The quasi-geostrophic ellipsoidal vortex model

Dritschel, David G.; Reinaud, Jean Noel; McKiver, William J.

doi:10.1017/s0022112004008377

Cited by 42 publications

(53 citation statements)

References 22 publications

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“…These solutions are obtained from the limiting forms of three-dimensional ellipsoidal volumes of uniform potential vorticity (cf. Dritschel, Reinaud and McKiver (2004)) for which the vertical axis length is shrunk to zero. By infinitely stretching one of the axes of the ellipse, one obtains a filament of buoyancy which exhibits the same structure for the internal velocity distribution, namely a linear dependence on the cross-filament coordinate.…”

Section: Stability Of the Surface Buoyancy Filamentmentioning

confidence: 99%

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

Reinaud

Dritschel

Carton

2016

Geophysical & Astrophysical Fluid Dynamics

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This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective 'self'-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs -termed "cooperative" and "adverse" shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.

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Section: Stability Of the Surface Buoyancy Filamentmentioning

confidence: 99%

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

Reinaud

Dritschel

Carton

2016

Geophysical & Astrophysical Fluid Dynamics

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“…This question was answered in the affirmative by Meacham Meacham (1992) and by Zhmur and Shchepetkin (1991) who discovered a class of three dimensional solutions to the QG equations in which the PV takes a uniform value inside an ellipsoidal domain. The discovery of these exact single-ellipsoid solutions originated a large literature concerned with using these solutions to study two or more interacting vortices (see Miyazaki et al 2001, Dritschel et al 2004, McKiver 2015. A particularly important research topic has been to determine the conditions under which ellipsoidal vortices can merge, as discussed in Reinaud and Dritschel (2005).…”

Section: Introductionmentioning

confidence: 99%

“…In addition to deriving the truncated moment model, we also adapt the Hamiltonian ELlipsoidal Model (HELM) originated by Dritschel et al (2004) to the evolution of QG ellipsoidal vortices of vanishing vertical thickness, i.e. to elliptical lenses.…”

Section: Introductionmentioning

confidence: 99%

Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability

Bersanelli

Dritschel

Lancellotti

et al. 2016

Geophysical & Astrophysical Fluid Dynamics

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We study pairwise interactions of elliptical quasi-geostrophic (QG) vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical "lenses" inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting nonelliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full QG dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f ), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions. ARTICLE HISTORY

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“…for vortical interactions has recently been extended to a three-dimensional ellipsoidal model (Dritschel, Reinaud & McKiver 2004). …”

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An elliptical-pore model for late-stage planar viscous sintering

Crowdy

2004

J. Fluid Mech.

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A simple 'elliptical-pore model' of the shrinkage of compressible pores in late-stage planar viscous sintering is proposed. The model is in the spirit of matched asymptotics and relies on splitting the flow into an 'inner' and 'outer' problem. The inner problem in the vicinity of any given pore involves solving for its free-surface evolution exactly using complex-variable methods. The outer flow due to all other pores is assumed to be given by an assembly of point sinks/sources. As a test of the model, the evolution of a singly infinite periodic row of compressible pores is considered in detail. The effectiveness of the simple model is tested by comparison with a full numerical simulation. A novel boundary integral method based on Cauchy potentials and conformal mapping is used. In the case of pores with constant pressure, it is found that pores shrink faster than if in isolation. Compressible pores obeying the ideal gas law are also studied and are found to tend to a quasi-steady non-circular state. A higher-order model is also presented and compared with numerical simulations of the viscous sintering of a doubly periodic array of pores in Stokes flow.

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The quasi-geostrophic ellipsoidal vortex model

Cited by 42 publications

References 22 publications

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability

An elliptical-pore model for late-stage planar viscous sintering

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