Friction and Diapycnal Mixing at a Slope: Boundary Control of Potential Vorticity

Abstract Although atmospheric forcing by wind stress or buoyancy flux is known to change the ocean’s potential vorticity (PV) at the surface, less is understood about PV modification in the bottom boundary layer. The adjustment of a geostrophic current over a sloped bottom in a stratified ocean generates PV sources and sinks through friction and diapycnal mixing. The time-dependent problem is solved analytically for a no-slip boundary condition, and scalings are identified for the change in PV that arises during the adjustment to steady state. Numerical experiments are run to test the scalings with different turbulent closure schemes. The key parameters that control whether PV is injected into or extracted from the fluid are the direction of the geostrophic current and the ratio of its initial speed to its steady-state speed. When the current is in the direction of Kelvin wave propagation, downslope Ekman flow advects lighter water under denser water, driving diabatic mixing and extracting PV. For a current in the opposite direction, Ekman advection tends to restratify the bottom boundary layer and increase the PV. Mixing near the bottom counteracts this restratification, however, and an increase in PV will only occur for current speeds exceeding a critical value. Consequently, the change in PV is asymmetric for currents of the opposite sign but the same speed, with a bias toward PV removal. In the limit of a large speed ratio, the change in PV is independent of diapycnal mixing.

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Estuarine Boundary Layer Mixing Processes: Insights from Dye Experiments*

Journal of Physical Oceanography ◽

10.1175/jpo3088.1 ◽

2007 ◽

Vol 37 (7) ◽

pp. 1859-1877 ◽

Cited By ~ 34

Author(s):

Robert J. Chant ◽

Wayne R. Geyer ◽

Robert Houghton ◽

Elias Hunter ◽

James Lerczak

Keyword(s):

Boundary Layer ◽

Richardson Number ◽

Flood Tide ◽

Buoyancy Flux ◽

Bottom Boundary Layer ◽

Buoyancy Frequency ◽

Entrainment Rate ◽

Diapycnal Mixing ◽

Bottom Boundary ◽

Shear Production

Abstract A series of dye releases in the Hudson River estuary elucidated diapycnal mixing rates and temporal variability over tidal and fortnightly time scales. Dye was injected in the bottom boundary layer for each of four releases during different phases of the tide and of the spring–neap cycle. Diapycnal mixing occurs primarily through entrainment that is driven by shear production in the bottom boundary layer. On flood the dye extended vertically through the bottom mixed layer, and its concentration decreased abruptly near the base of the pycnocline, usually at a height corresponding to a velocity maximum. Boundary layer growth is consistent with a one-dimensional, stress-driven entrainment model. A model was developed for the vertical structure of the vertical eddy viscosity in the flood tide boundary layer that is proportional to u2*/N∞, where u* and N∞ are the bottom friction velocity and buoyancy frequency above the boundary layer. The model also predicts that the buoyancy flux averaged over the bottom boundary layer is equal to 0.06N∞u2* or, based on the structure of the boundary layer equal to 0.1NBLu2*, where NBL is the buoyancy frequency across the flood-tide boundary layer. Estimates of shear production and buoyancy flux indicate that the flux Richardson number in the flood-tide boundary layer is 0.1–0.18, consistent with the model indicating that the flux Richardson number is between 0.1 and 0.14. During ebb, the boundary layer was more stratified, and its vertical extent was not as sharply delineated as in the flood. During neap tide the rate of mixing during ebb was significantly weaker than on flood, owing to reduced bottom stress and stabilization by stratification. As tidal amplitude increased ebb mixing increased and more closely resembled the boundary layer entrainment process observed during the flood. Tidal straining modestly increased the entrainment rate during the flood, and it restratified the boundary layer and inhibited mixing during the ebb.

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The experimental generation of double Kelvin waves

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1971.0190 ◽

1971 ◽

Vol 326 (1564) ◽

pp. 39-52 ◽

Cited By ~ 3

Keyword(s):

Boundary Layer ◽

Kelvin Waves ◽

Bottom Boundary Layer ◽

Maximum Frequency ◽

Kelvin Wave ◽

Bottom Slope ◽

Shallow Water Theory ◽

Constant Depth ◽

Bottom Boundary ◽

The Right

Experiments carried out with a rotating model basin confirm the existence of a type of slow oscillation (double Kelvin wave) predicted by linearized shallow-water theory. Such oscillations may occur in the neighbourhood of any zone where a bottom slope separates two regions of uniform depth. The energy is propagated along the contours of constant depth, with the shallower water always to the right of the direction of propagation (in the northern hemisphere). The theoretical dispersion relation is well verified, including the existence of a maximum frequency, and consequently a vanishing group-velocity, at a certain wavenumber. When the wavemaker is operated at a frequency greater than this maximum, steady currents are sometimes generated. The effects of curvature of the bottom contours are discussed, as well as the loss of energy by viscous dissipation in the bottom boundary-layer.

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Centrifugal and Symmetric Instability during Ekman Adjustment of the Bottom Boundary Layer

Journal of Physical Oceanography ◽

10.1175/jpo-d-20-0027.1 ◽

2020 ◽

Vol 50 (6) ◽

pp. 1793-1812 ◽

Cited By ~ 1

Author(s):

Jacob O. Wenegrat ◽

Leif N. Thomas

Keyword(s):

Boundary Layer ◽

Flow Field ◽

Potential Vorticity ◽

Lower Boundary ◽

Bottom Boundary Layer ◽

Ekman Transport ◽

Surface Boundary ◽

Layer Potential ◽

Bottom Boundary ◽

Symmetric Instability

AbstractFlow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.

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