Recent discovery and exploration of domain wall (DW) conduction in ferroelectrics promises to substantially modify the concept of the polarization reversal. We show by example of lithium niobate that the presence of DW conduction not only resolves the long standing problem of non-realistically high domain formation energy, but also leads to the exponential electric field dependences exp(−E_n/E) and exp(−E_l/E) for the rates of nucleation (n) and lateral (l) growth with characteristic fields E_n ≈ 75 and E_l ≈ 15 kV/mm. The kinetics of the polarization reversal shows distinct stages of nucleation, lateral growth, and coalescence of separate domains. It corresponds, in agreement with experiment, to the common exponential law exp(E^*) for the reversal time with E_l < E^* < E_n. To the best of our knowledge, this study is the first one explaining theoretically this law.

We consider a classical problem about dynamic instability that leads to the Langmuir circulation. The problem statement assumes that there is initially a wind-driven shear flow and a plane surface wave propagating in the direction of the flow. The unstable mode is a superposition of i) shear flow and ii) surface waves both modulated in the horizontal spanwise direction and iii) circulation that is made up with vortices forming near-surface rolls whose axis are coaligned along the shear flow streamlines and whose transverse size corresponds to the modulation period. The novelty of our approach is that we, firstly, take into account the scattering of the initial surface wave on the slow current. Second, we find the interference of the scattered and the initial waves generating a Stokes drift modulated in the same direction. Third, we establish the subsequent effect of the circulation by the vortex force created by the nonlinear interaction of the initial shear flow and the modulated part of the Stokes drift. S. Leibovich & A.D.D. Craik previously showed that the third part of the mechanism could maintain the Langmuir circulation. We calculate the growth rate which is approximately twice smaller than that obtained by A.D.D. Craik. The vertical structure of the circulation in the mode consists of two vortices that corresponds to the next mode in Craik’s model.
Vergeles, S. S., & Vointsev, I. A. (2024). Role of wave scattering in instability-induced Langmuir circulation. Physics of Fluids, 36(3), 034119 (2024).

We present analytical study of the interaction between inertial waves and geostrophic mean flow in a rotating incompressible fluid, that was investigated experimentally e.g. in [1]. In order to reveal mechanisms of the interaction, we have considered such simplified model, where excited waves propagate from the outside into the region with a stationary shear flow with straight streamlines is present. Such model possesses homogeneity in time and in space coordinates along the axis of rotation and shear flow direction. We demonstrate for one polarization of a monochromatic inertial wave there is a threshold value of the mean flow velocity at which wave is trapped by the flow and transfers to it both energy and momentum. The mathematical description of the wave trapping in inviscid limit is equivalent to the one-dimensional quantum mechanical problem of the fall of a particle in inverse square potential −1/r^2. We show analytically how the presence of small viscosity yields the dissipation of trapped inertial wave. Then we provide a comparison with the trapping of internal waves by large-scale flow with a mean vertical shear – the effect known for ocean currents [2].
[1] D.D. Tumachev, S.V. Filatov, S.S. Vergeles, A.A. Levchenko, JETP Letters, 118(6), 426-432 (2023)
[2] John R. Booker and Francis P. Bretherton. The critical layer for internal gravity waves in a shear flow. JFM, 27(3):513–539, 1967.