Nonlinear Processes in Oceanic and Atmospheric Flows


Optimal wavelets for the realization of microcanonical multiplicative cascades in geophysical flows

Author: O. Pont, A. Turiel and C.J. Perez-Vicente, Universitat de Barcelona.

Names and affiliation of other authors:
Antonio Turiel, ICM, CSIC
Conrad J. Perez-Vicente, Universitat de Barcelona

Oral or poster: Poster

Downloadable poster file:

Optimal wavelets for the realization of microcanonical multiplicative cascades in geophysical flows

(poster_2.pdf, 20811094 bytes)

A growing evidence shows that turbulent flows develop cascade processes, which are intimately linked to the spatial arrangement and temporal evolution of the flow. In cascade processes, energy is successively transfered from large to small scales through a multiplicative relation. Classical approaches to turbulent cascading are based in global statistical descriptors. In this work, we propose a wavelet-based microcanonical approach in which cascades are characterized locally, i.e., at each position and scale. Wavelet bases provide a powerful scheme to represent cascade processes, explicitly separating the scales at which the cascade takes place. The kernel of these projections is called mother wavelet and it is a fast-decaying waveform. We show that any signal has an optimal mother wavelet for which the multiplicative relation between scales is locally verified.
In this work we have processed time sequences of satellite daily maps of Sea Surface Temperature. We have shown that optimized wavelet bases evidence the locations, scales and times at which the heat cascade transfer is taking place on ocean surface. This allows identifying the precise pathway followed by turbulence-induced energy transfer.Technical applications of the presented methodology include data inference and fusion, and time forecasting. On the more fundamental side, our methods could be used to retrieve dynamical information of the flow such as stream lines, local diffusivities and energy transfer.

*Satellite images from NASA and ESA

Nonlinear Processes in Oceanic and Atmospheric Flows. July 2-4, 2008. Castro Urdiales, Cantabria, Spain.