Skip to main content Accessibility help
×
Home
Hostname: page-component-78bd46657c-lnsrr Total loading time: 0.193 Render date: 2021-05-08T11:40:10.415Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations

Published online by Cambridge University Press:  12 May 2004

PETER P. SULLIVAN
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80307, USA
JAMES C. McWILLIAMS
Affiliation:
Department of Atmospheric and Oceanic Sciences and Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90095, USA
W. KENDALL MELVILLE
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0213, USA

Abstract

We devise a stochastic model for the effects of breaking waves and fit its distribution functions to laboratory and field data. This is used to represent the space–time structure of momentum and energy forcing of the oceanic boundary layer in turbulence-resolving simulations. The aptness of this breaker model is evaluated in a direct numerical simulation (DNS) of an otherwise quiescent fluid driven by an isolated breaking wave, and the results are in good agreement with laboratory measurements. The breaker model faithfully reproduces the bulk features of a breaking event: the mean kinetic energy decays at a rate approaching $t^{-1}$, and a long-lived vortex (eddy) is generated close to the water surface. The long lifetime of this vortex (more than 50 wave periods) makes it effective in energizing the surface region of oceanic boundary layers. Next, a comparison of several different DNS of idealized oceanic boundary layers driven by different surface forcing (i.e. constant current (as in Couette flow), constant stress, or a mixture of constant stress plus stochastic breakers) elucidates the importance of intermittent stress transmission to the underlying currents. A small amount of active breaking, about 1.6% of the total water surface area at any instant in time, significantly alters the instantaneous flow patterns as well as the ensemble statistics. Near the water surface a vigorous downwelling–upwelling pattern develops at the head and tail of each three-dimensional breaker. This enhances the vertical velocity variance and generates both negative- and positive-signed vertical momentum flux. Analysis of the mean velocity and scalar profiles shows that breaking effectively increases the surface roughness $z_o$ by more than a factor of 30; for our simulations $z_o/\lambda \,{\approx}\, 0.04$ to 0.06, where $\lambda$ is the wavelength of the breaking wave. Compared to a flow driven by a constant current, the extra mixing from breakers increases the mean eddy viscosity by more than a factor of 10 near the water surface. Breaking waves alter the usual balance of production and dissipation in the turbulent kinetic energy (TKE) budget; turbulent and pressure transports and breaker work are important sources and sinks in the budget. We also show that turbulent boundary layers driven by constant current and constant stress (i.e. with no breaking) differ in fundamental ways. The additional freedom provided by a constant-stress boundary condition permits finite velocity variances at the water surface, so that flows driven by constant stress mimic flows with weakly and statistically homogeneous breaking waves.

Type
Papers
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *