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Stable and Unstable Evolution of Modons Perturbed by Surface Term, Bottom Friction, and Bottom Topography Incorporating Nonlinear Ekman Pumping

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  • 1 Laboratory for Severe Storm Research, Department of Atmospheric Sciences, Peking University, Beijing, China
  • | 2 Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan
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Abstract

The evolution, both stable and unstable, of contrarotating vortex pairs (“modons”) perturbed by upper-surface and bottom Ekman pumping is investigated using a homogeneous model with a variable free upper-surface and bottom topography. The Ekman pumping considered here differs from the classical Ekman pumping in that the divergence-vorticity term in the vorticity equation, nonlinear and omitted in previous studies, is explicitly included. Under the influence of both nonlinear Ekman pumping and the beta term, eastward- and westward-moving modons behave very differently.

Eastward-moving modons are stable to the upper-surface perturbation but westward-moving modons are not. The latter move southwestward, triggering the tilt instability: the beta effect deepens the cyclones but weakens the anticyclone, and the vortex pair disperses into wave packets.

Eastward-moving modons are stable to bottom friction in the sense that they diminish in time gradually at a rate independent of the signs of the vortices. Westward-moving modons behave differently depending on the strength of bottom friction. Cyclones decay faster than anticyclones, triggering the tilt instability in westward-moving modons, but only if the bottom friction is very weak. For sufficiently strong bottom friction, in contrast, modons decay monotonically: the cyclones still decay faster than anticyclones, but no wave packets formed before the modons completely dissipate.

Westward-moving modons are always unstable to topographic forcing. Eastward-moving modons have varying behavior controlled by the height and width of the topography. Below a critical height, determined by the width, modons survive the topographic interaction: their trajectory meanders but the two contrarotating vortices always remain bound together after escaping the topography. Above the critical height, modons disassociate: the two vortices separate and disperse into wave packets. When the width of the topography is comparable to modon width, there exists a stable window within the unstable region of the topographic height in which the modons also survive the topographic encounter.

Corresponding author address: Dr. Benkui Tan, Laboratory for Severe Storm Research, Department of Atmospheric Sciences, Peking University, Beijing 100871, China. Email: bktan@pku.edu.cn

Abstract

The evolution, both stable and unstable, of contrarotating vortex pairs (“modons”) perturbed by upper-surface and bottom Ekman pumping is investigated using a homogeneous model with a variable free upper-surface and bottom topography. The Ekman pumping considered here differs from the classical Ekman pumping in that the divergence-vorticity term in the vorticity equation, nonlinear and omitted in previous studies, is explicitly included. Under the influence of both nonlinear Ekman pumping and the beta term, eastward- and westward-moving modons behave very differently.

Eastward-moving modons are stable to the upper-surface perturbation but westward-moving modons are not. The latter move southwestward, triggering the tilt instability: the beta effect deepens the cyclones but weakens the anticyclone, and the vortex pair disperses into wave packets.

Eastward-moving modons are stable to bottom friction in the sense that they diminish in time gradually at a rate independent of the signs of the vortices. Westward-moving modons behave differently depending on the strength of bottom friction. Cyclones decay faster than anticyclones, triggering the tilt instability in westward-moving modons, but only if the bottom friction is very weak. For sufficiently strong bottom friction, in contrast, modons decay monotonically: the cyclones still decay faster than anticyclones, but no wave packets formed before the modons completely dissipate.

Westward-moving modons are always unstable to topographic forcing. Eastward-moving modons have varying behavior controlled by the height and width of the topography. Below a critical height, determined by the width, modons survive the topographic interaction: their trajectory meanders but the two contrarotating vortices always remain bound together after escaping the topography. Above the critical height, modons disassociate: the two vortices separate and disperse into wave packets. When the width of the topography is comparable to modon width, there exists a stable window within the unstable region of the topographic height in which the modons also survive the topographic encounter.

Corresponding author address: Dr. Benkui Tan, Laboratory for Severe Storm Research, Department of Atmospheric Sciences, Peking University, Beijing 100871, China. Email: bktan@pku.edu.cn

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