A contour-advective semi-Lagrangian numerical algorithm for the problem of interaction between a vortex and an isolated topographic feature on a ?-plane

Authors

  • A.A. Baranov Far Eastern Federal University (FEFU)
  • M.S. Permyakov Far Eastern Federal University (FEFU)

Keywords:

geophysical fluid dynamics, contour dynamics, contour advection, topography, β-plane, potential vorticity

Abstract

The main stages of a contour-advective semi-Lagrangian algorithm for the simulation of inviscid incompressible flows with variable depth on the rotating Earth are considered. The numerical results for the case when a vortex encounters an axisymmetric topographic feature on a β-plane are discussed. The accuracy of the method for different values of the its parameters is numerically estimated. The contour-advective method is compared with the finite-difference method. It is shown that the contour-advective semi-Lagrangian algorithm is very efficient to represent a fine-scale structures of potential vorticity fields.

Author Biographies

A.A. Baranov

M.S. Permyakov

References

  1. Dritschel D.G., Ambaum M.H. P. A contour-advective semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields // Quarterly Journal of the Royal Meteorological Society. 1997. 123, N 540. 1097-1130.
  2. Dritschel D.G., Polvani L.M., Mohebalhojeh A.R. The contour-advective semi-Lagrangian algorithm for the shallow water equations // Monthly Weather Review. 1999. 127, N 7. 1151-1165.
  3. Mohebalhojeh A.R., Dritschel D.G. The diabatic contour-advective semi-Lagrangian algorithms for the spherical shallow water equations // Monthly Weather Review. 2009. 137, N 9. 2979-2994.
  4. Fontane J., Dritschel D.G. The HyperCASL algorithm: a new approach to the numerical simulation of geophysical flows // Journal of Computational Physics. 2009. 228, N 17. 6411-6425.
  5. Dritschel D.G. Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows // Computer Physics Reports. 1989. 10, N 3. 77-146.
  6. Козлов В.Ф. Геофизическая гидродинамика вихревых пятен // Морской гидрофизический журнал. 1994. № 1. 26-35.
  7. Соколовский М.А., Веррон Ж. Динамика вихревых структур в стратифицированной вращающейся жидкости. М.; Ижевск: Ижевский институт компьютерных исследований, 2011.
  8. O’Farrell C., Dabiri J.O. Nested contour dynamics models for axisymmetric vortex rings and vortex wakes // Journal of Fluid Mechanics. 2014. 748. 521-548.
  9. Баранов А.А., Пермяков М.С. Анализ точности и вычислительной эффективности метода адвекции контуров на примере решения баротропного уравнения вихря // Вычислительные методы и программирование. 2014. 15. 337-350.
  10. Geffen J.H. G.M. van, Davies P.A. A monopolar vortex encounters an isolated topographic feature on a eta-plane // Dynamics of Atmospheres and Oceans. 2000. 32, N 1. 1-26.
  11. Zavala Sans’on L., González-Villanueva A., Flores L.M. Evolution and decay of a rotating flow over random topography // Journal of Fluid Mechanics. 2010. 642. 159-180.
  12. Макаров В.Г. Вычислительный алгоритм метода контурной динамики с изменяемой топологией исследуемых областей // Моделирование в механике. 1991. 5, № 4. 83-95.
  13. Баранов А.А., Пермяков М.С. Ускоренный алгоритм изменения топологии для метода адвекции контуров // Вычислительные методы и программирование. 2013. 14. 75-87.
  14. Эйджел Э. Интерактивная компьютерная графика. Вводный курс на базе OpenGL. М.: Вильямс, 2001.
  15. Schaerf T.M., Macaskill C. On contour crossings in contour-advective simulations. Part 1. Algorithm for detection and quantification // Journal of Computational Physics. 2012. 231, N 2. 465-480.
  16. Schaerf T.M., Macaskill C. On contour crossings in contour-advective simulations. Part 2. Analysis of crossing errors and methods for their prevention // Journal of Computational Physics. 2012. 231, N 2. 481-504.
  17. Мезингер Ф., Аракава А. Численные методы, используемые в атмосферных моделях. Л.: Гидрометеоиздат, 1982.

Published

2014-11-09

How to Cite

Баранов А.А., Пермяков М.С. A Contour-Advective Semi-Lagrangian Numerical Algorithm for the Problem of Interaction Between a Vortex and an Isolated Topographic Feature on a ?-Plane // Numerical methods and programming. 2014. 15. 621-630

Issue

Section

Section 1. Numerical methods and applications