# In Print

## Impact of Domain Wall Conduction on Ferroelectric Domain Reversal Kinetics

21 June in 11:30

__N.G. Masnev__, E.V. Podivilov, B.I. Sturman

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.## Role of wave scattering in instability-induced Langmuir circulation

21 June in 11:30 (short)

__I.A. Vointsev__, S.S. Vergeles

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).

Vergeles, S. S., & Vointsev, I. A. (2024). Role of wave scattering in instability-induced Langmuir circulation. Physics of Fluids, 36(3), 034119 (2024).

## The trapping of inertial waves by shear flow.

14 June in 11:30 (short)

__N.A. Ivchenko__, S.S. Vergeles

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.

[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.