Vortex Solutions for Thermohaline circulation Equations

Document Type : Research Paper

Author

Department of Mathematics, Shahed University, Tehran, Iran.

Abstract

The main objective of this article is to establish a new model and find some vortex axisymmetric solutions of finite core size for this model. We introduce the hydrodynamical equations governing the atmospheric circulation over the tropics, the Boussinesq equation with constant radial gravitational acceleration. Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them. These equations are critically important in mathematics. They are similar to the 3D Navier-Stokes and the Euler equations. The 2D Boussinesq  equations preserve some important aspects of the 3D Euler and Navier-Stokes equations such as the vortex stretching mechanism. The inviscid 2D Boussinesq equations are known as the Euler equations for the 3D axisymmetric swirling flows.This model is the most frequently used for buoyancy-driven fluids, such as many largescale geophysical flows, atmospheric fronts, ocean circulation, clued dynamics. In addition, they play an important role in the Rayleigh-Benard convection.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 12, Issue 1 - Serial Number 24
January 2023
Pages 197-211

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History

  • Receive Date: 06 March 2022
  • Revise Date: 10 July 2022
  • Accept Date: 11 July 2022

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