All pages tagged intermittency

Real turbulent flows display intense and short lived velocity fluctuations. This is the phenomenon of intermittency. In 1934 Leray introduced the idea of finite time singularities of the incompressible fluid equations with smooth initial data. Leray singularities occur at given points of space and time. Their analysis give a precise relation between the large velocity and the large acceleration one should observe, a result opposite to the prediction of K41 scaling laws. Leray-like scaling are amazingly well verified in the velocity records of turbulence measured in Modane wind tunnel. I'll introduce Leray's idea and make the connection with the presentation by Christophe Josserand at this conference.

By using a stereoscopic imaging technique, we could obtain a space-time resolved measurement of wave turbulence at the surface of water in a 13-m diameter tank. Wave are excited by meter-sized wedge wave makers that are close to omnidirectional. A frequency-wavenumber analysis shows that a turbulent regime develops that is made of a superposition of free waves and bound waves as expected for gravity surface waves. These bound waves result from triadic nonlinear interaction that provide energy to Fourier modes that are not lying on the linear dispersion relation (and thus non resonant). By performing a filtering in the Fourier space, we can remove the bound wave contribution to keep only the free wave one and we show, first, that the observed weak turbulence is indeed weakly nonlinear and, second, that the filtered field is much closer to Gaussian statistics. Furthermore the observed intermittency is strongly reduced so that the free-wave field is close to Gaussian at all scales.