Applied mathematics, nonlinear waves, free surface wave, integrable systems, spectral methods, mathematical physics, scientific computing, mathematical biology, potenial theory
312 Mathematics Building
UB North Campus
Buffalo NY, 14260-2900
Phone: (716) 645-8797
BS in Applied Physics and Mathematics, Moscow Institute of Physics and Technology (MIPT)
PhD in Applied Mathematics, University of New Mexico
My primary research interests lie in singularity formation in dynamical systems described by nonlinear PDEs,with particularapplications in fluid, biology and optics. Water waves and singularities that appear on freesurface of water in the form of angle formation, or self–intersection (for instance in a whitecapping event) are in my field of study.
Ocean waves are exciting from various aspects: the statistical description of wave turbulence in the ocean, the emergence of direct and inverse cascade, and the limits of applicability of the weak wave turbulence theory to name a few. A spectacular problem that stands at the crossroad of singularity formation, and statistical description of the ocean waves is the emergence of whitecaps at the crests of steep ocean waves. Such events are rare, yet of great importance for two reasons: they are the examples of singularity formation and they shed light into the mechanism of energy and momentum dissipation in the ocean. Given an isolated whitecap, one can measure the amount of momentum/energy that is transferred to the capillary scale, and the amount of vorticity introduced into the fluid. If a theory describing formation of a single whitecap was developed, it could then be employed in large scale statistical models of ocean wave turbulence and then used to model interaction with atmosphere and climate modelling.