Assistant Professor

Applied mathematics, nonlinear waves, free surface wave, integrable systems, spectral methods, mathematical physics, scientific computing, mathematical biology, potenial theory

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.

- A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Short branch cut approximation in D Hydrodynamics with Free Surface, submitted Proc. Roy. Soc. A (2020), https://arxiv.org/abs/2003.05085
- S.A. Dyachenko, Traveling capillary waves on the boundary of a disc, accepted Studies in Applied Math, 2020, https://arxiv.org/abs/1911.07557
- S. A. Dyachenko, On the dynamics of a free surface of an ideal fluid in a bounded domain in presence of surface tension, vol. 860, pp. 408-418, JFM (2019), https://arxiv.org/abs/1804.06947(2018)
- S. A. Dyachenko and Vera Mikyoung Hur, Stokes Waves with Vorticity II: Folds and Gaps, JFM, 2019, https://arxiv.org/pdf/1903.00097
- A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion, vol. 874, pp. 891-925, JFM (2019), https://arxiv.org/abs/1809.09584 (2018)
- P. M. Lushnikov, S. A. Dyachenko, D. A. Silantyev, New Conformal Maping for Adaptive Resolving of the Complex Singularities of Stokes Wave, Proc. Roy. Soc. A (2017), v. 473, dx.doi.org/10.1098/rspa.2017.0198
- S. Dyachenko, A. Zlotnik, A., Korotkevich, M. Chertkov, Operator Splitting Method for Dynamic Simulations of Flows in Natural Gas Transport Networks., Physica D (2017), https://doi.org/10.1016/j.physd.2017.09.002
- S.A. Dyachenko, D.V. Zakharov, V.E. Zakharov, Primitive potentials andbounded solutions of the KdV equation., Physica D (2016), 333: 148-156, doi:10.1016/j.physd.2016.04.002
- S.A. Dyachenko, A.C. Newell, Whitecapping, Stud. in Appl. Math (2016), 137: 199-213, doi:10.1111/sapm/12126