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Mesoscale eddies are of utmost importance in understanding ocean dynamics and the transport of heat, salt, and nutrients. Accurate representation of these eddies in ocean models is essential for improving model predictions. However,…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…
Wave-sea ice interactions shape the transition zone between open ocean and pack ice in the polar regions. Most theoretical paradigms, implemented in coupled wave-sea ice models, predict exponential decay of the wave energy but some recent…
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…
Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic…
The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks…
The deep learning revolution is touching all scientific disciplines and corners of our lives as a means of harnessing the power of big data. Marine ecology is no exception. These new methods provide analysis of data from sensors, cameras,…
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…
Climate models are essential to understand and project climate change, yet long-standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid-scale processes, particularly…
Wind speed retrieval at sea surface is of primary importance for scientific and operational applications. Besides weather models, in-situ measurements and remote sensing technologies, especially satellite sensors, provide complementary…
The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical…
An inverse obstacle problem for the wave equation in a two layered medium is considered. It is assumed that the unknown obstacle is penetrable and embedded in the lower half-space. The wave as a solution of the wave equation is generated by…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…
The interaction of obliquely incident surface gravity waves with a vertical flexible permeable membrane wave barrier is investigated in the context of three-dimensional linear wave-structure interaction theory. A general formulation for…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
A bypass transition scenario in a wind-stress driven aqueous flow is analysed using a temporally developing boundary layer model with accelerating surface drift velocity. The parameters of the model are selected to mimic a wave-tank…