The anisotropy of boundary layer turbulence dictates there are at least two independent time- and height-dependent time scales characterizing the correlation behavior of the turbulence. A useful model for second-order correlation analysis of boundary layer turbulence thus consists of characterizing the instantaneous turbulence velocity u(Z,t) as the sum of two independent velocities. Here u(Z,t) is the longitudinal component of the turbulence measured as a time series at a height Z above the ground.
One of these velocities designates the isotropic part of the turbulence and scales with one scale while the other designates the anisotropic part and scales with a different scale. With this model, though, the key to an effective scale-characterization of the anisotropy requires a model of the isotropic sub-structure which reflects all known features of the autocorrelation f of the isotropic part in: (i) the dissipation range; (ii) the inertial subrange; and (iii) the large-scale domain.
We propose a simple closure for the K‡rm‡n-Howarth (K-H) equation which produces the correct features emphasized above. By "simple" we mean a closure in which the transfer term in the K-H equation is linear in the first derivative of f and thus yields an f which is greater than or equal to zero for all values of the time-lag (tau). The physical implications of this consequence are discussed. The proposed closure is a combination of the closures reported by Oberlack and Peters (1993) and Domaradzki and Mellor (1984) and invokes a formulation employed by Batchelor (1951) to capture the tau**2/3 dependence in f.
This approach will be tested using real atmospheric boundary layer turbulence data.
Batchelor, G. K., Proc. Camb. Phil. Soc. 47, 359 (1951).
Domaradzki, J. A., and Mellor, G. L., J. Fluid Mech. 140, 45 (1984).
Oberlack, M. and Peters, N., Appl. Sci. Res. 51, 533 (1993).