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John S. Carroll

Abstract

An experimental study of the vertical distribution of instantaneous local vertical temperature gradient and local temperature in terms of their first three moments and spectral properties is reported. These experiments were performed in air (Pr = 0.71) over the range 1.0 × 106 < Ra < 1 × 107. An approximate measure of the heat flux yielded the dependence Nu ≈ 0.21 Ra0.26. The shape of the vertical profiles of each variable and its moments is invarient with Ra (except at the level of inverse symmetry located at the mid-level in the fluid) when the vertical scale Z * = Nu Z/D is used. Based on the statistical properties observed, three vertical layers may be defined: 1) a conduction layer in which at least ½ of the heat flux is by conduction 0 ≲ Z * ≲ 0.5; 2) a transition or “power law” layer in which the nondimensional temperature gradient (β) ≈ Z −2, and 3) an interior region in which β ap; 0.0 and σ T Z −⅓.

Spectral data in the frequency domain for both gradient and temperature show a much stronger dependence on Z * than Ra. In general the bandwidth of variance increases with height for both variables but especially for temperature and at the lower frequencies. Spectra for temperature for Z * > 0.25 in a limited range of wavenumbers shows a distinctly bimodal or trimodal distribution with considerable variance at wavelengths λ ≲ 0.1 D and at λ ≳ D.

Comparison of the data with other relevant experiments is discussed. The model of Kraichnan (1962) is verified in nearly all major respects. The use of Z * and Z/L as similarity parameters between laboratory and the atmospheric surface boundary layer is proposed. In both laboratory and atmosphere, the vertical variation of the skewness in temperature appears to be the most sensitive indirect measure of the heat flux (NU or L).

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