RBF-vortex methods for the barotropic vorticity equation on a sphere

Xiao, Jianping; Wang, Lei; Boyd, John P.

doi:10.1016/j.jcp.2015.01.005

Cited by 7 publications

(3 citation statements)

References 75 publications

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“…Specifically, characteristics are traced back in time and the advected quantity is updated via interpolation. Related approaches include the Arbitrary Lagrangian-Eulerian method [23], particle-mesh methods [24,25], flux-form [26] and more recent hybrid schemes [27,28,29]. Furthermore, conservative SL schemes have been developed and successfully applied for transport on the sphere [30,31].…”

Section: Introductionmentioning

confidence: 99%

A Characteristic Mapping Method for Tracer Transport on the Sphere

Taylor¹,

Nave²

2021

Preprint

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A semi-Lagrangian method for the solution of the transport equation on a sphere is presented. The method evolves the inverse flow-map using the Characteristic Mapping (CM) [1] and Gradient-Augmented Level Set (GALS) [2] frameworks. Transport of the advected quantity is then computed by composition with the numerically approximated inverse flow-map. This framework allows for the advection of complicated sets and multiple quantities with arbitrarily fine-features using a coarse computational grid. We discuss the CM method for linear transport on the sphere and its computational implementation. Standard test cases for solid body rotation, deformational and divergent flows, and numerical mixing are presented. The unique features of the method are demonstrated by the transport of a multi-scale function and a fractal set in a complex flow environment.

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Section: Introductionmentioning

confidence: 99%

A Characteristic Mapping Method for Tracer Transport on the Sphere

Taylor¹,

Nave²

2021

Preprint

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“…They found that the strip rolls up into a chain of vortices connected by so-called, braids . Recently, Bosler et al [ 22 ] and Xiao et al [ 23 ] reported numerical results for a thin vortex strip and zonal jet on a rotating sphere by using a Lagrangian particle/panel method and the RBF-vortex method, respectively. Most of these studies considered only thin vortex strips and did not examine thoroughly the dependence of the evolution of the strip on the physical parameters.…”

Section: Introductionmentioning

confidence: 99%

“…We thus rely on the framework of the vortex contour dynamics for the nonlinear evolution. We will therefore not be using advanced numerical methods such as the spectral method [ 24 ] and the semi-Lagrangian or Lagrangian methods [ 22 , 23 , 25 , 26 ]. The vortex contour dynamics is efficient to accomplish our purpose, and provides an advantage over the spectral method because the stability of the vortex strip is described not as the growth of spectra of its global spherical harmonic representation, but rather, in terms of the local deformation of contour curves.…”

Section: Introductionmentioning

confidence: 99%

Stability of barotropic vortex strip on a rotating sphere

2018

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We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.

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Dynamics of Ideal Fluid on a Sphere

Skiba

2017

Mathematical Problems of the Dynamics of Incompressible Fluid on a Rotating Sphere

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RBF-vortex methods for the barotropic vorticity equation on a sphere

Cited by 7 publications

References 75 publications

A Characteristic Mapping Method for Tracer Transport on the Sphere

A Characteristic Mapping Method for Tracer Transport on the Sphere

Stability of barotropic vortex strip on a rotating sphere

Dynamics of Ideal Fluid on a Sphere

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