Wave Propagation in a Continuously Stratified Fluid

Author: Savage, James Crampton

Year: 1957

Degree: Dissertation (Ph.D.)

Advisor: Dix, Charles Hewitt

Committee Member: Unknown, Unknown

Option: Geophysics; Physics

DOI: 10.7907/SDVS-AN85

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

The problem consists of finding the pressure response to a pressure source in an acoustical system of a stratified fluid overlying a rigid surface; a uniform gravitational field of acceleration g is directed normal to the rigid surface. The stratification is to be understood as implying that [...], the gradient of the velocity of sound, and [...], the negative logarithmic gradient of the density, are directed parallel or antiparallel to the gravitational field. The magnitudes of the quantities involved are assumed to be appropriate to the atmosphere of the earth.

The first problem treated assumes [...] and [...] are constant, a situation which would obtain in an isothermal atmosphere. The pressure response exhibits 1) an appreciable phase shift upon reflection from the rigid surface at large angles of incidence, 2) a surface wave, and 3) appreciable distortion of the pulse shape.

The second problem neglects g and [...]. The solution given is asymptotically (high frequency) valid only in regions of the fluid reached by least time rays which have not been refracted through the horizontal. This solution indicates that the time average energy flux propagates along rays which differ from the least time rays by an amount dependent upon the frequency, i.e. such an atmosphere exhibits angular dispersion. Asymptotic expressions are derived for the magnitude of the time average energy flux and for the pressure pulse distortion.

Finally, variations in [...] and [...] are admitted simultaneously with the presence of a gravitational field. The solution is qualitatively the same as that of the preceding problem.

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