The transverse velocity fluctuation in the wake of a circular cylinder was measured…
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Fluids & Continuum Physics · Data analysis and model fitting in the laboratory
Fluid Dynamics, Ch Transition to turbulence
Problem
The transverse velocity fluctuation in the wake of a circular cylinder was measured at several Reynolds numbers just above the onset of vortex shedding. The mean-square fluctuation v′2 (in mm2s−2) was recorded as: Data (Re, v′2 in mm2s−2): (50,6.0), (60,24.0), (70,48.0), (80,66.0). Close to a supercritical Hopf bifurcation at Rec, the Landau equation predicts that the saturated mean-square amplitude should rise linearly with Re, v′2=m(Re−Rec), for some constant m.
((a)) Fit a least-squares straight line v′2=mRe+c to the four points, and give m and c.
((b)) Use the intercept to find Rec, and compare it with the accepted value Rec≈47 for a circular cylinder.
((c)) Compute the difference between each measured point and the fitted line, and use the size of these differences, relative to the range of v′2 spanned by the data, to decide whether the measurements are consistent with the square-root law of a supercritical Hopf bifurcation, or point instead to some other kind of onset.