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We study the two-dimensional surface quasi-geostrophic equations and the three-dimensional Hall-magnetohydrodynamics system forced by degenerate noise. In comparison with a vorticity formulation of the Navier–Stokes equations, the non-linear term of the surface quasi-geostrophic equations is more singular by one derivative. In comparison with the magnetohydrodynamics system, the Hall term of the Hall-magnetohydrodynamics system is also more singular by one derivative. We prove the existence and uniqueness of an invariant measure for the Galerkin approximations of the surface quasi-geostrophic equations and the Hall-magnetohydrodynamics system, both forced by degenerate noise which consists of only a few modes. [ABSTRACT FROM AUTHOR]

Surface currents in the Alboran Sea are characterized by a very fast evolution that is not well captured by altimetric maps due to sampling limitations. On the contrary, satellite infrared measurements provide high resolution synoptic images of the ocean at high temporal rate, allowing to capture the evolution of the flow. The capability of Surface Quasi-Geostrophic (SQG) dynamics to retrieve surface currents from thermal images was evaluated by comparing resulting velocities with in situ observations provided by surface drifters. A difficulty encountered comes from the lack of information about ocean salinity. We propose to exploit the strong relationship between salinity and temperature to identify water masses with distinctive salinity in satellite images and use this information to correct buoyancy. Once corrected, our results show that the SQG approach can retrieve ocean currents slightly better to that of near-real-time currents derived from altimetry in general, but much better in areas badly sampled by altimeters such as the area to the east of the Strait of Gibraltar. Although this area is far from the geostrophic equilibrium, the results show that the good sampling of infrared radiometers allows at least retrieving the direction of ocean currents in this area. The proposed approach can be used in other areas of the ocean for which water masses with distinctive salinity can be identified from satellite observations.

Representing all variables in double‐precision in weather and climate models may be a waste of computer resources, especially when simulating the smallest spatial scales, which are more difficult to accurately observe and model than are larger scales. Recent experiments have shown that reducing to single‐precision would allow real‐world models to run considerably faster without incurring significant errors. Here, the effects of reducing precision to even lower levels are investigated in the Surface Quasi‐Geostrophic system, an idealised system that exhibits a similar power‐law spectrum to that of energy in the real atmosphere, by emulating reduced precision on conventional hardware. It is found that precision can be reduced much further for the smallest scales than the largest scales without inducing significant macroscopic error, according to a −4/3 power law, motivating the construction of a “scale‐selective” reduced‐precision model that performs as well as a double‐precision control in short‐ and long‐range forecasts but for a much lower estimated computational cost. A similar scale‐selective approach in real‐world models could save resources that could be re‐invested to allow these models to be run at greater resolution, complexity or ensemble size, potentially leading to more efficient, more accurate forecasts. [ABSTRACT FROM AUTHOR]

In this paper we consider a periodic 2-dimensional quasi-geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution [ABSTRACT FROM AUTHOR]

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at least for short time. We show that they have real analytic Lagrangian paths. More precisely, we show that as long as a solution of any of these equations is in a class of regularity that assures Hölder continuous gradients of velocity, the corresponding Lagrangian paths are real analytic functions of time. The method of proof is conceptually straightforward and general, and we address the combinatorial issues head-on. [ABSTRACT FROM AUTHOR]

In this paper, we study the sub-critical dissipative quasi-geostrophic equations ( S α ) . We prove that there exists a unique local-in-time solution for any large initial data θ 0 in the space X 1 − 2 α ( R 2 ) defined by (1) . Moreover, we show that ( S α ) has a global solution in time if the norms of the initial data in X 1 − 2 α ( R 2 ) are bounded by 1/4. Also, we prove a blow-up criterion of the local-in-time solution of ( S α ) . [ABSTRACT FROM AUTHOR]

Surface currents in the Alboran Sea are characterized by a very fast evolution that is not well captured by altimetric maps due to sampling limitations. On the contrary, satellite infrared measurements provide high resolution synoptic images of the ocean at high temporal rate, allowing to capture the evolution of the flow. The capability of Surface Quasi-Geostrophic (SQG) dynamics to retrieve surface currents from thermal images was evaluated by comparing resulting velocities with in situ observations provided by surface drifters. A difficulty encountered comes from the lack of information about ocean salinity. We propose to exploit the strong relationship between salinity and temperature to identify water masses with distinctive salinity in satellite images and use this information to correct buoyancy. Once corrected, our results show that the SQG approach can retrieve ocean currents slightly better to that of near-real-time currents derived from altimetry in general, but much better in areas badly sampled by altimeters such as the area to the east of the Strait of Gibraltar. Although this area is far from the geostrophic equilibrium, the results show that the good sampling of infrared radiometers allows at least retrieving the direction of ocean currents in this area. The proposed approach can be used in other areas of the ocean for which water masses with distinctive salinity can be identified from satellite observations. [ABSTRACT FROM AUTHOR]