Flow field expression in a superposition of dipole flows and identification of dipole moment by continuous wavelet transform

Continuous wabelet transforms suitable for incompressible flows are discussed. Bessel type wavelet is introduced and inverse transform is extended so that the divergence-free condition of the flow field is automatically satisfied. This extension results in the flow field expression in superposition of dipole flow fields. An efficient way to substitute a set of dipoles for the flow field is proposed to reduce the computational cost. Applications of the present transform for several two-dimensional flows are shown.