Electronic Resource
New York, NY
:
American Institute of Physics (AIP)
Physics of Fluids
5 (1993), S. 1644-1650
ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The Kelvin–Helmholtz (KH) instability is investigated for the case when linear monochromatic water waves of wave number k are propagating in a current whose undisturbed horizontal velocity profile is linear down to some depth h, and zero beneath. The present paper generalizes the work of Esch [J. Fluid Mech. 12, 192 (1962)] to the case of finite water depth D. Surface tension is neglected. The result of the analysis is a quartic equation for the phase velocity. The presence of a finite water depth tends to stabilize the flow field: The interval in kh, for which complex roots of the dispersion equation occur, becomes narrower as the depth decreases. Also, the growth rate of the flow decreases. The main results are illustrated graphically, and supplemented by analytic approximations in the limiting case when D/h lies close to unity.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858840
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