Ekman Dissipation of a Barotropic Modon

Swaters, Gordon E.; Flierl, Glenn R.

doi:10.1016/s0422-9894(08)70183-1

Cited by 6 publications

(4 citation statements)

References 27 publications

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“…The stability of eastward LRDs has been a subject of discussion in many studies [18][19][20], but most recently [23] employed a breeding method [30] in a high-resolution numerical model (equipped with the CABARET advection scheme), which resulted in the extraction of a growing A-component (a so-called critical D-mode) that was associated with the spontaneous symmetry breaking of the LRD. The breeding methodology involves the following steps:…”

Section: D-mode Instabilitymentioning

confidence: 99%

Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles

Davies,

Berloff,

Shevchenko

et al. 2023

Preprint

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Section: D-mode Instabilitymentioning

confidence: 99%

Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles

Davies,

Berloff,

Shevchenko

et al. 2023

Preprint

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“…As a result of this research over the past two decades, multipole solutions with potential vorticity distributions that are at least piecewise continuous have come to be known commonly as "modons." Moreover, there has been considerable activity in applying modon theory to a variety of geophysical scale phenomena (e.g., Swaters 1986Swaters , 1994aSwaters and Flierl 1989;Neven, 1993). The rotating barotropic analog to rectilinear multipolar modons was discovered by Mied et al (1992), hereafter MKL.…”

Section: Introductionmentioning

confidence: 99%

Rotating modons over isolated topography in a two-layer ocean

Kirwan

Mied

Lipphardt

1997

Z. angew. Math. Phys.

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The nonlinear quasigeostrophic equations for two layers with finite scale topography in the lower layer are reduced to steady form by focusing on solutions that rotate at a constant rate and also decay monotonically outside the topography. The solutions, here called rotating baroclinic modons, are a composition of one radially dependent azimuthal component and a basic axisymmetric component. Smoothness conditions (global continuity of the streamfunction and its first derivatives), when applied to the azimuthal mode, result in a complicated eigenvalue problem. The consequence of this is a single azimuthal mode with arbitrary amplitude. When applied to the axisymmetric solution component, the smoothness conditions allow for a vortex of arbitrary amplitude, a rider, in each layer. These riders determine the rotation rate, which may be cyclonic or anticyclonic, as well as other modon parameters. Two special cases of the theory are discussed and numerical examples of the general solutions are given. The solutions exhibit a rich variety of behavior with a countable infinity of exact solution multipoles. The paper concludes with a comparison of the properties of rotating and rectilinear baroclinic modons and some speculations on applications of the theory.Mathematics Subject Classification (1991). 76C99 (Incompressible inviscid fluids, vorticity flows).

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“…Several researchers have 52 N. ROBB McDONALD studied non-conservative effects using quasigeostrophic theory. For example, Swaters and Flierl (1989) and Swaters (1989) considered the decay of barotropic and equivalent barotropic modons subject to Ekman friction. Similarly McDonald and Clarke (1995) studied the decay of a barotropic modon subject to mixing.…”

Section: Introductionmentioning

confidence: 99%

Topographic wave radiation and modon decay

McDonald

1996

Geophysical & Astrophysical Fluid Dynamics

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The effect of topographic wave radiation on isolated eddies is modelled by an f-plane modon propagating parallel to an infinitely long escarpment. It is assumed that the lengthscale of the modon is much smaller than the lengthscale on which the topographic waves evolve. This enables the linearised equations of motion to be solved and the asymptotic (far-field, large-time) bchaviour of the topographic wave field is subsequently described. A steady wave-like response is found when the modon moves within the range of possible topographic wave phase speeds. An anomalous case exists when the modon speed is the same as the long topographic wave group speed. This implies that energy cannot escape from the vicinity of the modon and consequently the response eventually becomes nonlinear. It is shown that the appropriate equation to describe the evolution of topographic waves in this case is a forced KdV equation.In the cases of the steady linear response and the nonlinear response (for positive forcing), the energy flux carried by the topographic waves is calculated. Conservation of energy and Lagrangian conservation of vorticity extrema, along with a slowly varying assumption concerning the evolution of the modon, are used to show that the radius and speed of the modon decrease exponentially. The e-folding time associated with the decay is shown to be of possible significance when compared to typical ocean eddy lifetimes.

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Ekman Dissipation of a Barotropic Modon

Cited by 6 publications

References 27 publications

Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles

Linear Instability and Weakly Nonlinear Effects in Eastward Dipoles

Rotating modons over isolated topography in a two-layer ocean

Topographic wave radiation and modon decay

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