skip to main content


Title: On Baroclinic Instability over Continental Shelves: Testing the Utility of Eady-Type Models
Abstract

This study examines the utility of Eady-type theories as applied to understanding baroclinic instability in coastal flows where depth variations and bottom drag are important. The focus is on the effects of nongeostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate the individual effects and justified to have Eady-like basic states. For the nongeostrophic effect, the theory of Stone (1966) is shown to give reasonable predictions for the most unstable growth rate and wavelength. It is also shown that the growing instability in a fully nonlinear model can be interpreted as boundary-trapped Rossby wave interactions—that is, wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both the boundary dissipative and bottom slope effects can be represented by vertical velocities at the lower boundary of the unstable interior, via inducing Ekman pumping and slope-parallel flow, respectively, as proposed by the theories of Williams and Robinson (1974; referred to as the Eady–Ekman problem) and Blumsack and Gierasch (1972). The vertical velocities, characterized by a friction parameter and a slope ratio, modify the bottom wave and thus the scale selection. However, the theories have inherent quantitative limitations. Eady–Ekman neglects boundary layer responses that limit the increase of bottom stress, thereby overestimating the Ekman pumping and growth rate reduction at large drag. Blumsack and Gierasch’s (1972) model ignores slope-induced horizontal shear in the mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes.

 
more » « less
Award ID(s):
1829979 1260394
NSF-PAR ID:
10127623
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
American Meteorological Society
Date Published:
Journal Name:
Journal of Physical Oceanography
Volume:
50
Issue:
1
ISSN:
0022-3670
Page Range / eLocation ID:
p. 3-33
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    From 2014 through 2016 we instrumented the ~80-km-wide Norske Trough near 78°N latitude that cuts across the 250-km-wide shelf from Fram Strait to the coast. Our measurements resolve a ~10-km-wide bottom-intensified jet that carries 0.27 ± 0.06 Sv (1 Sv ≡ 106 m3 s−1) of warm Atlantic water from Fram Strait toward the glaciers off northeast Greenland. Mean shoreward flows along the steep canyon walls reach 0.1 m s−1 about 50 m above the bottom in 400-m-deep water. The same bottom-intensified vertical structure emerges as the first dominant empirical orthogonal function that explains about 70%–80% of the variance at individual mooring locations. We interpret the current variability as remotely forced wave motions that arrive at our sensor array with periodicities longer than 6 days. Coherent motions with a period near 20 days emerge in our array as a dispersive topographic Rossby wave that propagates its energy along the sloping canyon toward the coast with a group speed of about 63 km day−1. Amplitudes of wave currents reach 0.1 m s−1 in the winter of 2015/16. The wave is likely generated by Ekman pumping over the shelfbreak where sea ice is always mobile. More than 40% of the along-slope ocean current variance near the bottom of the canyon correlates with vertical Ekman pumping velocities 180 km away. In contrast, the impact of local winds on the observed current fluctuations is negligible. Dynamics appear linear and Rossby wave motions merely modulate the mean flow.

     
    more » « less
  2. Abstract. The Chukchi Slope Current is a westward-flowing currentalong the Chukchi slope, which carries Pacific-origin water from the Chukchishelf into the Canada Basin and helps set the regional hydrographicstructure and ecosystem. Using a set of experiments with an idealizedprimitive equation numerical model, we investigate the energetics of theslope current during the ice-covered period. Numerical calculations showthat the growth of surface eddies is suppressed by the ice friction, whileperturbations at mid-depths can grow into eddies, consistent with linearinstability analysis. However, because the ice stress is spatially variable,it is able to drive Ekman pumping to decrease the available potential energy(APE) and kinetic energy of both the mean flow and mesoscale eddies over avertical scale of 100 m, well outside the frictional Ekman layer. The rateat which the APE changes is determined by the vertical density flux, whichis negative as the ice-induced Ekman pumping advects lighter (denser) waterupward (downward). A scaling analysis shows that Ekman pumping will dominatethe release of APE for large-scale flows, but the effect of baroclinicinstability is also important when the horizontal scale of the mean flow isthe baroclinic deformation radius and the eddy velocity is comparable to themean flow velocity. Our numerical results highlight the importance of icefriction in the energetics of the slope current and eddies, and this may berelevant to other ice-covered regions. 
    more » « less
  3. Abstract

    A current along a sloping bottom gives rise to upwelling, or downwelling Ekman transport within the stratified bottom boundary layer (BBL), also known as the bottom Ekman layer. In 1D models of slope currents, geostrophic vertical shear resulting from horizontal buoyancy gradients within the BBL is predicted to eventually bring the bottom stress to zero, leading to a shutdown, or “arrest,” of the BBL. Using 3D ROMS simulations, we explore how the dynamics of buoyancy adjustment in a current‐ridge encounter problem differs from 1D and 2D temporal spin up problems. We show that in a downwelling BBL, the destruction of the ageostrophic BBL shear, and hence the bottom stress, is accomplished primarily by nonlinear straining effects during the initial topographic encounter. As the current advects along the ridge slopes, the BBL deepens and evolves toward thermal wind balance. The onset of negative potential vorticitymodes of instability and their subsequent dissipation partially offsets the reduction of the BBL dissipation during the ridge‐current interaction. On the upwelling side, although the bottom stress weakens substantially during the encounter, the BBL experiences a horizontal inflectional point instability and separates from the slopes before sustained along‐slope stress reduction can occur. In all our solutions, both the upwelling and downwelling BBLs are in a partially arrested state when the current separates from the ridge slope, characterized by a reduced, but non‐zero bottom stress on the slopes.

     
    more » « less
  4. Abstract

    An along‐isobath current in stratified waters leads to a bottom boundary layer. In models with no alongshore variation, cross‐isobath density transport in this bottom boundary layer reduce the velocity in the bottom boundary layer via thermal wind, and thus the bottom friction experienced by the current above the boundary layer—this is bottom‐boundary‐layer arrest. If, however, alongshore variation of the flow is allowed, the bottom boundary layer is baroclinically unstable. We show with high resolution numerical models that these instabilities reduce this arrest and allow bottom friction to decelerate the flow above the bottom boundary layer when the flow is in the Kelvin wave direction (so that the bottom Ekman transport is downwelling). Both the arrest of the bottom boundary layer and the release from this arrest are asymmetric; the friction experienced by flows in the direction of Kelvin‐wave propagation (downwave) is much greater than flows in the opposite direction. The strength of the near bottom currents, and thus the magnitude of bottom friction, is found to be governed by the destruction of potential vorticity near the bottom balanced by the offshore along‐isopycnal transport of this anomalous potential vorticity. A simple model of this process is created and used to quantify the magnitude of this effect and the resulting reduction of arrest of the bottom boundary layer.

     
    more » « less
  5. Three-phase (solid, melt, and gas) and two-phase (solid and melt) models of horizontal ribbon growth were compared to identify the significance of different gas effects. The boundary conditions at the melt–gas and solid–gas interfaces for two-phase simulations were obtained from decoupled simulations of the gas phase. The results showed that the gas shear stress strongly changes the flow and temperature fields and the position of the triple-phase line. Also, the gas pressure distribution determined the vertical position of the triple-phase line. In the absence of growth angle effects, the results of the two-phase model with specified convective heat transfer coefficient, shear stress, and pressure as boundary conditions along the gas phase interface closely matched that of the three-phase model. Even with non-zero growth angle effects, the two-phase model with all the boundary conditions agreed well with three-phase simulation results, despite increased deviations at higher pull speeds. Finally, the results indicated that gas-induced velocities are significant compared to the Marangoni and buoyancy velocities, which could lead to flow instabilities and the variations in solid shape as observed in HRG experiments. 
    more » « less