Accession Number:

AD0618511

Title:

NONLINEAR GRAVITY WAVES IN A THIN SHEET OF VISCOUS FLUID,

Descriptive Note:

Corporate Author:

CALIFORNIA INST OF TECH PASADENA HYDRODYNAMICS LAB

Personal Author(s):

Report Date:

1965-06-01

Pagination or Media Count:

37.0

Abstract:

A nonlinear theory of long gravity waves is developed for a highly viscous fluid of small depth. The expansion scheme of Lin and Clark for inviscid shallow waters is used, and discussions are then made for three different cases a OE, OE2, and OE3, where a is the dimension less amplitude and E is the dimensionless depth. In the first case a new partial differential equation is obtained which involves a nonlinear diffusion term. In the second case the governing equation is shown to be of Burgers type. In all three cases permanent waves are treated explicitly. A variety of wave forms is found in the third case when a OE3 monoclinal and polyclinal waves over an inclined bottom, as well as solitary and cnoidal waves on a vertical wall. Surface tension is not considered. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE