It is widely thought that in steady, gravity-driven, unobstructed soap-film flows, the velocity increases monotonically downstream. Here we show experimentally that the velocity increases, peaks, drops abruptly, then lessens gradually downstream. We argue theoretically and verify experimentally that the abrupt drop in velocity corresponds to a Marangoni shock, a type of shock related to the elasticity of the film. Marangoni shocks induce locally intense turbulent fluctuations and may help elucidate the mechanisms that produce two-dimensional turbulence away from boundaries.

In the Letter we refer to the point x ? , where the derivative of the velocity of the flow becomes singular, as the ''theoretical position of the shock.'' Note, however, that for consistency with our simple model of the flow [Eq.(2)] the theoretical position of the shock should be computed using the Rayleigh jump condition, which can be found in note 13 of the Letter. (We thank François Blanchette and Morris R. Flynn for bringing this point to our attention.) Although the Rayleigh jump condition places the shock slightly downstream of x ? , the interpretation of the experiments does not depend on the exact position of the shock, and remains valid as it appears in the Letter.

A photon correlation method is introduced for measuring components of the shear rate tensor in a turbulent soap film. This new scheme, which is also applicable to three-dimensional flows, is shown to give the same results as Laser Doppler velocimetry, but with less statistical noise. The technique yields the mean shear rate s, its standard deviation σ, and a simple mathematical transform of the probability density function P (s) of the shear rate itself.

We report measurements of the superfluid density, λ −2 (T ), in ferromagnet-on-superconductor (F/S) bilayers and S/F/S' trilayers comprising Nb with Ni, Py, CoFe, and NiV ferromagnets. Bilayers provide information about F/S interface transparency and the T dependence of λ −2 that inform interpretation of trilayer data. The Houzet-Meyer (H-M) theory accounts well for the measured dependence of λ −2 (0) and T c of F/S bilayers on thickness of F layer, d F , except that λ −2 (0) is slightly under expectations for CoFe/Nb bilayers. For Nb/F/Nb' trilayers, we are able to extract T c and and λ −2 for both Nb layers when F is thick enough to weaken interlayer coupling. The lower "T c " is actually a crossover identified by onset of superfluid in the lower-T c Nb layer. For Nb/NiV/Nb' trilayers, λ −2 (0) vs. d F for both Nb layers has a minimum followed by a recovery, suggestive of a π-junction.