Related papers: A fast Fourier spectral method for wave kinetic eq…
A fundamental question in wave turbulence theory is to understand how the "wave kinetic equation" (WKE) describes the long-time dynamics of its associated nonlinear dispersive equation. Formal derivations in the physics literature date back…
Using the 1D Majda-McLaughlin-Tabak model as an example, we develop numerical experiments to study the validity of the Wave Kinetic Equation (WKE) at the kinetic limit (i.e., small nonlinearity and large domain). We show that the dynamics…
The present thesis deals with the non-modal linear analysis of 3D perturbations in wall flows. In the first part,a solution to the Orr-Sommerfeld and Squire IVP, in the form of orthogonal functions expansion, is researched. The Galerkin…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
This paper presents a recent advancement that transforms the problem of decaying turbulence in the Navier-Stokes equations in $3+1$ dimensions into a Number Theory challenge: finding the statistical limit of the Euler ensemble. We redefine…
In this paper, we introduce a fast Fourier-Galerkin method for solving boundary integral equations on torus-shaped surfaces, which are diffeomorphic to a torus. We analyze the properties of the integral operator's kernel to derive the decay…
Fronts and near-inertial waves are energetic motions in the upper ocean that can interact and provide a route for kinetic energy (KE) dissipation of balanced oceanic flows. A quasilinear model is developed to study the KE exchanges between…
Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the original PDE with an extended system separating…
Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be…
We present a method to synthesize phase screens for multi-wavelength, atmospheric wave optics simulations using fast Fourier transforms. We validate our work by comparing the theoretical, two-wavelength optical path length structure…
In this paper we construct global strong dispersive solutions to the space inhomogeneous kinetic wave equation (KWE) which propagate $L^1_{xv}$ -- moments and conserve mass, momentum and energy. We prove that they scatter, and that the wave…
This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase potential flow wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
The random Fourier method (RFM) is widely employed for synthetic turbulence due to its mathematical clarity and simplicity. However, deviations remain between prescribed inputs and synthetic results, and the origin of these errors has not…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
We investigate a classical phase-space approach of matter-wave propagation based on the Truncated Wigner Equation (TWE). We show that such description is suitable for ideal matter waves in quadratic time-dependent confinement as well as for…
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…