TY - JOUR

T1 - Forcing of oceanic mean flows by dissipating internal tides

AU - Grisouard, Nicolas

AU - Bühler, Oliver

N1 - Funding Information:
Fruitful discussions with R. Ferrari, J. McWilliams, E. D’Asaro and especially L. Maas are acknowledged. The authors also thank three anonymous referees for helping us improve the article. Financial support under the USA National Science Foundation grants NSF/OCE 1024180 and NSF/DMS 1009213 is gratefully acknowledged.

PY - 2012/10/10

Y1 - 2012/10/10

N2 - We present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave-mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

AB - We present a theoretical and numerical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by the oscillatory flow of a barotropic tide over undulating topography and are also subject to dissipation. This extends the classic lee-wave drag problem of atmospheric wave-mean interaction theory to a more complicated oceanographic setting, because now the steady lee waves are replaced by oscillatory internal tides and, most importantly, because now the three-dimensional oceanic mean flow is defined by time averaging over the fast tidal cycles rather than by the zonal averaging familiar from atmospheric theory. Although the details of our computation are quite different, we recover the main action-at-a-distance result from the atmospheric setting, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, we derive an explicit expression for the effective mean force at leading order using a perturbation series in small wave amplitude within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and then compute the effective mean force numerically in a number of idealized examples with simple topographies.

KW - internal waves

KW - ocean processes

KW - topographic effects

UR - http://www.scopus.com/inward/record.url?scp=84865734595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865734595&partnerID=8YFLogxK

U2 - 10.1017/jfm.2012.303

DO - 10.1017/jfm.2012.303

M3 - Article

AN - SCOPUS:84865734595

SN - 0022-1120

VL - 708

SP - 250

EP - 278

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -