Self-consistent dynamics in the single wave model

This study explores the dynamics of an unstable jet of two-dimensional, incompressible fluid on the beta-plane. In the inviscid limit, standard weakly nonlinear theory fails to give a low-order description of this problem, partly because the simple shape of the unstable normal mode is insufficient to capture the structure of the forming pattern. That pattern takes the form of ‘cat's eyes’ in the vorticity distribution which develop inside the modal critical layers (slender regions to either side of the jet's axis surrounding the levels where the modal wave speed matches the mean flow). Asymptotic expansions furnish a reduced model which is a version of what is known as the single-wave model in plasma physics. The reduced model predicts that the amplitude of the unstable mode saturates at a relatively low level and is not steady. Rather, the amplitude evolves aperiodically about the saturation level, a result with implications for Lagrangian transport theories. The aperiodic amplitude ‘bounces’ are intimately connected with sporadic deformations of the vortices within the cat's eyes. The theory is compared with numerical simulations of the original governing equations. Slightly asymmetrical jets are also studied. In this case the neutral modes along the stability boundary become singular; an extension of the weakly nonlinear theory is presented for these modes.

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Chaotic mixing and transport in Rossby-wave critical layers

Journal of Fluid Mechanics ◽

10.1017/s0022112096004363 ◽

1997 ◽

Vol 334 ◽

pp. 315-351 ◽

Cited By ~ 44

Author(s):

KEITH NGAN ◽

THEODORE G. SHEPHERD

Keyword(s):

Rossby Wave ◽

Phase Speed ◽

Wave Model ◽

Chaotic Advection ◽

Transient Wave ◽

Single Wave ◽

Rossby Wave Breaking ◽

Lobe Dynamics ◽

Critical Layers ◽

Mixing And Transport

A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave.Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.

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Energy Transport in a Rotation-Modulated Pulsar Wind

International Astronomical Union Colloquium ◽

10.1017/s0252921100042007 ◽

1996 ◽

Vol 160 ◽

pp. 421-424 ◽

Cited By ~ 3

Author(s):

A. Melatos ◽

D. B. Melrose

Keyword(s):

Energy Transport ◽

Wave Model ◽

Termination Shock ◽

Displacement Current ◽

Nonlinear Plasma ◽

Poynting Flux ◽

Self Consistent ◽

Radiation Zone ◽

Pulsar Wind ◽

Nonlinear Plasma Wave

AbstractThe structure and energetics of a rotation-modulated pulsar wind are examined. It is shown that the displacement current in the wind asymptotically dominates the conduction current, creating an outer radiation zone whose inner boundary lies well inside the wind termination shock. A self-consistent nonlinear-plasma-wave model of the radiation zone predicts that the ratio of Poynting flux to kinetic-energy flux at the termination shock is small (~ 10−3for the Crab), in agreement with independent observational estimates.

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