Related papers: Discovering Boundary Equations for Wave Breaking u…

In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…

Using symbolic regression to discover physical laws from observed data is an emerging field. In previous work, we combined genetic algorithm (GA) and machine learning to present a data-driven method for discovering a wave equation. Although…

This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore…

Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…

We present an investigation of the fundamental physical processes involved in deep water wave breaking. Our motivation is to identify the underlying reason causing the deficiency of the eddy viscosity breaking model (EVBM) in predicting…

We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…

A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…

Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through…

This paper is devoted to the derivation and mathematical analysis of a wave-structure interaction problem which can be reduced to a transmission problem for a Boussinesq system. Initial boundary value problems and transmission problems in…

Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common…

Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…

A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the…

Using the same measurement techniques as those of Saket et al. (2017), we have investigated the breaking threshold proposed by Barthelemy et al. (arXiv:1508.06002v1, 2015b) but for different classes of unforced unidirectional wave groups in…

In numerical ocean models coast lines change the direction from one grid cell to its neighbor and the value for viscosity is set to be as small as possible. Therefore, model simulations are not converged with resolution and boundary…

Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…

Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…