The multifractal theory of turbulence, a framework to investigate the ocean

– Jordi Isern-Fontanet, ICM, Barcelona –

Résumé :

The mulifractal theory of turbulence provides a powerful framework that connects the scaling and geometrical properties of coarse grained fields 
in the limit of small scales with global statistics of the ow. As it is used here, this theory is based on three main contributions: Onsagers 
theory of ideal turbulence; the multifractal formalism; and different models of the turbulent cascade. But, our implementation differs from common 
approaches in that it is based on velocity gradients rather than energy dissipation or velocity differences. If temperatures are used instead of 
velocities, the singularity exponents that characterize the behavior of coarse grained fields at small scales have a simple interpretation. 
Indeed, they can be seen as a proxy measure for the intensity of fronts, on the basis that the strongest fronts are those with the most marked 
singularity, hence, also those with the smallest singularity exponents. In this talk I will review the basis of the multifractal theory of 
turbulence and show various examples of the insight obtained in different oceanographic problems such as the study of the energy cascade from 
in situ velocity measurements; the analysis of ocean models; or the comparison of different satellite products of Sea Surface Temperatures