Seminar “Nonlinear waves”


Dear Colleagues,

The next session of academician V.E. Zakharov seminar “Nonlinear Waves” will be held on Wednesday, April the 14th, 15:30 Moscow Time, at

“Upper-ocean Ekman currents: a new perspective on the century old problem”

Victor I. Shrira
Keele University, UK

Abstract: The work offers a new perspective on the ocean Ekman current response to arbitrary wind within the Stokes-Ekman paradigm. We focus on two aspects of the Ekman theory: (i) The effects of eddy viscosity varying in time and depth. The Ekman equations are an exact reduction of the Navier-Stokes. We derive and examine a wide class exact NS solutions which describes the dynamics of the Ekman boundary layer in terms of the Green’s function. We show that development of the Ekman current from rest invariably leads to profiles with inflection points in the profiles, which for boundary layers is a sufficient condition of instability. This suggests a more intense mixing in the surface layer. (ii) It is known that the account of wind waves strongly affects the Ekman current dynamics via the Stokes drift, which is described by the Stokes-Ekman model. Here by employing the known self-similar laws of wave field evolution we find explicit time dependence of the Stokes drift contribution. Since the dynamics of the Ekman response in the presence of evolving wave field have not been considered, the basic questions on how the Ekman current evolves and, especially, whether it grows or decays at large times, remain open. On solving analytically the Stokes-Ekman equation we find and analyse evolution of the Ekman current. We show that the system has a single time dependent attractor which can be described asymptotically. The large time asymptotics of the Ekman current is determined by the regime of wave field evolution: for the regimes typical of young waves the Ekman current grows with time to infinity, in contrast, for `old waves’ the Ekman current asymptotically decays. New mechanisms of interaction between the wave field and Ekman currents are also discussed.

Questions to Andrei Pushkarev,, +7(909) 949-96-13

E.A. Kuznetsov, A.N. Pushkarev


Speaker Title


V.Shrira Upper-ocean Ekman currents: a new perspective on the century old problem
07.04.2021 V.E.Zakharov Formation and non-formation of singularity on the surface of ideal fluid without gravity
31.03.2021 S.Dyachenko The Tale of Two Branch Points: Singularities in 2D flows
17.03.2021 E.A.Kuznetsov Breaking in the inviscid boundary layer (continuation)
10.03.2021 A.Mailybaev Hidden spatiotemporal symmetries in turbulence: effects of Galilean invariance
03.03.2021 A.Mailybaev Hidden spatiotemporal symmetries in statistics of turbulence
24.02.2021 E.A. Kuznetsov Breaking in inviscid boundary layer
17.02.2021 A. Pushkarev About ST6 model of wind energy input and wave energy dissipation source terms in operational forecasting of ocean waves
10.02.2021 S.V. Dremov Bound Coherent Structures Propagating on the Free Surface of Deep Water
03.02.2021 Vladimir Yankov Solitons, Vortices, Sun, and Tokamaks as Statistical Attractors
27.01.2021 Gregory Falkovich Fibonacci turbulence
20.01.2021 Sergei K. Turitsyn Intermediate asymptotics in nonlinear systems and coexistence of coherent structures and linear waves
13.01.2021 S. Nazarenko Self-similar evolution in wave turbulence and non-equilibrium
14-15.12.2020 24 speakers Joint seminar “Nonlinear Waves” with Scientific Council “Nonlinear Dynamics” RAS “Nonlinear Session – 20″
02.12.2020 A. Kamchatnov Optico-mechanical analogy and number of solitons
25.11.2020 V.Sirota Stationary scaling in small-scale turbulent dynamo problem
18.11.2020 M.Onorato Thermalization and anomalous correlators in the Fermi-Pasta-Ulam-Tsingou chain
11.11.2020 E.Kochurin Numerical Simulation of Collinear Capillary-Wave Turbulence
28.10.2020 Y.Stepanyants The asymptotic approach to the description of two-dimensional soliton patterns
21.10.2020 K.Zybin No feedback is possible in small-scale turbulent magnetic field
14.10.2020 S.Vergeles Steady axial magnetic field maintained in a columnar vortex in a rotating turbulent conducting fluid
07.10.2020 A.Slunyaev Direct numerical simulation of 3D rogue waves
30.09.2020 A.Gelash Solitonic model of the condensate
23.09.2020 R.Mullyadzhanov Solitons in a box-shaped wavefield with noise: perturbation theory and statistics
16.09.2020 P.Lushnikov Motion of singularities in fluid dynamics
09.09.2020 V.E.Zakharov Are the equations of deep water with the free surface integrable?
17.06.2020 E.Pelinovsky Bottom Pressure under Waves in Shallow Waters​
10.06.2020 N.Ussembayev On some new results in the Hamiltonian theory of weakly nonlinear surface waves
03.06.2020 V.Gordin Wind in the boundary layer of the Earth’s atmosphere. Observations and a generalized Ekman-Akkerblom model. The complex coefficient of the turbulent exchange is more adequate
27.05.2020 D.Agafontsev Adiabatically growing integrable turbulence
20.05.2020 A.Minakov Long-time asymptotics for the modified Korteweg-de Vries equation with step-like initial data
13.05.2020 S. Badulin Theory of wave turbulence for satellite altimetry: wave dynamics and climatology remote sensing of sea state
29.04.2020 V. Geogjaev Quadruplet form of Hasselmann equation
22.04.2020  A. Pushkarev Nonlinear Wind Waves Generation in Straits: Laser-Like and Self-Similar Regimes
15.04.2020 D. Kachulin Soliton turbulence in approximate and exact models for deep water waves
08.04.2020 E. Kuznetsov Compressible structures in two-dimensional hydrodynamic systems
01.04.2020 A. Dyachenko Multiple Soliton Interactions on the Surface of Deep Water
25.03.2020 I. Sibgatullin Linear and nonlinear wave attractors in stratified or rotating fluids
18.03.2020 E. Mikhailov Propagation of nonlinear waves in problems of magnetic field generation in the dynamo theory
11.03.2020 A. Gelash Synchronized breather interactions
04.03.2020 E. Prosviryakov Exact solutions of the Navier-Stokes equations for describing large-scale flows of the oceans and amplification of Stokes waves in a liquid
19.02.2020 V. Zakharov Chain solitons in KP-1 equation