Turbulent vorticity and helicity in stratified atmospheric boundary layer
Seminar Room 1, Newton Institute
AbstractTo measure the spatial derivative of velocity v, it is necessary to possess the sensors, which size much less than internal scale of turbulence. In a surface layer it is estimated by size of an order 1 mm. The concept of the acoustical method of vorticity measurements and the first results of its realization are obtained in IAP [Bovsheverov et al. 1971]. Helicity (a scalar product of the velocity v and the vorticity) is one of the important characteristics of large-scale atmospheric motions [Etling 1985, Moffat, Tsinober 1992; Kurgansky 2002, Chkhetiani 2001]. Direct experiments aimed at the measurement of turbulent helicity are extremely rare. They have been carried out under laboratory conditions in turbulence beyond a grid [Kholmyansky et al. 2001]. First helicity measurements in atmospheric boundary layer were made in IAP Zvenigorod station in 2004 [Koprov et al. 2005]. Experimental estimates of the spectrum of the turbulent helicity in the atmospheric boundary layer give the spectrum slope of about -5/3. Proceeding from the helicity and energy spectra, we obtain for dissipation ? ? 0.0003 m/s3, ? ? 0.003 m2/s3 and ? ? 0.0005 m/s3, ? ? 0.001m2/s3. Helicity components in day conditions shows considerably big intermittency than circulation. Average value for Hz has made 0.2 m/s2. The correlation factor between product factors in a day series at moderately unstable stratification has made 0.344. Similar indicators for Hx: average value of 0.46 m/s2, factor of correlation 0.215. In an evening series average values of both measured helicity components had the same sign, as in the afternoon, but on 1-2 order smaller values. Probability density functions (PDF) for circulations Zz, Zx, vertical velocity w and temperature T have been calculated at unstable and stable stratification. Asymmetry of Zz changes a sign at change of a sign on parameter of stratification whereas asymmetry for Zx is small and keeps a sign at any stratification. PDF of helicity components and complex triple two-point correlations of velocity and vorticity show strong non-gaussian character. Spectrum slope for these correlations is close to f -1. This fact corresponds to the "2/15" law for the helicity cascade [Chkhetiani 1996, 2010]. The data obtained for both the values of turbulent helicity in the atmospheric boundary layer and helicity spectra indicate the existence, at least in the region of the scales that have been considered, of parallel cas-cades of the energy and helicity. The importance of the determination of actual helicity cascades in natural systems is also stimulated by the fact that numerical calculations of the Navier-Stokes equations manifest certain effects of nonzero helicity on the energy transfer over the spectrum. This emphasizes the role of helicity in the formation of large-scale structures.
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