Dipole decomposition of two-dimensional incompressible flows

Abstract

A decomposition method of a given two-dimensional incompressible flow field into a dipole sequence is developed. Necessary condition for dipole sequence is revealed using a wavelet transform of di-vorticity of the given flow. Subsequently, a practical way to extract dipole sequence by a recurrence formula is proposed. Each obtained dipole is characterized not only by the dipole moment but also by its own length scale. The reconstructed flow fields always give divergence-free fields even if the successive correction with the recurrence formula is truncated at a finite number. Typical two-dimensional flows are decomposed into dipoles, and graphical representations of extracted dipoles are shown. Many columns of dipoles and isolated dipoles in various length scale are found in a two-dimensional turbulent flow.