Related papers: Explicit wave-averaged primitive equations using a…
We derive the formal solution to the dispersion relation for linear surface waves on a horizontal mean current with arbitrary vertical dependence. The problem is cast in a Green's function framework for the Rayleigh equation, neglecting…
We express the mean curvature flow of Lagrangian submanifolds in pseudo-Riemannian manifolds endowed with the Kim-McCann-Warren metric within the framework of generalized mean curvature flow on Kim-McCann manifolds. While generalized mean…
In this paper, we develop a new strategy to study Lagrangain mean curvature equation on open sets of $\mathbb{R}^{n}(n\geq2)$. By establishing an Allard-type regularity theorem, we obtain an interior Hessian estimate of solutions to this…
We provide an in-depth exploration of the mass-transport properties of Pollard's exact solution for a zonally-propagating surface water-wave in infinite depth. Without resorting to approximations we discuss the Eulerian mass transport of…
We consider a fully nonlinear parabolic equation with nonlinear Neumann type boundary condition, and show that the longtime existence and convergence of the flow. Finally we apply this study to the boundary value problem for minimal…
Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its…
Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained…
Suppose that $\mathcal{M}$ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in $\mathbb{C}^n$. We show that if $\mathcal{M}$ has a blow-down given by the static union of two Lagrangian subspaces with…
Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over…
We formulate a model of the two-way interactions between surface gravity waves and ocean currents. The model couples the transport of wave action in the four-dimensional (horizontal) position--wavevector phase space with the…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
We develop a technique of multiple scale asymptotic expansions along mean flows and a corresponding notion of weak multiple scale convergence. These are applied to homogenize convection dominated parabolic equations with rapidly…
The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
The frozen Gaussian approximation (FGA) is an effective tool for modeling high frequency wave propagation. In previous works, the convergence of the FGA has established for strict hyperbolic systems. In this work, we derive the frozen…
Approximate analytical solutions of the modified Langevin equation are obtained. These solutions are relatively simple and enough accurate. They are illustrated by considering a mean-field model of a system with interacting…
In this paper, we construct global-in-time forward and backward Lagrangian flow maps along the pressure gradient generated by weak solutions of the Porous Media Equation. The main difficulty is that when the initial data has compact…
A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean…
We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a…
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential…