On the contribution of ocean fronts to the anomalous scaling of the structure functions

The upper ocean is crowded with fronts of different intensities and extensions,  which are known to play a major role in the dynamics of the oceanic upper layers and contribute to set some properties such as the spectral slopes of Sea Surface Temperatures (SST), among others. Here, we show that the upper layers of the ocean can be modeled by the multifractal theory of turbulence and, then, we use this theory to predict the link between the most intense fronts and the scaling properties of the structure functions. This prediction is, finally, verified with a wide range of observations and numerical simulations.

In particular, we show that the behavior of thermal gradients at small enough scales can be characterized by singularity exponents. Then, we use the singularity exponents of thermal gradients as a measure of the intensity of thermal fronts; and the fractal dimension of the set of points with the same singularity exponent, known as the singularity spectrum, as a measure of their extension. This allows us to connect fronts with the structure functions of temperature using the multifractal formalism. Assuming that the turbulent cascade can be modeled with the log-Poisson model, we analytically shown that the anomalous scaling of the structure functions is a function of the intensity of the strongest front, i.e. the smallest singularity exponent. This prediction is verified using the SST provided by numerical simulations of an upwelling system; simulations of the global ocean; and satellite observations. Moreover, we show that the predicted relationship is also valid for other variables such as velocities.

Our results not only provide insight on the functioning of the upper ocean, but also provide a guide to develop and adjust numerical models. Indeed, our results imply that numerical models have to correctly model, or parametrize, those processes generating the most intense fronts, in order to properly reproduce some of the statistics of ocean temperatures.