Experimental determination of the von K\'{a}rm\'{a}n constant in turbulent two dimensional soap film flows*

We report measurements in both the viscous layer and in the log region of a two dimensional (2D) flowing soap film. The turbulence is created by a horizontal grid (a comb) and decays downstream where measurements are made. We report a sequence of measurements at film width Reynolds numbers of 10${^4}$ -10${^5}$, and fit our velocity profile data to a putative law of the wall form which is a reasonable representation of our data at the higher Reynolds numbers studied. We report our results for the von K\'{a}rm\'{a}n constant, and compare with calculations from theory and numerical simulation. Our findings indicate that the von K\'{a}rm\'{a}n constant in 2D is less than the accepted value in 3D.