High order accurate vortex methods with explicit velocity kernels

Beale, J. Thomas; Majda, Andrew J.

doi:10.1016/0021-9991(85)90176-7

Cited by 245 publications

(153 citation statements)

References 8 publications

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“…Thus ␦ can be seen as the scale beyond which fluctuations are locally averaged, see Soteriou and Ghoniem, 16 Lundgren et al 20 The cutoff functions used in this study have been proposed by Beale and Majda. 21 They rely on Gaussian functions and lead to a second-order accuracy for the velocity field, hereafter referred to as K2, or a fourth-order one, K4:…”

Section: Formulation and Numerical Schemesmentioning

confidence: 99%

The baroclinic secondary instability of the two-dimensional shear layer

2000

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The focus of this study is on the numerical investigation of two-dimensional, isovolume, high Reynolds and Froude numbers, variable-density mixing layers. Lagrangian simulations, of both the temporal and the spatial models, are performed. They reveal the breaking-up of the strained vorticity and density-gradient braids, connecting two neighboring primary structures. The secondary instability arises where the vorticity has been intensified by the baroclinic torque. A simplified model of the braid of the variable-density mixing layer, consisting of a strained vorticity and density-gradient filament, is analyzed. It is concluded that the physical mechanism responsible for the secondary instability is the forcing of the vorticity field by the baroclinic torque, itself sensitive to perturbations. This mechanism suggests a rapid route to turbulence for the variable-density mixing layer.

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Section: Formulation and Numerical Schemesmentioning

confidence: 99%

The baroclinic secondary instability of the two-dimensional shear layer

2000

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“…an element that will have no intrinsic spatial scale). Rather, the field of a point dipole (16) is to be desingularized through convolution with a Beale and Majda (1985) fourthorder smoothing kernel…”

Section: "Dipole Creation" In Three Dimensionsmentioning

confidence: 99%

Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories

Summers

2002

Nonlin. Processes Geophys.

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Abstract. An impulse-based model is developed to represent a coupling between turbulent flow in the atmosphere and turbulent flow in the ocean. In particular, it is argued that the atmosphere flowing horizontally over the ocean surface generates a velocity fluctuation field in the latter's near-surface flow. The mechanism for this can be understood kinematically in terms of an exchange of tangentially-oriented fluid impulse at the air-sea interface. We represent this exchange numerically through the creation of Lagrangian elements of impulse density. An indication of the efficacy of such a model would lie in its ability to predict the observed fractal dimension of lateral trajectories of submerged floats set adrift in the ocean. To this end, we examine the geometry of lateral tracer-paths determined from the present model.

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“…The standard thin-tube method 17 is a simplified version of general vortex element method 20 for three-dimensional incompressible flows. In the thin-tube model, a slender vortex is represented by a single chain of overlapping vortex elements.…”

Section: ͑17͒mentioning

confidence: 99%

“…The smoothing function f (x) is chosen so as to enhance accuracy. 20 The velocity at a point x can be obtained by inserting ͑19͒ into ͑5͒ and performing the integration. The result is the following desingularized version of the BiotSavart law:…”

Section: ͑17͒mentioning

confidence: 99%

On the motion of slender vortex filaments

Zhou

1997

Physics of Fluids

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Several approaches for slender vortex motion ͑the local induction equation, the Klein-Majda equation, and the Klein-Knio equation͒ are compared on a specific example of sideband instability of Kelvin waves on a vortex. Numerical experiments on this model problem indicate that all these equations yield qualitatively similar behavior, and this behavior is different from the behavior of a nonslender vortex with variable cross-section. It is found that the boundaries between stable, recurrent, and chaotic regimes in the parameter space of the model problem depend on the equation used. The boundaries of these domains in the parameter space for the Klein-Majda equation and for the Klein-Knio equation are closely related to the core size. When the core size is large enough, the Klein-Majda equation always exhibits stable solutions for our model problem. Various conclusions are drawn; in particular, the behavior of turbulent vortices cannot be captured by these approximations, and probably cannot be captured by any slender vortex model with constant vortex cross-section. Speculations about the differences between classical and superfluid hydrodynamics are also offered.

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High order accurate vortex methods with explicit velocity kernels

Cited by 245 publications

References 8 publications

The baroclinic secondary instability of the two-dimensional shear layer

The baroclinic secondary instability of the two-dimensional shear layer

Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories

On the motion of slender vortex filaments

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