BS in Applied Physics and Mathematics, Moscow Institute of Physics and Technology (MIPT)
PhD in Applied Mathematics, University of New Mexico
My research is primarily centered on the formation of singularities in dynamical systems governed by nonlinear PDEs. These systems have applications in diverse fields such as fluids, biology, and optics. A significant aspect of my study involves water waves, particularly the singularities that manifest as angle formations or self-intersections on water surfaces, as seen in whitecapping events.
Ocean waves offer a rich area of exploration, especially when considering the statistical description of wave turbulence and the boundaries of weak wave turbulence theory. A standout issue in this domain is the emergence of whitecaps on steep ocean waves. These events, though infrequent, are pivotal for two reasons: they exemplify singularity formation and provide insights into the mechanisms of energy and momentum dissipation within the ocean. By examining a single whitecap, we can determine the momentum and energy directed to the capillary scale and the vorticity introduced into the fluid. Establishing a robust theory on whitecap formation could significantly enhance broader statistical models of ocean wave turbulence, furthering our understanding of ocean-atmosphere interactions and aiding in climate modeling.