On the initial formation of a defect structure in a two-dimensional mixing layer

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Abstract
Dislocations in the wave fronts downstream of the splitter plate in a two-dimensional (2-D) mixing layer are produced by oscillating two semi-span-flaps at different frequencies. Two frequency ratios are studied, 11:10 and 5:4. The vortices which grow from the two initially unstable wave trains form in the ratio of the frequencies: There are nh vortices per beat cycle on the high-frequency side, and nl vortices per beat on the low-frequency side. The vortices interact in a central, interconnection zone. Dye injected from the splitter plate is swept into the vortices and recorded with a video camera. Two injection methods are used, sheet injection for full viewing of the interconnection zone, and point injection for estimates of spanwise velocity. For a given frequency ratio the spanwise velocity scales with the parameter, d/λh, where λn is the wavelength corresponding to the higher frequency, and d is the phase separation between wave crests. Furthermore, addition of the parameter, ζ2=(nh/nl)2, scales the results for the two separate frequency ratios.