Baroclinic Instability and Frontogenesis with Ekman Boundary Layer Dynamics Incorporating the Geostrophic Momentum Approximation

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  • 1 Department of Astro-Geophysics, University of Colorado, Boulder, CO 80309
  • | 2 Department of Meteorology, Nanjing University, Nanjing, China
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Abstract

The baroclinic instability of a two-dimensional uniform potential vorticity flow above a relatively thin viscous boundary layer is examined. The disturbance field is constrained by the geostrophic momentum approximation, and boundary layer dynamics are incorporated by prescribing the vertical velocity, derived by Wu and Blumen, at the bottom boundary of the inviscid layer. Characteristics of the instability and frontogenetical properties of the model are delineated by comparison with the results obtained using Ekman boundary layer dynamics to prescribe the vertical velocity at the boundary.

It is established that the unstable growth rates, phase speeds and qualitative aspects of the frontogenetical process are not significantly different from results obtained using Ekman boundary layer dynamics. However, significant modifications to the vertical velocity field at the lower boundary occur when the amplitude of the relative vorticity at the lower boundary attains a value equal to about f, the Coriolis parameter. In comparison with the vertical velocity field associated with Ekman layer dynamics, 1) the upward motion is smaller in cyclonic regions and larger in anticyclonic regions and 2) a broader band of relatively high values of upward motion exists. These features are interpreted in terms of the physical properties of the modified boundary layer dynamics.

Abstract

The baroclinic instability of a two-dimensional uniform potential vorticity flow above a relatively thin viscous boundary layer is examined. The disturbance field is constrained by the geostrophic momentum approximation, and boundary layer dynamics are incorporated by prescribing the vertical velocity, derived by Wu and Blumen, at the bottom boundary of the inviscid layer. Characteristics of the instability and frontogenetical properties of the model are delineated by comparison with the results obtained using Ekman boundary layer dynamics to prescribe the vertical velocity at the boundary.

It is established that the unstable growth rates, phase speeds and qualitative aspects of the frontogenetical process are not significantly different from results obtained using Ekman boundary layer dynamics. However, significant modifications to the vertical velocity field at the lower boundary occur when the amplitude of the relative vorticity at the lower boundary attains a value equal to about f, the Coriolis parameter. In comparison with the vertical velocity field associated with Ekman layer dynamics, 1) the upward motion is smaller in cyclonic regions and larger in anticyclonic regions and 2) a broader band of relatively high values of upward motion exists. These features are interpreted in terms of the physical properties of the modified boundary layer dynamics.

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