On the local structure of helical turbulence

Abstract

513 The presence of helicity in correlation characteristics of turbulent flows is one of the observed manifestations of mirror-symmetry violation. Helicity is defined as the scalar product of the flow velocity and vorticity. Along with energy, helicity is a second-order invariant of the motion of an ideal fluid. This phenomenon is observed in both laboratory and natural geo- and astrophysical flows. Helical characteristics of turbulence related to the angular-moment accumulation in smallscale motions are among the main sources of magnetic field generation in rotating objects. Enhanced helicity is observed in many coherent vortex structures over a broad range of scales. This was devoted to the local structure of turbulent helicity. It is shown that the helicity dissipation can be determined from the results of simultaneous measurements of the velocity and vorticity components using the exact relations obtained previously [1] for the helical component of the third-order two-point correlation tensor. Among immediate consequences of these relations are (i) the power-law helicity spectrum with an exponent of ‐5/3, which has been obtained previously only qualitatively [2] and is now observed both under natural conditions and in numerical simulations [3‐5] and (ii) the more hypothetical helicity spectrum with an exponent of ‐4/3 that is typical “exclusively” of a helical cascade [2]. Very few measurements of helicity in turbulent flows are known, since such measurements are related to fairly complicated problems encountered in the measurement of multicomponent velocity-field gradients. The known experiments were carried out for turbulent flows behind a wire grid and in a jet [6, 7]. The existence of a helicity cascade, obeying a ‐5/ 3 power law, along with an energy cascade was confirmed by recent observations [8] of the atmospheric boundary layer at altitudes ~ 50 km [8] using an acoustic circulometer at the Obukhov Institute of Atmospheric Physics (Moscow) capable of measuring velocity and helicity simultaneously. The measured values of helicity were close to theoretical estimates. Without making hypotheses concerning the helicity cascade nature, let us consider correlation characteristics of homogeneous helical turbulence. The pair velocity correlation 〈 v i ( x ) v j ( x + r ) 〉 is described by the following function: