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| %% EXAMPLE 10: Adaptive sine-taper SPOD. | ||
| % The time-resolved particle image velocimetry data provided along with | ||
| % this example are a subset of the database of a Mach 0.6 turbulent open | ||
| % cavity flow by Zhang et al. [1]. If you are using the database in your | ||
| % research or teaching, please include explicit mention of Zhang et al. | ||
| % [1]. The test database consists of 4000 snapshots of the streamwise | ||
| % velocity component of a turbulent open cavity flow. This is a canonical | ||
| % example of a mixed broadband-tonal turbulent flow, which requires sharp | ||
| % peak resolution at tonal frequencies and smooth spectrum estimates of | ||
| % broadband regions. If you are using this code for your research, please | ||
| % cite Yeung & Schmidt [2]. | ||
| % | ||
| % References: | ||
| % [1] Zhang, Y., Cattafesta, L. N., and Ukeiley, L., Spectral analysis | ||
| % modal methods (SAMMs) using non-time-resolved PIV, Exp. Fluids 61, 226, 1–12, 2020, | ||
| % DOI 10.1007/s00348-020-03057-8 | ||
| % [2] Yeung, B. C. Y., Schmidt, O. T. Adaptive spectral proper orthogonal decomposition | ||
| % of broadband-tonal flows, Theor. Comput. Fluid Dyn. 38, 355–374, 2024, | ||
| % DOI 10.1007/s00162-024-00695-0 | ||
| % | ||
| % B. Yeung (byeung@ucsd.edu) and O. T. Schmidt (oschmidt@ucsd.edu) | ||
| % Last revision: 10-Sep-2024 | ||
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| clc, clear variables | ||
| addpath('utils') | ||
| load(fullfile('cavity_data','cavityPIV.mat'),'u','x','y','dt'); | ||
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| %% Standard Welch SPOD of the test database using one sine window. | ||
| % We manually specify a window length of 256 and an overlap | ||
| % of 128 snaphots. A sine function is automatically used as the window. | ||
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| % SPOD using a sine window of length 256 and 128 snaphots overlap | ||
| nDFT = 256; | ||
| nOvlp = 128; | ||
| [L,P,f] = spod_adapt(u,nDFT,[],nOvlp,dt); | ||
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| %% Plot the SPOD spectrum and some modes. | ||
| figure | ||
| loglog(f,L) | ||
| xlabel('frequency'), ylabel('SPOD mode energy'), title('Welch SPOD') | ||
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| %% Multitaper SPOD using six sine windows. | ||
| % We can achieve higher frequency resolution and resolve down to lower | ||
| % minimum frequencies using six sine windows of length equal to the | ||
| % number of snapshots. Specify nWin as a vector of length 4000. | ||
| % Multitaper SPOD neither requires nor benefits from overlap, so we leave | ||
| % nOvlp empty. | ||
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| % SPOD using six sine windows of length 4000 and 0 overlap | ||
| nWin = 6*ones(size(u,1),1); | ||
| [L,P,f] = spod_adapt(u,nWin,[],[],dt); | ||
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| %% Plot the SPOD spectrum. | ||
| figure | ||
| loglog(f,L) | ||
| xlabel('frequency'), ylabel('SPOD mode energy'), title('multitaper SPOD') | ||
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| %% Adaptive multitaper SPOD. | ||
| % To combine both sharp peak resolution and smooth spectrum estimates of | ||
| % broadband regions, we allow the window number to vary with frequency. | ||
| % The adaptive algorithm requires only a tolerance and determines the | ||
| % window number autonomously. No spectral estimation parameters | ||
| % are needed. | ||
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| % SPOD using the adaptive algorithm with a tolerance of 1e-4 | ||
| % Can take a long time to compute | ||
| clear opts | ||
| opts.adaptive = true; | ||
| opts.tol = 1e-4; | ||
| [L,P,f,~,nWin] = spod_adapt(u,[],[],[],dt,opts); | ||
|
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| %% Plot the SPOD spectrum and window number. | ||
| figure | ||
| yyaxis left | ||
| loglog(f,L) | ||
| xlabel('frequency'), ylabel('SPOD mode energy'), title('adaptive multitaper SPOD') | ||
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| yyaxis right | ||
| semilogx(f,nWin) | ||
| ylabel('number of windows') | ||
|
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| %% Plot some SPOD modes (Rossiter modes) | ||
| figure | ||
| count = 1; | ||
| for fi = [470 770 1063] | ||
| for mi = [1 2] | ||
| subplot(3,2,count) | ||
| contourf(x,y,real(squeeze(P(fi,:,:,mi))),11,'edgecolor','none'), axis equal tight, clim(max(abs(clim))*[-1 1]) | ||
| xlabel('x'), ylabel('y'), title(['f=' num2str(f(fi),'%.2f') ', mode ' num2str(mi) ', \lambda=' num2str(L(fi,mi),'%.2g')]) | ||
| count = count + 1; | ||
| end | ||
| end | ||
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| % %% Multitple SPOD using non-uniform window number. | ||
| % % If the (potentially non-uniform) window number is known a priori, e.g., | ||
| % % based on physical knowledge, it can be provided directly. As an example, | ||
| % % we use the nWin computed previously to recover the same results as before. | ||
| % | ||
| % % SPOD using sine windows of length 4000, 0 overlap, and | ||
| % % frequency-dependent window number | ||
| % if length(nWin)<size(u,1), nWin(size(u,1)) = 0; end % zero-pad nWin to length 4000 | ||
| % [L,P,f] = spod_adapt(u,nWin,[],[],dt); | ||
| % | ||
| % %% Plot the SPOD spectrum. | ||
| % % The spectrum should be identical to the previous figure. | ||
| % figure | ||
| % loglog(f,L) | ||
| % xlabel('frequency'), ylabel('SPOD mode energy'), title('multitaper SPOD with non-uniform window number') |
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