Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by high-frequency radar, and its relation to wind regimes using the maximum-entropy principle

Two years (2021–2022) of high-frequency-radar (HFR) sea surface current data in the Gulf of Trieste (northern Adriatic Sea) are analysed. Two different timescales are extracted using a superstatistical formalism: a relaxation time and a larger timescale over which the system is Gaussian. We propose obtaining an ocean current probability density function (PDF) combining (i) a Gaussian PDF for the fast fluctuations and (ii) a convolution of exponential PDFs for the slowly evolving variance of the Gaussian function rather than for the thermodynamic beta=1/sigma^2 in a system with a few degrees of freedom, as the latter has divergent moments. The Gaussian PDF reflects the entropy maximization for real-valued variables with a given variance. On the other hand, if a positive variable, as a variance, has a specified mean, the maximum-entropy solution is an exponential PDF. In our case the system has 2 degrees of freedom, and therefore the PDF of the variance is the convolution of two exponentials. In the Gulf of Trieste there are three distinct main wind forcing regimes: bora, sirocco, and low wind, leading to a succession of different sea current dynamics on different timescales. The universality class PDF successfully fits the observed data over the 2 observation years and also for each wind regime separately with a different variance of the variance PDF, which is the only free parameter in all the fits.