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Abstract Recent scaling theories for the eddy fluxes in the two-layer quasigeostrophic (QG) model assume a flat-bottom boundary. Here, we discuss an organizing principle for how rough topography (i.e., topography with length scales similar to or smaller than the eddy scale) modifies the fully developed state of baroclinic turbulence. In particular, we focus on random, homogeneous topography in the two-layer QG model on anfplane, forced by a zonal shear and dissipated by linear drag. We present a suite of numerical simulations using idealized monoscale topography, systematically modifying the topographic length and height scales and the strength of the drag. We outline the dependence of the eddy diffusivityD, barotropic eddy energyE, and eddy mixing length, on the two nondimensional control parameters:, controlling the strength of the drag, and, controlling the strength of topographic–advective interactions. Two distinct regimes are identified and quantitatively predicted by a regime transition parameterα, which depends on bothand. Onceαsurpasses ancritical value, all eddy scales are reduced below their flat-bottom values and become much less sensitive to the drag coefficient. Spectral energy budgets reveal that energy pathways are importantly reorganized in this regime compared to the flat-bottom limit. We show how this phenomenology extends to more realistic, multiscale topography and to three-layer QG simulations.
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Parameterizing Nonpropagating Form Drag over Rough Bathymetry
Abstract Slowly evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this “wave” drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly nonlinear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law () for lowNh/u0(linear wave dynamics) to a linear drag law () for highNh/u0flows (nonlinear blocking and hydraulic dynamics), whereNis the stratification,his the height of the topography, andu0is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced near-bottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the subinertial topographic scales can account for 2.7 TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.
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- Award ID(s):
- 1756882
- PAR ID:
- 10515925
- Publisher / Repository:
- American Meteorological Society
- Date Published:
- Journal Name:
- Journal of Physical Oceanography
- Volume:
- 51
- Issue:
- 5
- ISSN:
- 0022-3670
- Format(s):
- Medium: X Size: p. 1489-1501
- Size(s):
- p. 1489-1501
- Sponsoring Org:
- National Science Foundation
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