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Register a new userScaling properties in the production range of shear dominated flows
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Added by
Carlo Massimo Casciola
Publication date
2005
fields
Physics
and research's language is
English
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Recent developments in turbulence are focused on the effect of large scale anisotropy on the small scale statistics of velocity increments. According to Kolmogorov, isotropy is recovered in the large Reynolds number limit as the scale is reduced and, in the so-called inertial range, universal features -namely the scaling exponents of structure functions - emerge clearly. However this picture is violated in a number of cases, typically in the high shear region of wall bounded flows. The common opinion ascribes this effect to the contamination of the inertial range by the larger anisotropic scales, i.e. the residual anisotropy is assumed as a weak perturbation of an otherwise isotropic dynamics. In this case, given the rotational invariance of the Navier-Stokes equations, the isotropic component of the structure functions keeps the same exponents of isotropic turbulence. This kind of reasoning fails when the anisotropic effects are strong as in the production range of shear dominated flows. This regime is analyzed here by means of both numerical and experimental data for a homogeneous shear flow. A well defined scaling behavior is found to exist, with exponents which differ substantially from those of classical isotropic turbulence. Contrary to what predicted by the perturbation approach, such a deep alteration concerns the isotropic sector itself. The general validity of these results is discussed in the context of turbulence near solid walls, where more appropriate closure models for the coarse grained Navier-Stokes equations would be advisable.
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The Refined Kolmogorov Similarity Hypothesis is a valuable tool for the description of intermittency in isotropic conditions. For flows in presence of a substantial mean shear, the nature of intermittency changes since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. In these conditions a new form of refined similarity law has been found able to describe the increased level of intermittency which characterizes shear dominated flows. Ideally a length scale associated with the mean shear separates the two ranges, i.e. the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. However, the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observed individually. In the present letter we give evidence of the coexistence of the two regimes and support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data.
A logarithmic scaling for structure functions, in the form $S_p sim [ln (r/eta)]^{zeta_p}$, where $eta$ is the Kolmogorov dissipation scale and $zeta_p$ are the scaling exponents, is suggested for the statistical description of the near-dissipation range for which classical power-law scaling does not apply. From experimental data at moderate Reynolds numbers, it is shown that the logarithmic scaling, deduced from general considerations for the near-dissipation range, covers almost the entire range of scales (about two decades) of structure functions, for both velocity and passive scalar fields. This new scaling requires two empirical constants, just as the classical scaling does, and can be considered the basis for extended self-similarity.
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