A linear model for the structure of turbulence beneath surface water waves

Teixeira, M. A.C. ORCID: https://orcid.org/0000-0003-1205-3233 (2011) A linear model for the structure of turbulence beneath surface water waves. Ocean modelling, 36 (1-2). pp. 149-162. ISSN 1463-5003 doi: 10.1016/j.ocemod.2010.10.007

Abstract/Summary

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/29239
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology No Reading authors. Back catalogue items
Publisher	Elsevier Inc.
Download/View statistics	View download statistics for this item