# Find Q-criterion and Lambda2 from velocity values

조회 수: 72 (최근 30일)
Hussein Kokash 2021년 10월 19일
편집: Nick Battista 2024년 5월 15일
Hello everyone, hope you are doing great.
I have a matlab code which reads a file that has x, y and z velocity values, as well as corresponding time for each value this is what it looks like:
clear all; clc
[file_list, path_n] = uigetfile('.txt', 'Multiselect', 'on');
filesSorted = natsortfiles(file_list);
if iscell(filesSorted) == 0;
filesSorted = (filesSorted);
end
for i = 1:length(filesSorted);
filename = filesSorted{i};
data = load([path_n filename]);
% Define x and y from the uploaded files
x = data (:,1);
y = data (:,2);
% Define Time for each value of the uploaded files
Time(i) = data (1,3);
Time_tp = Time';
end
Is there a way to get Lambda2 "λ" and Q-criterion values from the velocity data?
Thank you so much, stay safe

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### 답변 (1개)

Martino Pinto 2024년 1월 5일
편집: Martino Pinto 2024년 1월 5일
Hi! Here's a couple of functions that will do it:
function lambda2 = computeL2Criterion(u,v,w,grid_h)
% Computes the lambda2 criterion from the cartesian velocity
% field u,v,w and the grid spacing grid_h
[du_dx, du_dy, du_dz] = gradient(u,grid_h);
[dv_dx, dv_dy, dv_dz] = gradient(v,grid_h);
[dw_dx, dw_dy, dw_dz] = gradient(w,grid_h);
lambda2 = zeros(size(u));
for i = 1:size(u, 1)
for j = 1:size(u, 2)
for k = 1:size(u, 3)
% Calculate the symmetric and anti-symmetric parts of the velocity gradient tensor
S = [du_dx(i,j,k), (du_dy(i,j,k) + dv_dx(i,j,k)) / 2, (du_dz(i,j,k) + dw_dx(i,j,k)) / 2;
(dv_dx(i,j,k) + du_dy(i,j,k)) / 2, dv_dy(i,j,k), (dv_dz(i,j,k) + dw_dy(i,j,k)) / 2;
(dw_dx(i,j,k) + du_dz(i,j,k)) / 2, (dw_dy(i,j,k) + dv_dz(i,j,k)) / 2, dw_dz(i,j,k)];
Omega = [0, (du_dy(i,j,k) - dv_dx(i,j,k)) / 2, (du_dz(i,j,k) - dw_dx(i,j,k)) / 2;
(dv_dx(i,j,k) - du_dy(i,j,k)) / 2, 0, (dv_dz(i,j,k) - dw_dy(i,j,k)) / 2;
(dw_dx(i,j,k) - du_dz(i,j,k)) / 2, (dw_dy(i,j,k) - dv_dz(i,j,k)) / 2, 0];
M = S*S + Omega*Omega; % Combine deformation and rotation
eigenvalues = eig(M);
eigenvalues = sort(eigenvalues, 'descend');
lambda2(i,j,k) = eigenvalues(2);
end
end
end
end
function Q = computeQCriterion(U, V, W, grid_h)
% Computes the lambda2 criterion from the cartesian velocity
% field u,v,w and the grid spacing grid_h
[dxU, dyU, dzU] = gradient(U, grid_h);
[dxV, dyV, dzV] = gradient(V, grid_h);
[dxW, dyW, dzW] = gradient(W, grid_h);
S_xx = dxU;
S_yy = dyV;
S_zz = dzW;
S_xy = 0.5 * (dyU + dxV);
S_xz = 0.5 * (dzU + dxW);
S_yz = 0.5 * (dzV + dyW);
Omega_xy = 0.5 * (dyU - dxV);
Omega_xz = 0.5 * (dzU - dxW);
Omega_yz = 0.5 * (dzV - dyW);
Q = 0.5 * ((Omega_xy.^2 + Omega_xz.^2 + Omega_yz.^2) - ...
(S_xx.^2 + S_yy.^2 + S_zz.^2 + 2*(S_xy.^2 + S_xz.^2 + S_yz.^2)));
end
##### 댓글 수: 2없음 표시없음 숨기기
William Thielicke 2024년 2월 15일
How would computeQCriterion look like if the data is only 2-dimensional (U and V)?
Nick Battista 2024년 5월 14일
편집: Nick Battista 2024년 5월 15일
I believe Q-Criterion in two-dimensions would look like the following (PS- thanks for PIVlab; love it!)
function Qcrit = give_Me_Q_Criterion(U,V,dx,dy)
% U: horizontal component of velocity field (matrix)
% V: vertical component of velocity field (matrix)
% dx,dy: grid spacing
% Function that computes partial derivative of U with respect to x
dudx = D(U,dx,'x');
% Function that computes partial derivative of V with respect to x
dvdx = D(V,dx,'x');
% Function that computes partial derivative of U with respect to y
dudy = D(U,dy,'y');
% Function that computes partial derivative of V with respect to y
dvdy = D(V,dy,'y');
%-------------------------------------------------------
% Q Criterion (2d) = -Uy.*Vx - 0.5*Ux.^2 -0.5*Vy.^2
%-------------------------------------------------------
Qcrit = -dudy.*dvdx - 0.5*dudx.^2 - 0.5*dvdy.^2;

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