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The predictability of eight southern European tropical-like cyclones, seven of which Medicanes, is studied evaluating ECMWF operational ensemble forecasts against operational analysis data. Forecast cyclone trajectories are compared to the…
This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible…
In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
Shell models allow much greater scale separations than those presently achievable with direct numerical simulations of the Navier-Stokes equations. Consequently, they are an invaluable tool for testing new concepts and ideas in the theory…
Tropical cyclone (TC) trajectories are governed by large-scale steering flows with sensitive dependence on initial conditions, raising the question of whether targeted perturbations can induce track deviations. We present a case study…
It is well known that rapid changes in tropical cyclone motion occur during interaction with extratropical waves. While the translation speed has received much attention in the published literature, acceleration has not. Using a large data…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…
Tropical cyclones (TCs), driven by heat exchange between the air and sea, pose a substantial risk to many communities around the world. Accurate characterization of the subsurface ocean thermal response to TC passage is crucial for accurate…
Tropical cyclones occur over the Earth's tropical oceans, with characteristic genesis regions and tracks tied to the warm ocean surface that provides energy to sustain these storms. The study of tropical cyclogenesis and evolution on Earth…
We consider a mathematical model for the interactions of an elastic body fully immersed in a viscous, incompressible fluid. The corresponding composite PDE system comprises a linearized Navier-Stokes system and a dynamic system of…
Tropical cyclones that evolve from a non-tropical origin may pose a special challenge for predictions, as they often emerge at the end of a multi-scale cascade of atmospheric processes. Climatological studies have shown that the 'tropical…
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…
A general framework for the theory of statistical solutions on trajectory spaces is constructed for a wide range of equations involving incompressible viscous flows. This framework is constructed with a general Hausdorff topological space…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
Because geostationary satellite (Geo) imagery provides a high temporal resolution window into tropical cyclone (TC) behavior, we investigate the viability of its application to short-term probabilistic forecasts of TC convective structure…
The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of…