Multifractal Method for the Instantaneous Evaluation of the Stream Function in Geophysical Flows

Multifractal or multiaffine analysis is a promising new branch of methods in nonlinear physics for the study of turbulent flows and turbulentlike systems. In this Letter we present a new method based on the multifractal singularity extraction technique, the maximum singular stream-function method (MSSM), which provides a first order approximation to the stream function from experimental data in 2D turbulent systems. The essence of MSSM relies in relating statistical properties associated with the energy cascade in flows with geometrical properties. MSSM is a valuable tool to process sparse collections of data and to obtain instant estimates of the velocity field. We show an application of MSSM to oceanography as a way to obtain the current field from sea surface temperature satellite images; we validate the result with independent dynamical information obtained from sea level measurements.

Figure 1

Left: SST image from composite of AVHRR [19] images acquired 31st December, 2003. The covered area goes from 270° to 320° E, and from 20° to 50° N. Right: SSH map for the same region and time combining data from the Jason and ENVISAT satellite altimeters, [19, 31].

Figure 2

Left: 33% most singular points. Right: stream function (MSS) derived from the most singular points.

Figure 3

Detail of the comparison: we show the level sets from altimetry overimposed to a color representation of the MSS.