored by the National Science Foundation. Supported by the Office of Naval Research under Contract No. N00014-80-C0076.
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Office of Naval Research (ONR)N00014-80-C0076
Issue or Number:4
Record Number:CaltechAUTHORS:20150810-093141406
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150810-093141406
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59343
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:10 Aug 2015 16:40
Last Modified:03 Oct 2019 08:46

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