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Benkui Tan

Abstract

A theory is developed here to describe the propagation of nonlinear Rossby wave packets in a barotropic atmospheric model and their interactions by using the multiple-scale method. It is shown that the propagation of a single Rossby wave packet can be described by the nonlinear Schrödinger equation that has envelope soliton solutions. For two interacting packets with slightly different wavenumbers they satisfy a set of two coupled nonlinear Schrödinger equations. These equations are used to study the collision interactions of two envelope Rossby solitons. It is found that despite the complexity of the interaction, the energy of each soliton is conserved, while the shapes and velocities of the two solitons may be altered significantly by the interaction. The action of one soliton on another is realized by providing a field of force or potential for it through the cross-modulation terms.

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Benkui Tan

Abstract

In this paper, the classic Ekman pumping formulas for the vertical flow out of a boundary layer are generalized for both the layer above a rigid surface of variable slope and also for the boundary layer underneath a moving free surface. The assumptions that the density is constant and the geostrophic velocity does not vary with height in the boundary layer are relaxed without compromising the simplicity of the final approximation. Similarly, it proves to be unnecessary to assume a specific eddy viscosity law.

The pumping formulas obtained here are compared with the old ones and significant differences are found.

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Benkui Tan and Shikuo Liu

Abstract

In this paper the interactions between two marginally unstable baroclinic wave packets in the two-layer Phillips model are investigated by using the multiple-scale method. It is shown that the interactions can be described by a set of two coupled nonlinear Schrödinger equations. Except for two special cases the equations have only four invariants of motion and cannot be solved by the inverse scattering method.

The equations are solved numerically to study the collision interactions between two solitons. It is found that though the coefficients in the equations are fixed, the behavior of the two solitons may be quite different, which is closely related to the initial states of the two solitons (the speeds and the amplitudes of the solitons well before the interactions). For some initial conditions the collision interactions may be soliton-like in that the properties of the two solitons change very little, while for other initial conditions some “inelastic” phenomena are observed: one soliton may be destroyed by the other, or two solitons may change their speeds and directions of propagation and fuse into a new bound state.

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Benkui Tan and John P. Boyd

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.

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Y. Qiang Sun, Yuxin Jiang, Benkui Tan, and Fuqing Zhang

Abstract

Through successful convection-permitting simulations of Typhoon Sinlaku (2008) using a high-resolution nonhydrostatic model, this study examines the role of peripheral convection in the storm's secondary eyewall formation (SEF) and its eyewall replacement cycle (ERC). The study demonstrates that before SEF the simulated storm intensifies via an expansion of the tangential winds and an increase in the boundary layer inflow, which are accompanied by peripheral convective cells outside the primary eyewall. These convective cells, which initially formed in the outer rainbands under favorable environmental conditions and move in an inward spiral, play a crucial role in the formation of the secondary eyewall. It is hypothesized that SEF and ERC ultimately arise from the convective heating released from the inward-moving rainbands, the balanced response in the transverse circulation, and the unbalanced dynamics in the atmospheric boundary layer, along with the positive feedback between these processes.

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