Related papers: Toward Regional Characterizations of the Oceanic I…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
Starting from the classical formulation of the weak turbulence theory in a density stratified fluid, we derive a simplified version of the kinetic equation of internal gravity wave turbulence. This equation allows us to uncover scaling laws…
The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains…
Sea surface temperature (SST) forecasts help with managing the marine ecosystem and the aquaculture impacted by anthropogenic climate change. Numerical dynamical models are resource intensive for SST forecasts; machine learning (ML) models…
Regional climate change in the $21^{st}$ century will result from the interplay between human-induced changes and internal climate variability. Competing effects from greenhouse gas warming and aerosol cooling have historically caused…
Here we discuss some issues concerning the statistical properties of ocean surface waves. We show that, using the approach of weak turbulence theory, deviations from Gaussian statistics can be naturally included. In particular we discuss…
Over the years, the directional distribution functions of wind-generated wave field have been assumed to be unimodal. While details of various functional forms differ, these directional models suggest that waves of all spectral components…
Oceanic internal tides and other inertia-gravity waves propagate in an energetic turbulent flow whose lengthscales are similar to the wavelengths. Advection and refraction by this flow cause the scattering of the waves, redistributing their…
The Alber equation is a phase-averaged second-moment model for the statistics of a sea state, which recently has been attracting renewed attention. We extend it in two ways: firstly, we derive a generalized Alber system starting from a…
Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
Atmospheric flows exhibit fluctuations of all scales (space -time) ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). The apparently random fluctuations however exhibit long-range spatio-temporal…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
Maritime channel modeling is crucial for designing robust nearshore communication systems, yet reliable models that account for the dynamic marine environment with varying sea waves, wind conditions, and vessel motions remain scarce. This…
In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and…
Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal…
Problem of sound propagation in the ocean is considered. A novel approach of K. Hegewisch and S. Tomsovic for statistical modelling of acoustic wavefields in the random ocean is examined. The approach is based on construction of a wavefield…
The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the…
Turbulent water motions are important for the exchange of momentum, heat, nutrients, and suspended matter including sediments in the deep-sea that is generally stably stratified in density. To maintain ocean-density stratification, an…