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On the compressibility of surface currents in the Gulf of Finland, the Baltic Sea

We address ways of quantification of the ability of different substances in the marine environment to form areas with high concentrations (patches) in the surface layer. This ability is usually linked with the so-called property of (flow) compressibility of sea surface (understood as the relative weight of the potential component of a velocity field). We analyze the potential of using for this purpose a modified measure - the Finite Time Compressibility (FTC) that is directly related to the ability of clustering of passive tracers in some regions of the sea surface and that can be calculated in a straightforward way from surface velocities. Shown is that under reasonable assumptions and short time intervals the FTC is a direct extension of the classical flow compressibility. An explicit relationship between the two definitions is derived under these assumptions. The two quantities are generally slightly different and coincide for a particular value of 0.781. The maps of FTC are evaluated for the Gulf of Finland based on 3D velocity fields obtained using the Rossby Centre Ocean Model (Swedish Meteorological and Hydrological Institute) for 1991 and the TRACMASS code for tracking Lagrangian trajectories.