| Peer-Reviewed

Winds Generated by Flows and Riemannian Metrics

Received: 22 December 2016     Accepted: 9 January 2017     Published: 24 January 2017
Views:       Downloads:
Abstract

The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models.

Published in American Journal of Science, Engineering and Technology (Volume 2, Issue 1)
DOI 10.11648/j.ajset.20170201.13
Page(s) 15-19
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Flow, Metric, Geometric Dynamics, Wind, Stability

References
[1] R. Aris, Vectors, Tensors and the Basic Equations of Fluid Flow, Dover Publ. Inc., New York, 1989.
[2] V. I. Arnold, The Hamiltonian nature of the Euler equations of rigid body dynamics and of ideal fluid, Uspehi Matem. Nauk., XXIV, 3, 147, pp. 225-246, 1969.
[3] A. J. Chorin, J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 2000.
[4] S. Comsa, G. Cosovici, M. Craciun, J. Cringanu, N. Dumitriu, P. Matei, I. Rosca, O. Stanasila, A. Toma, C. Udriste (coordinator), Variational Calculus (in romanian), StudIS Publishing House, Iasi, 2013.
[5] D. Isvoranu, C. Udriste, Fluid flow versus Geometric Dynamics, BSG Proceedings, 13, pp. 70-82, 2006.
[6] G. Schubert, C. C. Counselman, J. Hansen, S. S. Limaye, G. Pettengill, A. Seiff, I. I. Shapiro, V. E. Suomi, F. Taylor, L. Travis, R. Woo, R.E. Young, Dynamics, winds, circulation and turbulence in the atmosphere of venus, Space Science Reviews, 20, 4, pp. 357-387, 1977.
[7] S. Treanta, On multi-time Hamilton-Jacobi theory via second order Lagrangians, U. P. B. Sci. Bull., Series A: Appl. Math. Phys., 76, 3, pp. 129-140, 2014.
[8] C. Udriste, Geometric Dynamics, Mathematics and Its Applications, 513, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000.
[9] C. Udriste, Geodesic motion in a gyroscopic field of forces, Tensor, N. S., 66, 3, pp. 215-228, 2005.
[10] C. Udriste, A. Udriste, From flows and metrics to dynamics and winds, Bull. Cal. Math. Soc., 98, 5, pp. 389-394, 2006.
Cite This Article
  • APA Style

    Savin Treanţă, Elena-Laura Dudaş. (2017). Winds Generated by Flows and Riemannian Metrics. American Journal of Science, Engineering and Technology, 2(1), 15-19. https://doi.org/10.11648/j.ajset.20170201.13

    Copy | Download

    ACS Style

    Savin Treanţă; Elena-Laura Dudaş. Winds Generated by Flows and Riemannian Metrics. Am. J. Sci. Eng. Technol. 2017, 2(1), 15-19. doi: 10.11648/j.ajset.20170201.13

    Copy | Download

    AMA Style

    Savin Treanţă, Elena-Laura Dudaş. Winds Generated by Flows and Riemannian Metrics. Am J Sci Eng Technol. 2017;2(1):15-19. doi: 10.11648/j.ajset.20170201.13

    Copy | Download

  • @article{10.11648/j.ajset.20170201.13,
      author = {Savin Treanţă and Elena-Laura Dudaş},
      title = {Winds Generated by Flows and Riemannian Metrics},
      journal = {American Journal of Science, Engineering and Technology},
      volume = {2},
      number = {1},
      pages = {15-19},
      doi = {10.11648/j.ajset.20170201.13},
      url = {https://doi.org/10.11648/j.ajset.20170201.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajset.20170201.13},
      abstract = {The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models.},
     year = {2017}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Winds Generated by Flows and Riemannian Metrics
    AU  - Savin Treanţă
    AU  - Elena-Laura Dudaş
    Y1  - 2017/01/24
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajset.20170201.13
    DO  - 10.11648/j.ajset.20170201.13
    T2  - American Journal of Science, Engineering and Technology
    JF  - American Journal of Science, Engineering and Technology
    JO  - American Journal of Science, Engineering and Technology
    SP  - 15
    EP  - 19
    PB  - Science Publishing Group
    SN  - 2578-8353
    UR  - https://doi.org/10.11648/j.ajset.20170201.13
    AB  - The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models.
    VL  - 2
    IS  - 1
    ER  - 

    Copy | Download

Author Information
  • Sections