Vortex solutions for thermohaline circulation equations. (English) Zbl 1538.76070
Summary: 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.
References:
| [1] | [1] M.A Abolfathi, “On the stability of 2-dimensional Pexider quadratic functional equation in non-Archimedean spaces”, Journal of Mahani Mathematical Research, (2022), 11(2),31-34. · Zbl 1513.39064 |
| [2] | [2] HM. Srivastava, and M. Izadi. “The Rothe-Newton approach to simulate the variable coecient convection-di usion equations.” Journal of Mahani Mathematical Research Center, (2022), 11(2), 141-157. · Zbl 1513.65334 |
| [3] | [3] M. Vanday Baseri, and H. Fatemidokht. “Survey of di erent techniques for detecting sel sh nodes in MANETs.” Journal of Mahani Mathematical Research Center, (2022), 11(2), 45-59. |
| [4] | [4] Md. Nur Alam, C. Tunc, New solitary wave structures to the (2+1)-dimensional KD and KP equations with spatio-temporal dispersion. Journal of King Saud University-Science. 32 (2020), 3400-3409. |
| [5] | [5] Md. Nur Alam, C. Tunc, The new solitary wave structures for the (2+1)-dimensional time-fractional Schrodinger equation and the space-time nonlinear conformable fractional Bogoyavlenskii equations. Alexandria Engineering Journal, 59 (2020), 2221-2232. |
| [6] | [6] T. Gallay, C. E. Wayne, Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R2, Arch. Ration. Mech. Anal., 163, (2012),209{258.} · Zbl 1042.37058 |
| [7] | [7] H. V. Helmholtz, Uber Integrale der hydrodynamischen Gleichungen, Journal fur die reine und angewandte Mathematik, 55, (1858), 25{55.} · ERAM 055.1448cj |
| [8] | [8] T. Hou, C. Li, Global well-posedness of the viscous Boussinesq equations, Discrete and Cont. Dyn. Syst, 12, (2005), 1{12. [9] M. kamandar, B. Raesi, Point Vortex Dynamics for the 2D Boussinesq Equations Over the Tropics, Iranian Journal of Science and Technology, Transactions A: Science (2022), 1-10.} · Zbl 1274.76185 |
| [9] | [10] L. Kelvin, On vortex motion, Trans. R. Soc. Edimb 25, (2000), 217-60. · JFM 01.0341.02 |
| [10] | [11] H. Lamb, Hydrodynamics, Cambridge Univ Press, Cambridge, 2002. · JFM 26.0868.02 |
| [11] | [12] T. Ma, Sh. wang, Phase Transition Dynamics, Springer, 2014. · Zbl 1285.82004 |
| [12] | [13] L. M. Milne-Thomson, Theoretical hydrodynamics, Dover Publications, 1998. · JFM 64.0848.12 |
| [13] | [14] R. J. Nagem, G. Sandri, D. Uminsky, C. E. Wayne, Generalized Helmholtz{Kirchho model for two-dimensional distributed vortex motion, SIAM Journal on Applied Dynamical Systems, 8, (2019), 160{179.}} · Zbl 1408.76205 |
| [14] | [15] P. K. Newton,The N-Vortex Problem: Analytical Techniques, Springer-Verlag, 2019. |
| [15] | [16] S. Ozer, T. Sengul, Transitions of Spherical Thermohaline Circulation to Multiple Equilibria, Journal of Mathematical Fluid Mechanics, 20, (2018), 499-515. · Zbl 1458.76046 |
| [16] | [17] L. Prandtl, Essentials of fluid dynamics, Hafner Pub. Co., 2004. |
| [17] | [18] M. Shari , B. Raesi, Vortex Theory for Two Dimensional Boussinesq Equations, Applied Mathematics and Nonlinear Sciences 5, 2, (2020), 67-84. · Zbl 1524.76162 |
| [18] | [19] S. G. L. Smith, R. J. Nagem, Vortex pairs and dipoles, Regular and Chaotic Dynamics, 18, (2013), 194-201. · Zbl 1273.76070 |
| [19] | [20] D. Uminsky, C. E. Wayne, A. Barbaro, A multi-moment vortex method for 2D viscous uids, Journal of Computational Physics, 231, (2012), 1705{1727.} · Zbl 1408.76210 |
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