We combine singular value decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued random fields. The so-called Tensorial Wavelet Transform Modulus Maxima (\\TWTMM{}) method is calibrated on synthetic self-similar 2D vector-valued multifractal measures and monofractal 3D vector-valued fractional Brownian fields. We report the results of some application of the \\TWTMM{} method to turbulent velocity and vorticity fields generated by Direct Numerical Simulations (DNS) of the incompressible Navier-Stokes equations. This study reveals the existence of an intimate relationship
$D_{\\pmb{v}}(h+1)=D_{\\boldsymbol{\\omega}}(h)$, between the singularity spectra of these two
vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.
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