Accession Number:

ADA151450

Title:

Water Wave Propagation Over Uneven Bottoms,

Descriptive Note:

Corporate Author:

FLORIDA UNIV GAINESVILLE DEPT OF COASTAL AND OCEANOGRAPHIC ENGINEERING

Personal Author(s):

• Kirby,J. T.

Report Date:

1985-01-01

Pagination or Media Count:

97.0

Abstract:

In Part I of this report, a time dependent form of the reduced wave equation of Berkhoff is developed for the case of water waves propagating over a bed consisting of ripples superimposed on an otherwise slowly varying mean depth which satisfies the mild slope assumption. The ripples are assumed to have wavelengths on the order of the surface wave length but amplitudes which scale as a small parameter along with the bottom slope. The theory is verified by showing that it reduces to the case of plane waves propagating over a non-dimensional, infinite patch of sinusoidal ripples, studied recently by Davis and Heathershaw and Mei. We then study two cases of interest--formulation and use of the coupled parabolic equations for propagation over patches of arbitrary form in order to study wave reflection, and propagation of trapped waves along an infinite ripple patch. In the second part, we use the results of Part 1 to extend the results for weakly-nonlinear wave propagation to the case of partial reflection from bottoms with mild-sloping mean depth with superposed small amplitude undulations. Keywords include Combined refraction-diffraction, Linear Surface Waves, Shallow and intermediate water depths, and Wave reflection.

Descriptors:

• *WATER WAVES
• *WAVE PROPAGATION
• *RIPPLES
• *WAVE EQUATIONS
• COUPLING(INTERACTION)
• FREQUENCY
• SURFACE WAVES
• TIME DEPENDENCE
• REFLECTION
• SHALLOW WATER
• DIFFRACTION
• LINEARITY
• SLOPE
• PARABOLAS
• REFRACTION
• EQUATIONS
• AMPLITUDE
• ROUGHNESS
• BOTTOM
• PLANE WAVES
• SHALLOW DEPTH
• NONLINEAR PROPAGATION ANALYSIS

Subject Categories:

• Numerical Mathematics
• Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE