Seminar “Nonlinear waves”

Dear Colleagues,
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The next session of academician V.E. Zakharov seminar “Nonlinear Waves” will be held on Wednesday, April the 14th, 15:30 Moscow Time, at https://bbb2.itp.ac.ru/b/ale-wkj-mvm

“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, dr.push@gmail.com, +7(909) 949-96-13

E.A. Kuznetsov, A.N. Pushkarev
Organizers