Figure 1

The new soap-film channel. (a) The film (shown in gray shading) hangs between two steel blades (shown in black shading) that are suspended using fishing lines (shown as thin solid lines) kept taut by weight W. The spacing between the blades sets the width of the channel $w$, which we vary between 1 and 3 cm. The blades are 0.5 mm thick (in the direction normal to the plane of the figure), 1.2 m long, and $\approx 1\mathrm{cm}$ wide. One of the blades has a serrated edge (size of the serrations $\approx 2\mathrm{mm}$; spacing between serrations $\approx 4\mathrm{mm}$). Reservoir RT contains a Newtonian soapy solution (2.5% of the commercial detergent “Dawn Nonultra” in water; kinematic viscosity $\nu =0.01{\mathrm{cm}}^2{\mathrm{s}}^{-1}$, the same as for pure water) [22], which flows through valve $V$ (which we use to control the flow rate) and into the film. The soapy solution is collected into reservoir RB and returned to reservoir RT through pump P. We carry our measurements of the frictional drag only on the straight edge of the channel, at distances of at least 30 cm and up to 85 cm from the inlet. (b) The film may be pierced with a cylindrical rod (diameter $\approx 6\mathrm{mm}$), resulting in a flow in which $\alpha =5/3$ (see text); the turbulence can be made visible at a particular instant by (c) interference fringes in white light. (Note that the image does not cover the entire width of the channel.) (d) The film may be pierced with the teeth of a comb (tooth diameter $\approx 1\mathrm{mm}$; tooth spacing $\approx 3\mathrm{mm}$), resulting in a flow in which $\alpha =3$; the turbulence can be made visible at a particular instant by (e) interference fringes in white light. (Note that the image does not cover the entire width of the channel.)Reuse & Permissions

Figure 2

Typical log-log plots of energy spectra computed from LDV measurements [20] carried out in the new soap-film channel. The slope of these log-log plots equals the value of the spectral exponent $\alpha$; unless otherwise noted, the plots correspond to the streamwise component of the energy spectrum, $E_{uu}(k_x)$. (a) Spectra on a transect of the channel [layout of Fig. 1a]. (b) Spectra on the centerline of the channel with a rod at the inlet [layout of Fig. 1b]. The distances indicated are measured downstream from the rod. (c) Spectra on a transect of the channel with a rod at the inlet [layout of Fig. 1b]. The transect is 30 cm downstream from the rod. The streamwise component $E_{uu}(k_x)$ is shown by thick lines, the transverse component $E_{vv}(k_x)$ is shown by thin lines; except for small $k$, both components collapse onto the same curve, signifying isotropy. (d) Spectra on a transect of the channel with a comb at the inlet [layout of Fig. 1d]. The transect is 30 cm downstream from the inlet. The streamwise component $E_{uu}(k_x)$ is shown by thick lines, the transverse component $E_{vv}(k_x)$ is shown by thin lines; except for small $k$, both components collapse onto the same curve, signifying isotropy.Reuse & Permissions

Figure 3

The mean velocity profile $u(y)$, the Reynolds shear stress profile ${\tau }_{\mathrm{Re}}(y)$, and the viscous shear stress profile ${\tau }_v(y)$ of a typical soap-film flow with $\alpha =5/3$. [Spectra of this flow are shown in Fig. 2c.] Points on the film closer than $\approx 20\mu \mathrm{m}$ (the diameter of the beam of the LDV) from the straight edge of the channel cannot be probed with the LDV; thus, the first data point, which we position at $y=0$, is at a distance of $\approx 20\mu \mathrm{m}$ from the straight edge of the channel. Inset: Zoom-in view of $u(y)$ in the viscous layer, where $du/dy=G$. The apparent slip velocity $u(0)$ can be ascribed to the complex flow immediately adjacent to the straight edge of the channel. In previous work [14] we have shown that the frictional drag does not depend on $u(0)$ (except perhaps through the Reynolds number).Reuse & Permissions

Figure 4

Log-log plot of the experimental data points (frictional drag $f$, Reynolds number Re), from independent experiments carried out in Bordeaux and Pittsburgh. The data points for $\alpha =5/3$ are shown using blue circles and stars, and the data points for $\alpha =3$ are shown using red squares and triangles.Reuse & Permissions