WAVE MOTION IN A VISCOUS-FLUID OF VARIABLE DEPTH

被引:6
作者
MILES, J
机构
[1] Institute of Geophysics and Planetary Physics University of California, San Diego, La Jolla
关键词
D O I
10.1017/S0022112090002002
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The linearized equations for wave motion of frequency to in a shallow, viscous liquid of variable depth h are reduced to a partial differential equation, £Z = 0, for the complex amplitude Z of the free-surface displacement on the assumptions of no slip at the bottom and Kh, K84 1, where K = w2/, and 8+ = (v/2a))i is a viscous lengthscale. It is shown that capillarity must be included in order to avoid an irregular singular point (which would imply the total absorption of an incoming wave) at h = 0, £Z then is fourth-order and has a regular singular point of exponents 2, 1, 0, 0 for h ~ crx[0. The requirements that the free-surface displacement and the shear force be bounded as h j 0 rule out the solutions of exponent 0 and imply a stationary contact line. This last prediction is supported by laboratory observation but is not consistent with the observed runup of long, non-breaking waves on real beaches (for which the condition of no slip presumably must be relaxed). The dissipation for sufficiently small capillarity and viscosity is equal to that calculated from a boundary-layer approximation (despite the violation of the assumption h > 8, on which that approximation is based). The viscous modification of the Stokes edge wave on a uniform, gentle slope is calculated through matched asymptotic approximations to the solution of £Z = 0. © 1990, Cambridge University Press. All rights reserved.
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页码:365 / 372
页数:8
相关论文
共 9 条
[1]  
Abramowitz M., 1964, HDB MATH FUNCTIONS
[2]   SPREADING OF LIQUIDS ON SOLID-SURFACES - STATIC AND DYNAMIC CONTACT LINES [J].
DUSSAN, EB .
ANNUAL REVIEW OF FLUID MECHANICS, 1979, 11 :371-400
[3]   MOTION OF A FLUID-FLUID INTERFACE ALONG A SOLID-SURFACE [J].
DUSSAN, EB ;
DAVIS, SH .
JOURNAL OF FLUID MECHANICS, 1974, 65 (AUG12) :71-&
[4]   EXCITATION OF EDGE WAVES BY WAVES BY INCIDENT ON A BEACH [J].
GUZA, RT ;
DAVIS, RE .
JOURNAL OF GEOPHYSICAL RESEARCH, 1974, 79 (09) :1285-1291
[5]  
Ince E. L., 1944, ORDINARY DIFFERENTIA, pviii+558
[6]  
Lamb H., 1932, HYDRODYNAMICS
[7]   WAVE REFLECTION FROM BEACHES [J].
MAHONY, JJ ;
PRITCHARD, WG .
JOURNAL OF FLUID MECHANICS, 1980, 101 (DEC) :809-&
[8]   EDGE WAVES ON A GENTLY SLOPING BEACH [J].
MILES, J .
JOURNAL OF FLUID MECHANICS, 1989, 199 :125-131
[9]   SURFACE-WAVES IN BASINS OF VARIABLE DEPTH [J].
MILES, J .
JOURNAL OF FLUID MECHANICS, 1985, 152 (MAR) :379-389