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In this work we propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in environmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save computational time, we rely on reduced basis techniques as a suitable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. We test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning. The quasi-geostrophic optimal control problem is also presented in its nonlinear version.

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Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.

The driving mechanisms behind the decadal reversal of the Ionian Sea upper layer circulation recently sparked a considerable discussion in the Mediterranean scientific community. It has been suggested that the reversal can be driven by variations in wind stress curl over the basin, baroclinic dynamics acting within the Adriatic‐Ionian System (AISys) or baroclinic dynamics driven by thermohaline properties at the AISys eastern boundary. Here we perform numerical simulations in order to assess the relative importance of remote forcings (wind stress, thermohaline fluxes, thermohaline open boundary conditions) on the vorticity and energy budget of the Ionian Sea. A mechanistic understanding of the AISys dynamics is achieved with an approach based on an increasing complexity in the model forcings and domain. Our experiments suggest that wind stress does not play a leading role in the vorticity and energy budgets of the Ionian Sea. Wind stress can reinforce or weaken the circulation but it is not able to reverse its sign. Its role becomes dominant only in the absence of inflows through the Antikythira Strait and Cretan Passage. Instead, reversals in the upper layer circulation of the Ionian Sea take place only in the presence of an active boundary on the Aegean Sea/Levantine Basin side and appear to be correlated with substantial exchanges of Availalble Potential Energy between the two basins (as observed at the end of the Eastern Mediterranean Transient). From an energetic point of view, AISys can be explained therefore only if the role of the Aegean Sea is explicitly considered.