Quantum turbulence in thermal counterflow of superfluid ${\text{} }^{4} \mathrm{He} $ is studied at length scales comparable to the mean distance $\ell $ between quantized vortices. The Lagrangian dynamics of solid deuterium particles, of radius ${R}_{p} $ about one order of magnitude smaller than $\ell $ , is analysed in a planar section of the experimental volume by using the particle tracking velocimetry technique. We show that the average amplitude of the acceleration of the particles seems to increase as the temperature decreases and applied heat flux increases and this can be explained by exploiting the two-fluid model of superfluid ${\text{} }^{4} \mathrm{He} $ . We also report that, at the probed length scales, the normalized distribution of the acceleration of the particles appears to follow an unexpected classical-like behaviour.

We show that, in turbulent two-fluid flows of superfluid ${}^4\mathrm{He}$, the statistically described dynamics of small particles suspended in the liquid does not depend on the type of imposed flow, at scales smaller than the average distance between quantized vortices, the quantum length scale of the flow. More precisely, regardless of the mechanically or thermally driven nature of the large-scale flow, the tails of the observed particle velocity statistical distributions, indicating the occurrence of large-magnitude events in the proximity of quantized vortices, display the same power-law shape, characteristic of the quantum description of superfluid ${}^4\mathrm{He}$. This property of quantum turbulence can be linked to the small-scale universality observed in classical turbulent flows of viscous fluids.

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.

We present a simple method of obtaining the turbulence kinetic energy spectrum from spatially resolved particle image velocimetry (PIV) data without need of use of Taylor hypothesis of frozen turbulence. Additionally, this method allows us to extract the velocity field components related to individual length scales resolved in the spectrum. We convolute the measured PIV velocity field with a band-pass filter, i.e., a difference of two Gauss functions with different widths, and the energy content of a such product we relate to the relevant length-scale of the used band. This is a “kind of wavelet transformation”, which, in respect to Fourier transformation, gives a good physical meaning to individual components.

The motions of micrometer-sized solid deuterium particles in liquid ${}^4\mathrm{He}$, at temperatures between approximately 1.2 and 3 K, are visualized in the proximity of an oscillating cylinder of rectangular cross section (3 mm high and 10 mm wide). The cylinder is oscillating vertically, perpendicularly to its cross-section width, at frequencies between 0.05 and 1.25 Hz, and amplitudes of 5 and 10 mm, resulting in Reynolds numbers $Re$ up to ${10}^5$. The aim of the reported experiments is to investigate systematically the macroscopic vortical structures shed at the cylinder sharp edges, by tracking the deuterium particles. We find that large-scale, millimeter-sized vortices are generated in the surrounding fluid by the oscillating cylinder, both in viscous He I and superfluid He II. An estimate of the strength of the shed vortical structures reveals that, for $Re>{10}^4$, the corresponding magnitudes are approximately equal in He I and He II if, in He II, the kinematic viscosity is suitably defined. For $Re<{10}^4$, the strength of the large-scale vortices is smaller in He II than in He I. Although the outcome is partly affected by the larger scatter of the He I data and possibly also by the much larger heat conductivity of superfluid ${}^4\mathrm{He}$, we argue that the fundamental physical reason for observing this difference is that, at these Reynolds numbers, the experimentally probed length scales in He II are smaller than the average distance between quantized vortices—the quantum length scale of the flow. The result strongly suggests that, similarly to thermal counterflow, both viscous and quantum features can be observed in mechanically driven flows of He II, depending on the length scales at which the quantum flow is probed.