Inhomogeneous Turbulence in the Vicinity of a Large Scale Co- Herent Vortex

– We study the statistics of turbulent velocity fluctuations in the neighbourhood of a strong large scale vortex at very large Reynolds number. At each distance from the vortex core, we observe that the velocity spectrum has a power law " inertial range " of scales and that intermittency – defined as the variation of the probability density function (PDF) of velocity increments as the length of the increment is varied – is also present. We show that the spectrum scaling exponents and intermittency characteristics vary with the distance to the vortex. They are also influenced by the large scale dynamics of the vortex. Introduction. – Much efforts have been devoted to the study of high Reynolds number turbulence, assuming the properties of local homogeneity and isotropy. Under these assumptions it has been shown [1] that, in between the integral scale at which energy is fed into the flow and the dissipative scale at which viscosity smoothes out the velocity gradients, there exists an " inertial range " where: (i) the velocity spatial power spectrum follows a power law E(k) ∼ ǫ 2/3 k −5/3 , (ii) the energy transfer rate ǫ is related to the third order structure function S 3 (r) = δu 3 (r) = −