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Gravity Waves Due to a Point Disturbance in a Plane Free Surface Flow of Stratified Fluids

Mei, C. C. and Wu, T. Yao-tsu (1964) Gravity Waves Due to a Point Disturbance in a Plane Free Surface Flow of Stratified Fluids. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:HydroLabRpt97-5

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Abstract

The fundamental solution of the gravity waves due to a two-dimensional point singularity submerged in a steady free surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Love's equations. The effect of density stratification p[sub]o(y) and the gravity effect are characterized by two flow parameters [sigma] = -(dp[sub]o/dy)/p[sub]o and [lambda] = gL/U^2, where [lambda]^-1/2 may be regarded as the internal Froude number if L assumes a characteristic value of [sigma]^-1. Two special cases of [sigma] and [lambda] are treated in this paper. In the first case of constant [sigma] (and arbitrary [lambda]) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as [lambda] > or < 1/2, in analogy to the corresponding states of channel flows. In addition to a potential surface wave, which exists only for [lambda]>1/2, there arises an internal wave which is attenuated at large distances for [lambda] > 1/4 and decays exponentially for [lambda] < 1/4. In the second example an asymptotic theory for large [lambda] is developed while [sigma](y) may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium.


Item Type:Report or Paper (Technical Report)
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http://resolver.caltech.edu/CaltechAUTHORS:20120830-161623975Related ItemUNSPECIFIED
Additional Information:This work was supported by the U. S. Office of Naval Research under Contract Nonr-220(35).
Record Number:CaltechAUTHORS:HydroLabRpt97-5
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:HydroLabRpt97-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:400
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:09 Jun 2005
Last Modified:26 Dec 2012 08:40

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