Thickness-weighted mean theory for the effect of surface gravity waves on mean flows in the upper ocean

Aiki, Hidenori and Greatbatch, Richard John (2012) Thickness-weighted mean theory for the effect of surface gravity waves on mean flows in the upper ocean Journal of Physical Oceanography, 42 . pp. 725-747. DOI 10.1175/JPO-D-11-095.1.

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Abstract

The residual effect of surface gravity waves on mean flows in the upper ocean is investigated using thickness weighted mean (TWM) theory applied in a vertically Lagrangian and horizontally Eulerian coordinate system. Depth-dependent equations for the conservation of volume, momentum, and energy are derived. These equations allow for (i) finite amplitude fluid motions, (ii) the horizontal divergence of currents and (iii) a concise treatment of both the kinematic and viscous boundary conditions at the sea surface. Under the assumptions of steady and monochromatic waves and a uniform turbulent viscosity, the TWM momentum equations are used to illustrate the pressure- and viscosity-induced momentum fluxes through the surface that are implicit in previous studies of the wave-induced modification of the classical Ekman spiral problem. The TWM approach clarifies, in particular, the surface momentum flux associated with the so-called virtual wave stress of Longuet-Higgins. Overall the TWM framework can be regarded as an alternative to the three-dimensional Lagrangian mean framework of Pierson. Moreover the TWM framework can be used to include the residual effect of surface waves in large-scale circulation models. In specific models that carry the TWM velocity appropriate for advecting tracers as their velocity variable, the turbulent viscosity term should be modified so that the viscosity acts only on the Eulerian mean velocity.

Document Type: Article
Keywords: Oceanography; Gravity waves; Lagrangian circulation/transport; Waves, oceanic; Wind waves; Isopycnal coordinates; Vertical coordinates
Research affiliation: OceanRep > GEOMAR > FB1 Ocean Circulation and Climate Dynamics > FB1-TM Theory and Modeling
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
DOI etc.: 10.1175/JPO-D-11-095.1
ISSN: 0022-3670
Date Deposited: 15 May 2012 11:56
Last Modified: 04 Sep 2013 09:19
URI: http://eprints.uni-kiel.de/id/eprint/14295

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