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Title

On Lagrangian drift in shallow-water waves on moderate shear

Author(s)

Phillips, W. R. C.;  Dai, A.;  Tjan, K. K.

Abstract

The Lagrangian drift in an O(ϵ) monochromatic wave field on a shear flow, whose characteristic velocity is O(ϵ) smaller than the phase velocity of the waves, is considered. It is found that although shear has only a minor influence on drift in deep-water waves, its influence becomes increasingly important as the depth decreases, to the point that it plays a significant role in shallow-water waves. Details of the shear flow likewise affect the drift. Because of this, two temporal cases common in coastal waters are studied, viz. stress-induced shear, as would arise were the boundary layer wind-driven, and a current-driven shear, as would arise from coastal currents. In the former, the magnitude of the drift (maximum minus minimum) in shallow-water waves is increased significantly above its counterpart, viz. the Stokes drift, in like waves in otherwise quiescent surroundings. In the latter, on the other hand, the magnitude decreases. However, while the drift at the free surface is always oriented in the direction of wave propagation in stress-driven shear, this is not always the case in current-driven shear, especially in long waves as the boundary layer grows to fill the layer. This latter finding is of particular interest vis-à-vis Langmuir circulations, which arise through an instability that requires differential drift and shear of the same sign. This means that while Langmuir circulations form near the surface and grow downwards (top down), perhaps to fill the layer, in stress-driven shear, their counterparts in current-driven flows grow from the sea floor upwards (bottom up) but can never fill the layer.

Publication type

Journal article

Research centre

Swinburne University of Technology

Source

Journal of Fluid Mechanics, Vol. 660 (Oct 2010), pp. 221-239

Publication year

2010

FOR Code(s)

0102 Applied Mathematics;  0915 Interdisciplinary Engineering

Keyword(s)

Free-surface flows;  Ocean processes;  Shallow-water flows;  Waves

Publisher

Cambridge University Press

ISSN

0022-1120

Publisher URL

http://dx.doi.org/10.1017/S0022112010002648

Copyright

Copyright © Cambridge University Press 2010. The published version of the paper is reproduced here in accordance with the copyright policy of the publisher.

Research Projects

Oceanic conditions within extreme tropical cyclones, Australian Research Council grant number LP0883888
Wave-induced upper-ocean mixing, Australian Research Council grant number DP1093517

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