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The Eady model of baroclinic instability has served as a theoretical foundation for understanding the scale, growth rate, and structure of mid-latitude atmospheric weather systems and oceanic mesoscale eddies. Over shallow continental shelves and slopes where bottom drag is important, baroclinic instability also occurs, which gives rise to vortices and meanders visible along density fronts from satellite images (Fig. 1). However, whether the Eady-type theories are applicable to explain the properties of shallow, oceanic unstable flows is largely untested. Using idealized experiments to isolate the influences of bottom drag and topographic slope, Chen et al. (2020) provides direct evidence for that the growing instability in shallow flows is consistent with the mutual reinforcement of boundary-trapped Rossby waves as found in the Eady model (Fig. 2). Yet, the theories have quantitative limitations, especially when applying to conditions with strong friction and steep topography due to the neglect of boundary layer response and horizontal shear, respectively. Potential corrections for the Eady-type theories are proposed.

Chen, S. N*., C. J. Chen, and J. A. Lerczak, 2020: On baroclinic instability over continental shelves: Testing the utility of Eady-type models. Journal of Physical Oceanography, 50, 3-33.

Fig. 1. Examples of coastal currents: (a) unstable Middle Atlantic Bight Shelf Break Jet (Garvine et al. 1988); (b) unstable Leeuwin Current (Pearce and Griffiths 1991); (c)unstable Alaska Coastal Current (fed by coastal discharge); (d) stable Chesapeake Bay outflow (fed by coastal discharge; Donato and Marmorino (2008).

Fig. 2. An example of baroclinically unstable coastal current. In this setup, the basic flow (e) has a constant isopycnal slope (color contour is salinity), is purely along-shore with no horizontal shear (u denoted by white contours) in a wide central region, and is inviscid. This example therefore mimics the Eady basic flow. Panels (a)-(d) show the top views of surface salinity, taken at day 7, 11, 13, and 15. (f) and (g) are the time series of eddy kinetic energy budget and estimated growth rate (black) and wavelength (red). In (h), the estimated most unstable mode (star symbols taken in (g)) agrees with Eady’s theory (i.e. max of black curve).