Calculation of shear and strain

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alex alex
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Calculation of shear and strain

I'm a little confused when it comes to the calculation of strain and shear rate. I know, what the matlab codes does

Gradient of u-velocity: [px1 py1] = gradient(u, hx, hy);
Gradient of v-velocity: [qx2 qy2] = gradient(v, hx, hy);

which gives the data for

px1 = du/dx, py1 = du/dy
qx2 = dv/dx, qy2 = dv/dy

To get the shear rate, pivlab calculates du/dy+dv/dx and for the strain rate du/dx-dv/dy.  If i comapre the calculation of a counter-rotating vortex pair with the literature (eg. Steinberg and Driscoll, 2009 http://www.sciencedirect.com/science/article/pii/S0010218009001850), I get the same results with artificial image pairs only if i calculate du/dx - dv/dy. But they say, the strain rate is calculated using du/dy + dv/dx, which would be the shear rate in pivlab and gives totally different results. Where is my mental error?

If I compare the calculated vorticity via the curl-function and the gradient dv/dx-du/dy, I get the same results, as it should be the case, but strain and shear totally confuse me. Maybe that's why chemists shouldn't touch the field of fluid dynamics, but still... can anybody enlighten me?