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⛄ 内容介绍
A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate epsilon, the length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, the Richardson number Ri, and the normalized rate of destruction of temperature variance eta(theta) equivalent to epsilon(theta)/epsilon. Here, the latter two parameters are collapsed into a single atmospheric stability parameter z/L usingMonin-Obukhov similarity theory, where z is the height above the Earth's surface, and L is the Obukhov length corresponding to {Ri ,eta(theta)}. Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale similar to 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.
⛄ 部分代码
Fitting the stability-corrected uniform-shear model
This example calls the function fitChougule to estimate the three (or four) parameters of the stability-corrected uniform shear model. The fitting procedure can include "missing information". For example, one may not know everything about the three velocity components or atmospheric stability. Thus, the fitting algorithm attempt to reconstruct the spatial structure of turbulence knowing only a fraction of it. The fitting algorithm is similar as fitMann [1]
[1] E. Cheynet (2022). Fitting the Uniform Shear Model to real data. Zenodo, 2020, doi:10.5281/ZENODO.3774088.
Table of Contents
Definition of the target parameters and model
Case 1: The stability parameter is unknown
Case 2: Only the along-wind velocity component is known
Case 3: Only the along-wind and across-wind velocity components are known
Case 4: Only the vertical velocity component is known
Definition of the target parameters and model
clearvars;close all;clc;
zeta = 0.6; % non dimensional stability parameter z0 = z/L
GAMMA = 3.2; % Shear parameter
L = 10; % m turbulence length scale
alphaEps =0.05; % m^(4/3)/s^2
% frequency steps
N1 = 30; % number of frequency steps
myIter = 10; % Number of iterationto solve the RDT equations
tic
[PHI,k11,k2_log,k3_log] = ChouguleTurb(alphaEps,GAMMA,L,zeta,'N1',N1,'Niter',myIter);
FM0= squeeze(trapz(k3_log,trapz(k2_log,PHI,2),3));
Su_Ch= FM0(end-N1+1:end,1,1)';
Sv_Ch= FM0(end-N1+1:end,2,2)';
Sw_Ch= FM0(end-N1+1:end,3,3)';
Suw_Ch= FM0(end-N1+1:end,1,3)';
k11_Ch = k11;
toc
% Plot the target spectra and cross-spectra
clf;close all;
figure
semilogx(k11,k11.*Su_Ch);
set(gca,'yscale','lin')
hold on
semilogx(k11,k11.*Sv_Ch);
semilogx(k11,k11.*Sw_Ch);
semilogx(k11,k11.*Suw_Ch);
xlabel('$k_1$ (m$^{-1}$)','interpreter','latex')
ylabel('$k_1 F(k_1) $ (m s$^{-2}$)','interpreter','latex')
axis tight
set(gcf,'color','w')
axis tight
grid on
grid minor
legend('u','v','w','uw')
⛄ 运行结果
⛄ 参考文献
[1] Chougule, A., Mann, J., Kelly, M., & Larsen, G. C. (2018). Simplification and validation of a spectral-tensor model for turbulence including atmospheric stability. Boundary-Layer Meteorology, 167(3), 371-397.
[2] E. Cheynet (2022). Uniform shear model including atmospheric stability. Zenodo. Retrieved yyyy-mm-dd. doi:10.5281/zenodo.3774066
