CENTRIFUGAL INSTABILITY OF AN OSCILLATORY FLOW OVER PERIODIC RIPPLES

被引:35
作者
HARA, T
MEI, CC
机构
[1] Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA
关键词
D O I
10.1017/S002211209000060X
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
An oscillating flow over a sandy beach can initiate and enhance the formation of bed ripples, with crests perpendicular to the direction of the ambient oscillation. Under certain circumstances, bridges may develop to span adjacent ripple crests, resulting in a brick pattern. It has been suggested that the onset of this transition is due to a three-dimensional centrifugal instability of an otherwise two-dimensional flow over periodic long-crested ripples. Here we analyse theoretically such an instability by assuming that the ripples are rigid and smooth. Two complementary cases are studied. We first consider a weak ambient oscillation over ripples of finite slope in Case (i). The three-dimensional disturbance is found to be localized in a small region either along the crests or along the troughs. In Case (ii) we analyse finite oscillations over ripples of mild slope. The region influenced by the instability is now comparable with a ripple wavelength and the unstable disturbance along adjacent ripples may interact with each other. Four types of harmonic and subharmonic instabilities are found. The associated steady streaming close to the ripple surface shows various tendencies of possible sand accumulations, some of which appear to be qualitatively relevant to the initiation of brick-patterned ripples. © 1990, Cambridge University Press. All rights reserved.
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页码:1 / 32
页数:32
相关论文
共 21 条
[1]  
Abramowitz M., 1965, HDB MATH FUNCTIONS
[2]   MOTION OF WAVES IN SHALLOW WATER - INTERACTION BETWEEN WAVES AND SAND BOTTOMS [J].
BAGNOLD, RA .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1946, 187 (1008) :1-&
[3]  
BATCHELOR GK, 1967, INTRO FLUID MECHANIC
[4]   SHEARING FLOW OVER A WAVY BOUNDARY [J].
BENJAMIN, TB .
JOURNAL OF FLUID MECHANICS, 1959, 6 (02) :161-205
[5]   STABILITY OF TIME-PERIODIC FLOWS [J].
DAVIS, SH .
ANNUAL REVIEW OF FLUID MECHANICS, 1976, 8 :57-74
[6]   ON THE STABILITY OF THE UNSTEADY BOUNDARY-LAYER ON A CYLINDER OSCILLATING TRANSVERSELY IN A VISCOUS-FLUID [J].
HALL, P .
JOURNAL OF FLUID MECHANICS, 1984, 146 (SEP) :347-367
[7]   OSCILLATING FLOWS OVER PERIODIC RIPPLES [J].
HARA, T ;
MEI, CC .
JOURNAL OF FLUID MECHANICS, 1990, 211 :183-209
[8]  
HARA T, 1990, THESIS MIT
[9]   STREAKED FLOW AROUND AN OSCILLATING CIRCULAR-CYLINDER [J].
HONJI, H .
JOURNAL OF FLUID MECHANICS, 1981, 107 (JUN) :509-520
[10]   DOUBLE STRUCTURES OF STEADY STREAMING IN THE OSCILLATORY VISCOUS-FLOW OVER A WAVY WALL [J].
KANEKO, A ;
HONJI, H .
JOURNAL OF FLUID MECHANICS, 1979, 93 (AUG) :727-+