banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Turbulent velocity spectra in superfluid flows
Rent this article for


Image of FIG. 1.
FIG. 1.

TSF wind tunnel probes: (a) probe ① or ③; (b) probe ②. All parts are tightly assembled. For probes ① and ③, the pressure reference is realized by holes on the outer CuNi cylinder at a distance from the tip; for probe ②, the pressure reference is taken in a region where the flow is quiescent with a controlled leak on the back of the shell. Néel wind tunnel probe: (c) Probe ④ is essentially similar to probe ② except that it works as an absolute pressure probe, without hole in its shell.

Image of FIG. 2.
FIG. 2.

Electronic diagram of the acquisition system for probes ① and ②. The pressure transducer is represented as a resistor bridge. The imbalance is preamplified by a low-noise preamplifier (JFET, typical noise input voltage ). The mean value of the imbalance signal is substracted using an inductor bridge and an adjustable RC filter to compensate for the phase shift.

Image of FIG. 3.
FIG. 3.

(a) TSF wind tunnel: Schematics of the test section and the probe locations for runs 1 and 2. For run 1, a removable cylinder can be inserted across the flow at a distance downstream the grid. It was originally designed to protect a hot-wire during the transient of the system. The stagnation pressure probe ①, located at a distance downstream the grid can either measure grid turbulence when the cylinder is removed or wake turbulence when the cylinder is inserted in the flow. Probe ① was not positioned on the pipe axis to avoid the wake of the hot-wire. For run 2, two stagnation pressure probes (② and ③) are available. (b) Néel wind tunnel: Schematics and picture of the test section and location of stagnation pressure probe ④.

Image of FIG. 4.
FIG. 4.

Grid turbulence velocity spectra acquired by probe ① for three different mean velocities both above and below the superfluid transition. The Helmholtz resonance frequency is found near 2 kHz. The solid lines are visual aids to find the corner frequency, . The high-frequency lines show the −5/3 scaling. Inset: Compensated grid flow energy spectrum for various conditions both above and below the superfluid transition (see text). The value of the plateau provides an estimate for the one-dimensional Kolmogorov constant for both He I and He II grid turbulence.

Image of FIG. 5.
FIG. 5.

Turbulence intensity measured for the two grid flow runs in the TSF wind tunnel for various velocities and temperatures, computed using the integral of the energy spectrum. Inset: Estimation of the envelope of the energy spectrum. The area below the envelope is the energy of the velocity fluctuations. The dots are experimental data points, the solid line is the estimated envelope below the spectrum, and the dashed line is the extrapolated spectrum (flat spectrum in the low-frequency limit and scaling in the high-frequency limit). The energy from the low-frequency increase is not taken in the turbulent energy estimate. However, this makes a relative difference smaller than a few percents in the final estimate.

Image of FIG. 6.
FIG. 6.

Left: picture of the removable cylinder in the TSF wind tunnel. The angle between the probe and the axis of the pipe is 17°. Right: picture of the grid.

Image of FIG. 7.
FIG. 7.

Velocity spectra in the near wake of a cylinder in the TSF wind tunnel both above and below the superfluid transition with mean velocity increasing from bottom to top. The high-frequency peak near 2 kHz is the sensor Helmholtz frequency.

Image of FIG. 8.
FIG. 8.

Velocity spectra for in the Néel wind tunnel for four mean velocities below the superfluid transition. The low-frequency corners give an estimate of the longitudinal integral scale .

Image of FIG. 9.
FIG. 9.

Same data as Fig. 8 plotted in a compensated fashion (see text).


Generic image for table
Table I.

Some physical properties of cryogenic helium for temperature and pressure values relevant to our experiments.

Generic image for table
Table II.

Summary of the main properties of the probes used in our experiments.

Generic image for table
Table III.

Main dimensions of the TSF wind tunnel (see Figs. 3 and 1 for the definition of the notations).

Generic image for table
Table IV.

Some integral scale measurements derived from the velocity power spectra obtained in run 1 (probe ①) and run 2 (probe ②). For comparison, Comte–Bellot and Corrsin predictions gives for run 1 and for run 2.

Generic image for table
Table V.

Typical relative weight of each term contributing to the signal measured by a stagnation pressure probe for various turbulence intensity using estimate (A6).


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Turbulent velocity spectra in superfluid flows