MATLAB Examples

# Example

The uniform-shear model is computed with the parameters used in Mann (1998) [1] and compared to the spectra from the Great belt experiment, which are displayed in Mann (1994). The three parameters of the uniform-shear model are:

1. , referred to as "alphaEps "
1. , referred to as "GAMMA"
1. , referred to as "L"

References: [1] Mann, J. (1994). The spatial structure of neutral atmospheric surface-layer turbulence. Journal of fluid mechanics, 273, 141-168.

## Initialisation

Basic parameter definitions

clearvars;close all;clc; U = 22.3; % Mean wind speed (m/s) z = 70; % altitude (m) GAMMA = 3.2; L = 61; % m alphaEps =0.11; % m^(4/3)/s^2 % frequency steps N1=100; k2max = log10(100); k3max = log10(100); k2min = -6; k3min = -6; % frequency vector f = logspace(log10(1/3600),log10(10),N1); %wavenumber k1 = 2*pi.*f./U; 

## Computation of the uniform shar model

% Compute Mann spectral tensor tic [PHI,k2,k3,k11,k2_log,k3_log] = MannTurb(alphaEps,GAMMA,L,'N1',N1,'N2',100,'N3',100,'k2max',k2max,'k3max',k3max,'k2min',k2min ,'k3min',k3min); toc 
Elapsed time is 10.096575 seconds. 

## Computation the corresponding single point spectra

FM= squeeze(trapz(k3_log,trapz(k2_log,PHI,2),3)); % Single point spectra is chosen FM = FM(end-N1+1:end,:,:); % set Suv = 0 and Svw = 0 FM(:,1,2)=0; FM(:,2,1)=0; FM(:,2,3)=0; FM(:,3,2)=0; 

## Comparison with the wind spectra from the great belt bridge experiment

% Load the spectral data estimated with a digitalization software from Mann (1994), so the resolution is not perfect load('GreatBeltSpectra.mat') clf;close all; figure hold on;box on; plot(k11,k11'.*FM(:,1,1),'k',k11,k11'.*FM(:,2,2),'r',k11,k11'.*FM(:,3,3),'b',k11,k11'.*FM(:,1,3),'g'); plot(fu1,Su1,'k.--',fv1,Sv1,'r.--',fw1,Sw1,'b.--',fuw1,Suw1,'g.--') legend('Computed (u)','Computed (v)','Computed (w)','Computed (uw)','full-scale (u)','full-scale (v)','full-scale (w)','full-scale (uw)','location','northeast') set(gca,'Xscale','log') ylim([-0.2,0.5]) xlim([0.0005,0.5]) xlabel('k_{1} (m^{-1}) ') ylabel('k_{1} Fij, (i,j) = (u,v,w)'); grid on grid minor set(gcf,'color','w') 

## Computation of the wind co-coherence

Warning: Due to the particular numerical implementation, there exist
potentialy large numerical errors at high frequency, which have been put as "nan" in the
present code.
% lateral separation dy = 15; % lateral separation (m) dz = 0; % vertical separation (m) tic [newK1,coh] = MannCoherence(PHI,k11,k2,k3,dy,dz,k2_log,k3_log); toc figure hold on;box on; plot(newK1.*dy,squeeze(coh(1,1,:)),'k',newK1.*dy,squeeze(coh(2,2,:)),'r',newK1.*dy,squeeze(coh(3,3,:)),'b') xlabel('k_{1} dy ') ylabel('co-coherence'); legend('u','v','w') grid on grid minor set(gcf,'color','w') xlim([0,2]) % vertical separation dy = 0; % lateral separation (m) dz = 20; % vertical separation (m) tic [newK1,coh] = MannCoherence(PHI,k11,k2,k3,dy,dz,k2_log,k3_log); toc figure hold on;box on; plot(newK1.*dz,squeeze(coh(1,1,:)),'k',newK1.*dz,squeeze(coh(2,2,:)),'r',newK1.*dz,squeeze(coh(3,3,:)),'b') xlabel('k_{1} dz ') ylabel('co-coherence'); legend('u','v','w') grid on grid minor set(gcf,'color','w') xlim([0,2]) 
Elapsed time is 11.211229 seconds. Elapsed time is 11.464289 seconds.