Sonic Eddy Model of the Turbulent Boundary Layer

The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.

Lack of Plasma-like Screening Mechanism in Sedimentation of a Non-Brownian Suspension

We investigate qualitatively a uniform non-Brownian sedimenting suspension in a stationary state. As a base of our analysis we take the BBGKY hierarchy derived from the Liouville equation. We then show that assumption of the plasma-like screening relations can cancel some long-range terms in the hierarchy but it does not provide integrable solutions for correlation functions. This suggests breaking the translational symmetry of the system. Therefore a non-uniform structure can develop to suppress velocity fluctuations and make the range of correlations finite.

Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear

We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of...

Reynolds' Turbulence Solution

This study revisits the Reynolds-averaged Navier--Stokes equations (RANS) and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds' averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of on the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

Turbulent flow in curved channels

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

Magnetic and Velocity Fluctuations in the Near-Sun Region from 0.1−0.3 au Observed by Parker Solar Probe

The fluctuations observed in the slow solar wind at 1 au by the WIND spacecraft are shown by recent studies to consist of mainly magnetic-field directional turning and magnetic-velocity alignment structure (MVAS). How these structures are created has been a question because the nature of the fluctuations in the near-Sun region remains unknown. Here, we present an analysis of the measurements in the slow solar wind from 0.1−0.3 au by Parker Solar Probe during its first six orbits. We present the distributions in the C vb ′ – σ r plane of both the occurrence and average amplitudes of the fluctuations, including the magnetic field, the velocity, and the Elsässer variables, where C vb ′ is the correlation coefficient between the magnetic and velocity fluctuations multiplied by the opposite sign of the radial component of the mean magnetic field and σ r is the normalized residual energy. We find that the dominant composition is the outward-propagating Alfvénic fluctuations. We find Alfvénic fluctuations with C vb ′ > 0.95 , in which the amplitudes of z + reach 60 km s−1 and those of z − are close to the observational uncertainty. We also find a region with high C vb ′ and moderate minus σ r in which the fluctuations are considered MVAS being magnetic dominated with the amplitude of magnetic fluctuations reaching 60 km s−1. We provide empirical relations between the velocity fluctuation amplitude and C vb ′ . The comparison between these results and those observed at 1 au may provide some clues as to the nature and evolution of the fluctuations.

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

3D-LDA diagnostics of a swirled flow in the model of an improved four-vortex furnace

The three-component Laser Doppler Anemometry method (3D-LDA) was used to study the internal aerodynamics of an experimental model of a promising furnace with a four-vortex scheme for burning coal fuel. Distributions of the averaged velocity and velocity fluctuations are obtained. There are no the pronounced peaks in the spectrum of velocity fluctuations, so we can speak about the stability of the investigated flow. The studied model is characterized by a high level of velocity fluctuations, provided for effective mixing of the pulverized coal mixture in the combustion chamber of the furnace.