TY - JOUR

T1 - Beta-plane turbulence above monoscale topography

AU - Constantinou, Navid C.

AU - Young, William R.

N1 - Publisher Copyright:
© 2017 Cambridge University Press.

PY - 2017/9/25

Y1 - 2017/9/25

N2 - Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of on parameters such as the planetary potential vorticity (PV) gradient and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow in the limiting cases of weak and strong forcing. If is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow is an unoccupied mean. If is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an 'eddy saturation' regime in which is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

AB - Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of on parameters such as the planetary potential vorticity (PV) gradient and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow in the limiting cases of weak and strong forcing. If is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow is an unoccupied mean. If is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an 'eddy saturation' regime in which is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

KW - geostrophic turbulence

KW - quasi-geostrophic flows

KW - topographic effects

UR - http://www.scopus.com/inward/record.url?scp=85029482271&partnerID=8YFLogxK

U2 - 10.1017/jfm.2017.482

DO - 10.1017/jfm.2017.482

M3 - Article

SN - 0022-1120

VL - 827

SP - 415

EP - 447

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -