We consider the problem of a thin liquid layer falling down an inclined plate that is subjected to non-uniform heating. The plate temperature is assumed to be linearly distributed and both directions of the temperature gradient with respect to the flow are investigated. The film flow is not only influenced by gravity and mean surface tension, but in addition by the thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. Applying the long-wave theory, a nonlinear evolution equation is derived. When the plate temperature is decreasing in the downstream direction, linear stability analysis exhibits a film stabilization, compared to a uniformly heated film. In contrast, for increasing temperature along the plate, the film becomes less stable. Numerical solution of the evolution equation indicates the existence of permanent finite-amplitude waves of different kinds. The shape of the waves depends mainly on the mean flow and the mean surface tension, but their amplitudes and phase speeds are influenced by thermocapillarity.

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The current knowledge about spatial and temporal dynamics of the Black Sea's thermohaline structure is incomplete because of missing data and sparse distribution of existing measurements in space and time. This study presents 56 year continuous simulations of the Black Sea's hydrodynamics using the 3D General Estuarine Transport Model (GETM), without incorporating any relaxation toward climatological or observational data fields. This property of the model allows us to estimate independent temporal trends, in addition to resolving the spatial structure. The simulations suggest that the intermediate layer temperature is characterized by a weak positive trend (warming), whereas the surface temperature does not show a clear linear trend. Different salinity trends have been established at the surface (negative), upper (weaker negative) and main halocline (positive). Three distinct dynamic periods are identified (1960–1970, 1970–1995, 1995–2015), which exhibit pronounced changes in the Black Sea's thermohaline properties and basin circulation. Strengthening of the main cyclonic circulation, accompanied by intensification of the mesoscale anticyclonic eddy formation is found. Both events strongly affect the sea surface salinity but contribute in opposing directions. Specifically, strong composite large‐scale circulation leads to an increase in sea surface salinity, while enhanced formation of mesoscale anticyclones decreases it. Salinity evolution with time is thus the result of the competition of these two opposing yet interdependent processes.