ALEXANDER M BALK portrait
  • Professor, Mathematics

Publications

  • Alexander M. Balk (2019). Poloidal flow generation in the dynamics of Rossby waves. Phys. Rev. Research. Vol. 1, 033180. Published, 12/2019.
    https://journals.aps.org/prresearch/pdf/10.1103/Ph...
  • A. M. Balk (2018). Mode generation via interaction. Phys. Rev. E. Vol. 98, 062208-(1:5). Published, 12/11/2018.
    https://journals.aps.org/pre/pdf/10.1103/PhysRevE....
  • A. M. Balk (2017). Rossby wave extra invariant in the Galerkin approximation. Physics Letters A. Vol. 381, 2510-2513. Published, 06/2017.
    http://dx.doi.org/10.1016/j.physleta.2017.05.047
  • A. M. Balk, An extra invariant for the system of four wave packets in one spatial dimension, Wave Motion 61 (2016) 11-19. Published, 01/04/2016.
  • A. M. Balk, Large-scale quasi-geostrophic magnetohydrodynamics, ApJ (Astrophysical Journal) 796 (2014) 143 (8pp). Published, 12/15/2014.
  • A. M. Balk, The Rossby wave extra invariant in 3D fluid dynamics and the generation of zonal jets, Nonlin. Processes Geophys. 21 (2014) 49-59. Published, 01/10/2014.
  • A. M. Balk, Extra Invariant: From Shallow Water to 3-dimensional oceans, Abstract. American Mathematical Society (Tucson, AZ). Published, 10/2012.
  • A. M. Balk, F. van Herden, P. B. Weichman, T. Yoshikawa, The Extra Invariant for Rossby Waves and the Emergence of Zonal Jets, Abstract. 2-nd International Workshop ``Nonlinear Processes in Oceanic and Atmospoheric Flows'', Institute for the Mathematical Sciences (Madrid, Spain). Published, 07/2012.
  • A. M. Balk, Adiabatic invariants for the dynamics of rotating three-dimensional fluid, Preprint arXiv:1206.1018. Published, 06/2012.
  • A. M. Balk and P. B. Weichman, Anisotropic inverse cascade toward zonal flow in magnetically confined plasmas, Preprint arXiv:1106.2746 (2011). Published, 06/2011.
  • A. M. Balk, F. van Heerden, and P. B. Weichman, Rotating Shallow Water Dynamics: Extra Invariant and the Formation of Zonal Jets, Phys. Rev. E 83, 046320-(1-12). Published, 04/2011.
  • A. M. Balk and V. E. Zakharov, Cascade generation of zonal flows by the drift wave turbulence, Phys. Lett. A 373, 4049-4052. Published, 08/2009.
  • A. M. Balk and T. Yoshikawa, The Rossby Wave Extra Invariant in the Physical Space, Physica D: Nonlinear Phenomena 238, 384-394. Published, 03/2009.
  • A. M. Balk and F. van Heerden, Conservation style of the extra invariant for Rossby waves, Physica D: Nonlinear Phenomena 223, 109-120. Published, 10/2006.
  • A. M. Balk, Wave turbulent diffusion due to the Doppler shift , Journal of Statistical Mechanics: Theory and experiment P08018 (2006) 1-13. Published, 08/2006.
  • A. M. Balk, Angular distribution of Rossby wave energy, Phys. Lett. A 345 (2005) 154-160. Published, 07/2005.

Research Statement

My main research interest at the present is in the Rossby waves. These are the waves that represent huge vortices in the ocean and atmosphere, due to the the earth's rotation. People encounter the same kind of waves (from the mathematical viewpoint) in the nuclear fusion, when they try to confine hot plasma by a strong magnetic field. We have found that the nonlinear dynamics of Rossby waves has an unexpected extra invariant (in addition to the energy and momentum). It was proved that this invariant is unique. Recently, we have found that this invariant implies that the energy organizes itself, transfering from small scale eddies to large scale zonal jets (along the parallels). This is a widely observed phenomenon on Earth and other planets (in particular, on Jupiter and Saturn). My other long-standing research interest is in Turbulence. Particularly, I am concerned with the Wave Turbulence. Examples are the rough sea (due to the water waves), the climate (due to the Rossby waves) or optical turbulence (due to the electromagnetic waves). Recently I have developed the statistical near identity transformation (SNIT) to derive the averaged equations of wave turbulence.

Research Keywords

  • Waves, Nonlinear, Turbulence, Rossby waves, Drift waves, Dynamo

Presentations

  • American Mathematical Society, Western Section, Tucson, Arizona. Contributed Talk, Presented, 10/2012.
  • 2-nd International Workshop: Nonlinear processes in oceanic and atmospheric flows, Institute for the Mathematical Sciences (Madrid, Spain). Contributed Talk, Presented, 07/2012.
  • Aspen Center for Physics (Aspen, CO), Research Program "Stochastic Flows and Climate Modeling". Contributed Talk, Presented, 06/2012.
  • Woods Hole Oceanographic Institution (Woods Hole, Massachusetts); Program on Geophysical Fluid Dynamics: ``Shear Turbulence: Onset and Structure''. Invited Talk/Keynote, Presented, 07/18/2011.
  • American Mathematical Society Sectional Meeting, Special Session "Turbulence, Singularities, and Nonlinear Waves in Fluid Dynamics, Optics, and Plasmas". Contributed Talk, Presented, 10/23/2021.
    http://www.ams.org/amsmtgs/2283_abstracts/1172-85-...

Languages

  • Russian, fluent.