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Eddy structure in the convective boundary layer—new measurements and new concepts
Author(s) -
Hunt J. C. R.,
Kaimal J. C.,
Gaynor J. E.
Publication year - 1988
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49711448202
Subject(s) - skewness , convective boundary layer , eddy , physics , wavenumber , turbulence , convection , spectral line , boundary layer , second moment of area , anisotropy , computational physics , planetary boundary layer , meteorology , mechanics , mathematics , optics , thermodynamics , statistics , quantum mechanics
An analysis is developed for the eddy structure in the convective boundary layer (CBL) both in terms of thermals and downdraughts and in terms of moments, spectra and cross‐correlations of the vertical component of velocity, w . Using previous measurements of the area of thermals, we calculate the contributions from the average velocity 〈 W U 〉 in updraughts and (wD) in downdraughts to the total variance w̄ 2 and the third moment w̄ 3 . We conclude that the variability in 〈 W U 〉 (i.e. variance and skewness) produces more than half the contributions to w̄ 2 and w̄ 3 . The mean value of 〈 W D 〉 is the major contributor to the mode w̄ 2 in the probability distribution of w, but small‐scale turbulence is also important. The results of a statistical theory of eddies near the ground is explained in physical terms, in particular the cross‐correlation of w at two points (normalized on w̄ 2 at the reference height Zr) in the lower part of the CBL, R zzr = z/z, where zr > z. The new theory for the cospectrum of w 2 and w accounts for the contribution by the thermals at large scales and predicts that the eddies at small scaies are anisotropic, leading to a universal cospectral form that falls off as k −2 at the high frequency end ( k being the wavenumber). Measurements at the Boulder Atmospheric Observatory in convective conditions are presented for a range of zi/L values (zi is depth of the CBL and L the Monin‐Obukhov length). The results for w̄ 3 and w̄ 3 plotted in mixed layer variables, agree with measurements made over the sea and over flat land for z < 0.5zi. The mode, w̌ shows some variation with height, and reaches a maximum value of 0.5 w *, where w * is the convection velocity. Rzzr agrees with the theoretical prediction to within ±20%. The cospectra of w at z and z r also conform to the theoretical form but with large scatter at low frequencies. All these measurements, except for w̄ 2 are effectively functions of z/zi and independent of zi/L, even when |z/L| w̄ 3 1, because they are controlled by large‐scale motions. It is shown that the small scales provide an increasing proportion of w̄ 3 as z/zi decreases. This explains why large eddy simulations (LES) give incorrect values of w̄ 3 but correct values of w 3 /δz. The implications of these results for diffusion calculations and LES modelling are discussed.