Structure functions in nocturnal atmospheric boundary layer turbulence

This paper analyzes odd and even higher-order moments for longitudinal velocity increment Delta u(x, r), where x is the longitudinal coordinate and r is the separation distance, based on the canonical and a modified normalization for skewness of longitudinal velocity derivative partial derivative u/partial derivative x. Two types of data were used, stably stratified turbulence data from the nocturnal atmospheric boundary layer taken during the Mountain Terrain Atmospheric Modeling and Observations field campaign and from the direct numerical simulation of homogeneous and isotropic turbulence in a box at four Reynolds numbers and four different grid resolutions. Third moment data normalized by the same moment of third order for modulus vertical bar Delta u(x, r)vertical bar representing modified skewness of the velocity increment showed a better collapse at all Reynolds numbers in the inertial and viscous subranges than canonical normalized skewness with normalization parameter <(Delta u(x, r))(2)>(3/2), where <..> represents the ensemble average. The analysis also considered odd pth-order classical structure functions <Delta u(x, r)(P)> with Kolmogorov-theory based normalization <Delta u(x, r)(P)>/(epsilon r)(P/3) for the inertial subrange, where s is the rate of dissipation, and a modulus-based structure function <vertical bar Delta u(x, r)vertical bar(P)>/(epsilon r)(P/3). Both types of structure functions of order p = 1-6 were computed using different normalizations, and corresponding scaling exponents were assessed for the inertial and viscous subranges. Scaling for modulus-based structure functions in the viscous subrange was identified as <vertical bar Delta u(x, r)vertical bar(P)> proportional to r(P.(5/6)). In the viscous subrange, the velocity increment varied linearly with r for the classical third moment <Delta u(x, r)(3)> proportional to r(3) based on the velocity increment while the classical fifth moment <Delta u(x, r)(5)> did not provide any meaningful scaling exponent. A plausible qualitative explanation linking these effects to anisotropy of nocturnal stratified turbulence is proposed.