PNAS publishes collaborative research that sheds light on steep ocean wave dynamics

Wave dynamics.

In a new collaborative study published in the Proceedings of the National Academy of Sciences (PNAS), a team of researchers from the University of Washington, SUNY at Buffalo and the University of New Mexico have unveiled the dominant mechanism behind wave-breaking of tall oceanic waves. The research team includes Prof. Bernard Deconinck (UW), Prof. Sergey Dyachenko (UB), Prof. Pavel Lushnikov (UNM) and Dr. Anastassiya Semenova (UW).

Understanding the complex dynamics of wave breaking and the formation of whitecaps is essential for predicting ocean wave behavior and improving oceanic models. This pivotal work, which describes instabilities of traveling waves known as the Stokes waves, marks a substantial step forward in the field of nonlinear waves, marine sciences and oceanography. 

  • Read the PNAS research article, "The dominant instability of near-extreme Stokes waves", here.
  • Read the PHYS ORG news story, Oceanic waves represent fundamental challenges in nonlinear science, say mathematicians"  here.

UB Mathematics Faculty Profile

  • Sergey Dyachenko


    Sergey Dyachenko, PhD.

    Sergey Dyachenko


    Sergey Dyachenko


    Assistant Professor

    Research Interests

    Applied mathematics; nonlinear waves; scientific computing; free surface waves


    BS in Applied Physics and Mathematics, Moscow Institute of Physics and Technology (MIPT)

    PhD in Applied Mathematics, University of New Mexico

    Research Summary

    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.

    Selected Publications

    • B Deconinck, SA Dyachenko, PM Lushnikov, A Semenova, The dominant instability of near-extreme Stokes waves, 2023 Proceedings of the National Academy of Sciences 120 (32), e2308935120,
    • SA Dyachenko, A Semenova, Quasiperiodic perturbations of Stokes waves: Secondary bifurcations and stability, J of Comp. Phys., Volume 492, 2023, 112411,
    • SA Dyachenko, Vera Mikyoung Hur, & D Silantyev, Almost extreme waves, JFM, 955, A17, 2023 doi:10.1017/jfm.2022.1047
    • SA Dyachenko, Traveling capillary waves on the boundary of a fluid disc, Stud Appl Math. 2022; 148: 125–140.
    • AI Dyachenko, SA Dyachenko, PM Lushnikov, VE Zakharov, Short branch cut approximation in 2D Hydrodynamics with Free Surface, Proc. Roy. Soc. A, vol. 477, 2021,
    • 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),
    • S.A. Dyachenko, Traveling capillary waves on the boundary of a disc, accepted Studies in Applied Math, 2020,
    • 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),
    • S. A. Dyachenko and Vera Mikyoung Hur, Stokes Waves with Vorticity II: Folds and Gaps, JFM, 2019,
    • 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), (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,
    • S. Dyachenko, A. Zlotnik, A., Korotkevich, M. Chertkov, Operator Splitting Method for Dynamic Simulations of Flows in Natural Gas Transport Networks., Physica D (2017),
    • 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