On the solution of Long’s equation over terrain

Humi, M. (2004) On the solution of Long’s equation over terrain. Il nuovo cimento C, 27 (3). pp. 219-229. ISSN 1826-9885

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Several authors that investigated the numerical solutions of Long’s equation over terrain found that the solution depends weakly on the nonlinear terms in this equation. The objective of this paper is to provide analytical proof of this statement in the context of gravity waves over topography. Furthermore we show that under mild restrictions the equation can be transformed to a Lienard-type equation and identify the “slow variable” that controls the nonlinear oscillations in this equation. Using the phase averaging method we derive also an approximate formula for the attenuation of the stream function perturbation with height. This result is generically related to the nonlinear terms in Long’s equation.

Item Type: Article
Uncontrolled Keywords: Winds and their effects ; Gravity waves, tides, and compressional waves ; Integrable systems
Subjects: 500 Scienze naturali e Matematica
Depositing User: Marina Spanti
Date Deposited: 14 Mar 2020 11:02
Last Modified: 14 Mar 2020 11:02
URI: http://eprints.bice.rm.cnr.it/id/eprint/15236

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