Abstract
Length scales determined by maximum turbulent kinetic energy (TKE), the integral scale, and two length scales based on Reynolds stress-tensor anisotropy are compared to the often stated outer length scales of boundary-layer depth and distance from the earth’s surface, \(z\). The scales are calculated using sonic anemometer data from two elevations, 5 and 50 m above the ground at the main tower site of the CASES-99 field campaign. In general, none of these scales agrees with the other, although the scale of maximum TKE is often similar to the boundary-layer depth during daytime hours, and the length scales derived from anisotropy characteristics are sometimes similar to \(\kappa \!z, z\), and \(2z\) depending on scale definition and thermal stability. Except for the scale with the strictest isotropy threshold, the turbulence is anisotropic for each of the various candidates for the outer scale. Length scales for maximum buoyancy flux and temperature variance are evaluated and the turbulence characteristics at these scales are almost always found to be anisotropic.
Highlights
Turbulent motion of a fluid occurs over a broad range of scales
And the maximum turbulent kinetic energy (TKE) scale is the scale at which the sum of the spectra of the variances is a maximum
The length scale of maximum TKE is determined from the multiresolution spectral peaks and the integral scale is determined from wind-speed autocorrelation calculations
Summary
Turbulent motion of a fluid occurs over a broad range of scales. The smallest scales are usually defined as the scale at which the motion dissipates into heat due to the viscosity of the fluid. Most turbulence text books and turbulence applications use either the outer scale or integral scale as the term to describe the larger scales of turbulent motion (Hinze 1959; Tatarski 1961; Tennekes and Lumley 1972; Schlichting 1987; Gifford 1989; Kaimal and Finnigan 1994; Stull 1997) In this context, the outer scale is the largest scale of turbulence at the point of measurement, not to be confused with the outer-layer scale that is associated with the scales of turbulence far from the surface. At the rate of 20 data points s−1, sonic anemometers can resolve scales only down to about 0.5 m at wind speeds typical of the CASES-99 experiment This is nowhere near the scale of dissipation, ∼1 mm, but is adequate for examining the outer scale.
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