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Nonlinear stratified spindown over a slope

Published online by Cambridge University Press:  05 June 2013

Jessica A. Benthuysen  and
Leif N. Thomas
Jessica A. Benthuysen*
Affiliation:
MIT/WHOI Joint Program, Woods Hole, MA 02543, USA CSIRO Marine and Atmospheric Research, Hobart, Tasmania, 7000, Australia Centre for Australian Weather and Climate Research, Hobart, Tasmania, 7000, Australia
Leif N. Thomas
Affiliation:
Department of Environmental Earth System Science, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: jessica.benthuysen@csiro.au
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Abstract

Nonlinear stratified spindown of an along-isobath current over an insulated slope is shown to develop asymmetries in the vertical circulation and vertical relative vorticity field. During spindown, cyclonic vorticity is weakened to a greater extent than anticyclonic vorticity near the boundary because of buoyancy advection. As a consequence, Ekman pumping is weakened over Ekman suction. Momentum advection can weaken Ekman pumping and strengthen Ekman suction. Time-dependent feedback between the geostrophic flow and the frictional secondary circulation induces asymmetry in cyclonic and anticyclonic vorticity away from the boundary. Buoyancy advection over a slope can modify the secondary circulation such that anticyclonic vorticity decays faster than cyclonic vorticity outside the boundary layer. In contrast, momentum advection can cause cyclonic vorticity to spin down faster than anticyclonic vorticity. A scaling and analytical solutions are derived for when buoyancy advection over a slope can have a more significant impact than momentum advection on these asymmetries. In order to test this scaling and analytical solutions, numerical experiments are run in which both buoyancy and momentum advection are active. These solutions are contrasted with homogeneous or stratified spindown over a flat bottom, in which momentum advection controls the asymmetries. These results are applied to ocean currents over continental shelves and slopes.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 371 - 403
Copyright
©2013 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Benthuysen, J. A. 2010 Linear and nonlinear stratified spindown over sloping topography. PhD thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution.Google Scholar
Benthuysen, J. A. & Thomas, L. N. 2012a Asymmetries in vertical vorticity and vertical velocity arising during nonlinear homogeneous spindown. Phys. Fluids 24, 076601.Google Scholar
Benthuysen, J. A. & Thomas, L. N. 2012b Frictional and diapycnal mixing at a slope: boundary control of potential vorticity. J. Phys. Oceanogr. 42, 1509–1523.Google Scholar
Benton, G. S., Lipps, F. B. & Tuann, S.-Y. 1964 The structure of the Ekman layer for geostrophic flows with lateral shear. Tellus XVI, 186–199.Google Scholar
Chapman, D. C. 2002 Deceleration of a finite-width, stratified current over a sloping bottom: frictional spindown or buoyancy shutdown? J. Phys. Oceanogr. 32, 336–352.2.0.CO;2>CrossRefGoogle Scholar
Charney, J. G. & Eliassen, A. 1949 A numerical method of predicting the perturbations of the middle-latitude westerlies. Tellus 1, 38–54.Google Scholar
Crank, J. & Nicolson, P. 1947 A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Proc. Camb. Phil. Soc. 43, 50–67.Google Scholar
Hart, J. E. 1995 Nonlinear Ekman suction and ageostrophic effects in rapidly rotating flows. Geophys. Astrophys. Fluid Dyn. 79, 201–222.Google Scholar
Hart, J. E. 2000 A note on nonlinear corrections to the Ekman layer pumping velocity. Phys. Fluids 12, 131–135.Google Scholar
Holton, J. R. 1965 The influence of viscous boundary layers on transient motions in a stratified rotating fluid: Part I. J. Atmos. Sci. 22, 402–411.Google Scholar
MacCready, P. & Rhines, P. B. 1991 Buoyant inhibition of Ekman transport on a slope and its effect on stratified spin-up. J. Fluid Mech. 223, 631–661.Google Scholar
Pedlosky, J. 2008 On the weakly nonlinear Ekman layer: thickness and flux. J. Phys. Oceanogr. 38, 1334–1339.Google Scholar
Shchepetkin, A. F. & McWilliams, J. C. 2005 The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Model. 9, 347–404.CrossRefGoogle Scholar
Stahr, F. R. & Sanford, T. B. 1999 Transport and bottom boundary layer observations of the North Atlantic Deep Western Boundary Current at the Blake Outer Ridge. Deep-Sea Res. II 46, 205–243.Google Scholar
Thomas, L. N. & Rhines, P. B. 2002 Nonlinear stratified spin-up. J. Fluid Mech. 473, 211–244.Google Scholar
Thorpe, S. A. 1987 Current and temperature variability on the continental slope. Phil. Trans. R. Soc. Lond. A 323, 471–517.Google Scholar
Zavala Sansón, L. 2001 The asymmetric Ekman decay of cyclonic and anticyclonic vortices. Eur. J. Mech. (B/Fluids) 20, 541–556.Google Scholar
Zavala Sansón, L. & van Heijst, G. J. F. 2000 Nonlinear Ekman effects in rotating barotropic flows. J. Fluid Mech. 412, 75–91.Google Scholar