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Contract number
Time span of the project

As of 30.01.2020

Number of staff members
scientific publications
General information

Name of the project: Nonlinear wave dynamics

Strategy for Scientific and Technological Development Priority Level: д

Goals and objectives

Research directions: Analytic, numerical and experimental research in nonlinear wave theory: extreme wave, wave collapses and solitons in different nonlinear media

Project objective: Research of nonlinear wave phenomena on the surface of liquid (ocean)

The practical value of the study

  • For the first time we have produced a spatial equation for waves on water that describes real experiments in laboratory pools.
  • We have conducted numerical research of formation of killer waves within a nonlinear compact equation. We have compared this probability of probability predicted by the linear model. We have shown that nonlinear effects significantly, by several orders of magnitude, increase possibility of formation of killer waves compared to the standard dispersion mechanism.
  • Our team has investigated a nonlinear-dissipative model of the spectrum of wind waves that allows to theoretically explain formation of the classical Phillips spectrum for short waves on water. We have developed the theory of self-similarity of wind disturbance.
  • The Laboratory has studied the mechanism of formation of killer waves that can be later implemented in models that will be able to forecast where, when and in what circumstances such a wave will form next time.
  • We have developed an asymptotic theory for research of modulation instability of condensates. It has been shown that superregular soliton solutions are an important scenario of modulation instability that an be observed in experiments. Together with Peregrine breathers and Kuznetsov solitons they completely describe the solution scenario of development of modulation instabilities from localized disturbances.
  • We have numerically studied statistical features of the direct Kraichnan cascade for two-dimensional hydrodynamic turbulence in the presence of pumping and subsidence of the viscous type. It has been shown that quasi-shock turbulence waves are formed due to contractility of the field of vorticity rotor and their Fourier-images in the form of jets show significant impact on behavior of turbulence of the direct cascade.

Education and career development: 7 bachelors dissertations and 7 masters dissertations have been defended


University of Arizona (USA), Tokyo University (Japan), Brazilian National Institute of Pure and Applied Mathematics (Brazil): joint scientific research

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Agafontsev D.S., Kuznetsov E.A., Mailybaev A.A.
Development of High Vorticity Structures in Incompressible 3D Euler Equations. Physics of Fluids 27(8): 085102-1–085102-18 (2015).
Pushkarev A., Zakharov V.
Limited Fetch Revisited: Comparison of Wind Input Terms, in Surface Wave Modeling. Ocean Modelling 103(3): 18–37 (2016).
Arkhipov D.G., Vozhakov I.S., Markovich D.M., Tsvelodub О.Yu.
The Symmetry in the Problem of Wave Flow Regimes of a Thin Layer of Viscous Fluid. European Journal of Mechanic – B/Fluids 59: 52–56 (2016).
Dyachenko A.I., Kachulin D.I., Zakharov V.E.
Super Compact Equation for Water Waves. Journal of Fluid Mechanics 828: 661–679 (2017).
Guzanov V.V., Bobylev A.V., Heinz O.M., Kharlamov S.M., Kvon A.Z., Markovich D.M.
Characterization of 3-D Wave Flow Regimes on Falling Liquid Films. International Journal of Multiphase Flow 99: 474–484 (2018).
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