Hostname: page-component-f554764f5-qhdkw Total loading time: 0 Render date: 2025-04-20T06:35:34.471Z Has data issue: false hasContentIssue false
  • English
  • Français

The sandpaper theory of flow–topography interaction for multilayer shallow-water systems

Published online by Cambridge University Press:  25 July 2024

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]
Get access Rights & Permissions [Opens in a new window]

Abstract

Seafloor roughness profoundly influences the pattern and dynamics of large-scale oceanic flows. However, these kilometre-scale topographic patterns are unresolved by global numerical Earth system models and will remain subgrid for the foreseeable future. To properly represent the effects of small-scale bathymetry in analytical and coarse-resolution numerical models, we develop the stratified ‘sandpaper’ theory of flow–topography interaction. This model, which is based on the multilayer shallow-water framework, extends its barotropic antecedent to stratified flows. The proposed theory is successfully tested on the configuration representing the interaction of a zonal current with a corrugated cross-flow ridge.

JFM classification

Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Topographic effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 988 , 10 June 2024 , A52
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Andrews, D.G. & Mcintyre, M.E. 1976 Planetary waves in horizontal and vertical shear: the generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci. 33 2031–2048.2.0.CO;2>CrossRefGoogle Scholar
Arbic, B.K. & Flierl, G.R. 2004 Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom Ekman friction: application to midocean eddies. J. Phys. Oceanogr. 34, 2257–2273.2.0.CO;2>CrossRefGoogle Scholar
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
Charney, J. 1948 On the scale of atmospheric motions. Geophys. Publ. 17, 1–17.Google Scholar
Charney, J. 1971 Geostrophic turbulence. J. Atmos. Sci. 28, 1087–1095.2.0.CO;2>CrossRefGoogle Scholar
Chassignet, E.P. & Xu, X. 2017 Impact of horizontal resolution (1/12° to 1/50°) on Gulf Stream separation, penetration, and variability. J. Phys. Oceanogr. 47, 1999–2021.CrossRefGoogle Scholar
Dewar, W.K. 1986 On the potential vorticity structure of weakly ventilated isopycnals: a theory of subtropical mode water maintenance. J. Phys. Oceanogr. 16, 1204–1216.2.0.CO;2>CrossRefGoogle Scholar
Goff, J.A. 2020 Identifying characteristic and anomalous mantle from the complex relationship between abyssal hill roughness and spreading rates. Geophys. Res. Lett. 47, e2020GL088162.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
Goldsmith, E.J. & Esler, J.G. 2023 Wave propagation through a stationary field of clouds: a homogenisation approach. Q. J. R. Meteorol. Soc. 149, 3455–3476.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
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
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
LaCasce, J. & Groeskamp, S. 2020 Baroclinic modes over rough bathymetry and the surface deformation radius. J. Phys. Oceanogr. 50, 2835–2847.CrossRefGoogle Scholar
Li, Y. & Mei, C.C. 2014 Scattering of internal tides by irregular bathymetry of large extent. J. Fluid Mech. 747, 481–505.CrossRefGoogle Scholar
Marshall, D.P., Williams, R.G. & Lee, M.M. 1999 The relation between eddy-induced transport and isopycnic gradients of potential vorticity. J. Phys. Oceanogr. 29, 1571–1578.2.0.CO;2>CrossRefGoogle Scholar
Mashayek, A. 2023 Large-scale impacts of small-scale ocean topography. J. Fluid Mech. 964, F1.CrossRefGoogle Scholar
McDougall, T.J. & Dewar, W.K. 1998 Vertical mixing and cabbeling in layered models. J. Phys. Oceanogr. 28, 1458–1480.2.0.CO;2>CrossRefGoogle Scholar
Mei, C.C. & Vernescu, M. 2010 Homogenization Methods for Multiscale Mechanics. World Scientific Publishing.CrossRefGoogle Scholar
Metzger, E.J., et al. 2014 US Navy operational global ocean and Arctic ice prediction systems. Oceanography 27, 32–43.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
Palóczy, A. & LaCasce, J.H. 2022 Instability of a surface jet over rough topography. J. Phys. Oceanogr. 52, 2725–2740.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. 2020 Control of baroclinic instability by submesoscale topography. J. Fluid Mech. 882, A14.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. 2023 a A generalized theory of flow forcing by rough topography. J. Fluid. Mech. 961, A24.CrossRefGoogle Scholar
Radko, T. 2023 b The sandpaper theory of flow-topography interaction for homogeneous shallow-water systems. J. Fluid. Mech. 977, A9.CrossRefGoogle Scholar
Rhines, P.B. & Young, W.R. 1982 A theory of the wind-driven circulation. Part I. Mid-ocean gyres. J. Mar. Res. 40 (Suppl), 559–596.Google 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
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
Wunsch, C. 1997 The vertical partition of oceanic horizontal kinetic energy. J. Phys. Oceanogr. 27, 1770–1794.2.0.CO;2>CrossRefGoogle Scholar
Zavala Sansón, L. & van Heijst, G.J.F. 2002 Ekman effects in a rotating flow over bottom topography. J. Fluid Mech. 471, 239–255.CrossRefGoogle Scholar