A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Journal Article · Sun Oct 01 00:00:00 UTC 2023 · Journal of Physical Oceanography

DOI:https://doi.org/10.1175/JPO-D-22-0191.1· OSTI ID:2007672

Choi, Jang-Geun ^[1]; Pringle, James ^[2]; Lippmann, Thomas ^[3]

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1. a Center for Ocean Engineering, University of New Hampshire, Durham, New Hampshire
2. b Department of Earth Science, University of New Hampshire, Durham, New Hampshire
3. a Center for Ocean Engineering, University of New Hampshire, Durham, New Hampshire, b Department of Earth Science, University of New Hampshire, Durham, New Hampshire

Abstract

A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number ( S = αN / f , where α , N , and f are the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases with S , asymptotically matching Lentz and Chapman for S < 1. When the solution conserves interior potential vorticity, the momentum transport is proportional to S ² for S < 1 and is in better agreement with numerical simulations.

• Sponsoring Organization: USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Water Power Technologies Office
• Grant/Contract Number: EE0009450
• OSTI ID: 2007672
• Alternate ID(s): OSTI ID: 2580152
• Journal Information: Journal of Physical Oceanography, Journal Name: Journal of Physical Oceanography Journal Issue: 10 Vol. 53; ISSN 0022-3670
• Publisher: American Meteorological Society
• Country of Publication: United States
• Language: English