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A generalized theory of flow forcing by rough topography

Published online by Cambridge University Press:  24 April 2023

Timour Radko Open the ORCID record for Timour Radko [Opens in a new window]
Timour Radko*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA
*
†Email address for correspondence: [email protected]
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Abstract

An analytical model is developed which explores the impact of irregular sea-floor roughness on large-scale oceanic flows. The previously reported asymptotic ‘sandpaper’ theory of flow-topography interaction represents relatively swift currents and exhibits singular behaviour in the weak flow limit. The present investigation systematically spans a wider parameter space and identifies the principal dissimilarities in the topographic regulation of slow and fast currents. The fast flows are controlled by the Reynolds stresses produced by topographically generated eddies. In contrast, relatively weak flows are more affected by the eddy-induced bottom form drag. The asymptotic models for fast and slow currents are then combined to arrive at a concise description of flow forcing by small-scale topography in homogeneous and multilayer models. The proposed closure is validated by comparing corresponding topography-resolving and parametric simulations.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 961 , 25 April 2023 , A24
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Balmforth, N.J. & Young, Y.-N. 2002 Stratified Kolmogorov flow. J. Fluid Mech 450, 131–167.CrossRefGoogle Scholar
Balmforth, N.J. & Young, Y.-N. 2005 Stratified Kolmogorov flow. Part 2. J. Fluid Mech. 528, 23–42.CrossRefGoogle Scholar
Benilov, E.S. 2000 The stability of zonal jets in a rough-bottomed ocean on the barotropic beta plane. J. Phys. Oceanogr. 30, 733–740.2.0.CO;2>CrossRefGoogle Scholar
Benilov, E.S. 2001 Baroclinic instability of two-layer flows over one-dimensional bottom topography. J. Phys. Oceanogr. 31, 2019–2025.2.0.CO;2>CrossRefGoogle Scholar
Bleck, R. 2002 An oceanic general circulation model framed in hybrid isopycnic–Cartesian coordinates. Ocean Model. 4, 55–58.CrossRefGoogle Scholar
Dewar, W.K., Berloff, P. & Hogg, A.M. 2011 Submesoscale generation by boundaries. J. Mar. Res. 69, 501–522.CrossRefGoogle Scholar
Dewar, W.K. & Hogg, A.M. 2010 Topographic inviscid dissipation of balanced flow. Ocean Model. 32, 1–13.CrossRefGoogle Scholar
Eden, C., Olbers, D. & Eriksen, T. 2021 A closure for lee wave drag on the large-scale ocean circulation. J. Phys. Oceanogr. 51, 3573–3588.Google Scholar
Gama, S., Vergassola, M. & Frisch, U. 1994 Negative eddy viscosity in isotropically forced 2-dimensional flow – linear and nonlinear dynamics. J. Fluid Mech. 260, 95–126.CrossRefGoogle Scholar
Goff, J.A. & Jordan, T.H. 1988 Stochastic modeling of seafloor morphology: inversion of sea beam data for second-order statistics. J. Geophys. Res. 93, 13589–13608.CrossRefGoogle Scholar
Goldsmith, E.J. & Esler, J.G. 2021 Wave propagation in rotating shallow water in the presence of small-scale topography. J. Fluid Mech. 923, A24.CrossRefGoogle Scholar
Gulliver, L. & Radko, T. 2022 topographic stabilization of ocean rings. Geophys. Res. Lett. 49, e2021GL097686.CrossRefGoogle Scholar
Gulliver, L.T. & Radko, T. 2023 Virtual laboratory experiments on the interaction of a vortex with small-scale topography. Phys. Fluids 35, 021703.CrossRefGoogle Scholar
Holloway, G. 1987 Systematic forcing of large-scale geophysical flows by eddy-topography interaction. J. Fluid Mech. 184, 463–476.CrossRefGoogle Scholar
Holloway, G. 1992 Representing topographic stress for large-scale ocean models. J. Phys. Oceanogr. 22, 1033–1046.2.0.CO;2>CrossRefGoogle Scholar
Hughes, C.W. & De Cuevas, B.A. 2001 Why western boundary currents in realistic oceans are inviscid: a link between form stress and bottom pressure torques. J. Phys. Oceanogr. 31, 2871–2885.2.0.CO;2>CrossRefGoogle Scholar
Jackson, L., Hughes, C.W. & Williams, R.G. 2006 Topographic control of basin and channel flows: the role of bottom pressure torques and friction. J. Phys. Oceanogr. 36, 1786–1805.CrossRefGoogle Scholar
Johnson, E.R. 1978 Trapped vortices in rotating flow. J. Fluid Mech. 86, 209–224.CrossRefGoogle Scholar
Klymak, J.M., Balwada, D., Garabato, A.N. & Abernathey, R. 2021 Parameterizing nonpropagating form drag over rough bathymetry. J. Phys. Oceanogr. 51, 1489–1501.CrossRefGoogle Scholar
LaCasce, J., Escartin, J., Chassignet, E.P. & Xu, X. 2019 Jet instability over smooth, corrugated, and realistic bathymetry. J. Phys. Oceanogr. 49, 585–605.CrossRefGoogle Scholar
Li, Q.Y., Sun, L. & Xu, C. 2018 The lateral eddy viscosity derived from the decay of oceanic mesoscale eddies. Open J. Mar. Sci. 8, 152–172.CrossRefGoogle Scholar
Manfroi, A. & Young, W. 1999 Slow evolution of zonal jets on the beta plane. J. Atmos. Sci. 56, 784–800.2.0.CO;2>CrossRefGoogle Scholar
Manfroi, A. & Young, W. 2002 Stability of beta-plane Kolmogorov flow. Physica D 162, 208−232.CrossRefGoogle Scholar
Marshall, D. 1995 Topographic steering of the antarctic circumpolar current. J. Phys. Oceanogr. 25, 1636–1650.2.0.CO;2>CrossRefGoogle Scholar
Mei, C.C. & Vernescu, M. 2010 Homogenization Methods for Multiscale Mechanics. World Scientific Publishing. London.CrossRefGoogle Scholar
Merryfield, W.J. 2005 Ocean mixing in 10 steps. Science 308, 641–642.CrossRefGoogle ScholarPubMed
Meshalkin, L. & Sinai, Y. 1961 Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous fluid. J. Appl. Math. Mech. 25, 1700–1705.CrossRefGoogle Scholar
Naveira Garabato, A.C., Nurser, A.G., Scott, R.B. & Goff, J.A. 2013 The impact of small-scale topography on the dynamical balance of the ocean. J. Phys. Oceanogr. 43, 647–668.CrossRefGoogle Scholar
Nikurashin, M., Ferrari, R., Grisouard, N. & Polzin, K. 2014 The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean. J. Phys. Oceanogr. 44, 2938–2950.CrossRefGoogle Scholar
Novikov, A. & Papanicolau, G. 2001 Eddy viscosity of cellular flows. J. Fluid Mech. 446, 173–198.CrossRefGoogle Scholar
Parseval, M.-A. 1806 Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficients constants. Mém. prés. par divers savants. Acad. des Sciences, Paris 1, 638–648.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.CrossRefGoogle Scholar
Radko, T. 2011 a On the generation of large-scale structures in a homogeneous eddy field. J. Fluid Mech. 668, 76–99.CrossRefGoogle Scholar
Radko, T. 2011 b Eddy viscosity and diffusivity in the modon-sea model. J. Mar. Res. 69, 723–752.CrossRefGoogle Scholar
Radko, T. 2020 Control of baroclinic instability by submesoscale topography. J. Fluid Mech. 882, A14.CrossRefGoogle Scholar
Radko, T. 2021 Barotropic instability of a time-dependent parallel flow. J. Fluid Mech. 922, A11.CrossRefGoogle Scholar
Radko, T. 2022 a Spin-down of a barotropic vortex by irregular small-scale topography. J. Fluid Mech. 944, A5.CrossRefGoogle Scholar
Radko, T. 2022 b Spin-down of a baroclinic vortex by irregular small-scale topography. J. Fluid Mech. 953, A7.CrossRefGoogle Scholar
Radko, T. & Kamenkovich, I. 2017 On the topographic modulation of large-scale eddying flows. J. Phys. Oceanogr. 47, 2157–2172.CrossRefGoogle Scholar
Stewart, A.L., McWilliams, J.C. & Solodoch, A. 2021 On the role of bottom pressure torques in wind-driven gyres. J. Phys. Oceanogr. 51, 1441–1464.CrossRefGoogle Scholar
Taylor, G.I. 1923 Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. A 104, 213–218.Google Scholar
Vanneste, J. 2000 Enhanced dissipation for quasi-geostrophic motion over small-scale topography. J. Fluid Mech. 407, 105–122.CrossRefGoogle Scholar
Vanneste, J. 2003 Nonlinear dynamics over rough topography: homogeneous and stratified quasi-geostrophic theory. J. Fluid Mech. 474, 299–318.CrossRefGoogle Scholar
Wåhlin, A.K. 2002 Topographic steering of dense currents with application to submarine canyons. Deep-Sea Res. Part I: Oceanogr. Res. Pap. 49, 305–320.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar