Barotropic Decay of Baroclinic Waves in a Two-Layer Beta-Plane Model

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  • 1 Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey
  • | 2 Geophysical Fluid Dynamics Laboratory/NOAA, Princeton, New Jersey
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Abstract

A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercritically is shown to depend on whether or not the meridional shell in the upper layer is strong enough to produce a critical latitude for the wave.

If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric growth and baroclinic decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays barotropically toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillation. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonies of the fundamental wave.

By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.

Abstract

A two-layer quasi-geostrophic model is used to study the effects of a meridionally sheared zonal flow on the life cycle of a weakly unstable baroclinic wave. In most of the cases analyzed, the fluid is inviscid with the exception of scale-selective fourth-order horizontal diffusion. The initial zonal flow is identically zero in the lower layer. The character of the eddy life cycle in the limit of weak supercritically is shown to depend on whether or not the meridional shell in the upper layer is strong enough to produce a critical latitude for the wave.

If the shear is sufficiently weak, the wave undergoes periodic amplitude vacillation characterized by symmetric growth and baroclinic decay. However, when the meridional shear is strong enough to allow for the existence of a critical layer, the flow undergoes an asymmetric life cycle which resembles that found by Simmons and Hoskins in a primitive equation model on the sphere: the wave grows baroclinically but decays barotropically toward a wave-free state. Throughout the barotropic decay stage, the wave is breaking and being absorbed either at or before the critical layer. As the supercriticality is increased, strong reflection begins to occur at the location of the wave breaking, resulting in irregular amplitude vacillation. Consistent with critical layer theory, when a reflecting state is created the solution is sensitive to the inclusion of higher zonal harmonies of the fundamental wave.

By relaxing the potential vorticity distribution back to an unstable state, periodic solutions are obtained in which each episode of growth and decay is similar to that found in these nearly inviscid solutions.

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