ALEXANDER M BALK portrait
  • Professor, Mathematics

Publications

  • A. M. Balk (date unknown). A. M. Balk, Extra Invariant: From Shallow Water to 3-dimensional oceans, Abstract. American Mathematical Society (Tucson, AZ). Accepted, .
  • A. M. Balk, (date unknown). 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). Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, Large-scale quasi-geostrophic magnetohydrodynamics, ApJ (Astrophysical Journal) 796 (2014) 143 (8pp). Accepted, .
  • A. M. Balk (date unknown). Mode generation via interaction. Phys. Rev. E. Vol. 98, 062208-(1:5). Accepted, .
  • Alexander M. Balk (date unknown). Poloidal flow generation in the dynamics of Rossby waves. Phys. Rev. Research. Vol. 1, 033180. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk and F. van Heerden, Conservation style of the extra invariant for Rossby waves, Physica D: Nonlinear Phenomena 223, 109-120. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk and V. E. Zakharov, Cascade generation of zonal flows by the drift wave turbulence, Phys. Lett. A 373, 4049-4052. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, Wave turbulent diffusion due to the Doppler shift , Journal of Statistical Mechanics: Theory and experiment P08018 (2006) 1-13. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, Angular distribution of Rossby wave energy, Phys. Lett. A 345 (2005) 154-160. Accepted, .
  • A. M. Balk (date unknown). Rossby wave extra invariant in the Galerkin approximation. Physics Letters A. Vol. 381, 2510-2513. Accepted, .
  • A. M. Balk (date unknown). 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). Accepted, .
  • A. M. Balk (date unknown). A. M. Balk and T. Yoshikawa, The Rossby Wave Extra Invariant in the Physical Space, Physica D: Nonlinear Phenomena 238, 384-394. Accepted, .
  • A. M. Balk (date unknown). 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. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, An extra invariant for the system of four wave packets in one spatial dimension, Wave Motion 61 (2016) 11-19. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, Adiabatic invariants for the dynamics of rotating three-dimensional fluid, Preprint arXiv:1206.1018. Accepted, .
  • A. M. Balk (date unknown). A. M. Balk and P. B. Weichman, Anisotropic inverse cascade toward zonal flow in magnetically confined plasmas, Preprint arXiv:1106.2746 (2011). Accepted, .
  • A. M. Balk (date unknown). A. M. Balk, Spectral anti-broadening due to four-wave mixing in optical fibers, arXiv:1502.02285 (2015). Accepted, .

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.

Presentations

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

Languages

  • Russian, Fluent.