Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs

Loading and heating of a large flat plate at Mach 7 in the Langley 8-foot high-temperature structures tunnel

Surface pressure and cold-wall heating rate distributions (wall-temperature to total-temperature ratio approximately 0.2) were obtained on a large, flat calibration panel at a nominal Mach number of 7 in an 8-foot high-temperature structures tunnel. Panel dimensions were 42.5 by 60.0 in. Test objectives were: (1) to map available flat-plate loading and heating provided by the facility and (2) to determine effectiveness of leading-edge bluntness, boundary-layer trips, and aerodynamic fences in generating a uniform, streamwise turbulent flow field over the test surface of a flat-sided panel holder

Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow

Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients

Self similarity of two point correlations in wall bounded turbulent flows

The structure of turbulence at a height y from a wall is affected by the local mean shear at y, by the direct effect of the wall on the eddies, and by the action of other eddies close to or far from the wall. Some researchers believe that a single one of these mechanisms is dominant, while others believe that these effects have to be considered together. It is important to understand the relative importance of these effects in order to develop closure models, for example for the dissipation or for the Reynolds stress equation, and to understand the eddy structure of cross correlation functions and other measures. The specific objective was to examine the two point correlation, R sub vv, of the normal velocity component v near the wall in a turbulent channel flow and in a turbulent boundary layer. The preliminary results show that even in the inhomogeneous turbulent boundary layer, the two-point correlation function may have self similar forms. The results also show that the effects of shear and of blocking are equally important in the form of correlation functions for spacing normal to the wall. But for spanwise spacing, it was found that the eddy structure is quire different in these near flows. So any theory for turbulent structure must take both these effects into account

Solar silicon via the Dow Corning process

Carbon, as a reductant for quartz, must be made available so as to have suitable reactivity in conjunction with high purity, especially with respect to boron and phosphorus. A detailed experimental plan was developed to do this. Different sources of carbon were selected to be subjected to various purification methods and reactivity-enhancement processes. A developmental scale arc furnace was installed to perform quartz-carbon reactivity testing

Hypersonic structures: An aerodynamicist's perspective, or one man's dream is another man's nightmare

The relationship between hypersonic aerodynamic and structural design is reviewed. The evolution of the hypersonic vehicle design is presented. Propulsion systems, structural materials, and fuels are emphasized

Driving forces in free visual search : An ethology

Peer reviewedPostprin

Taking stock of SLSN and LGRB host galaxy comparison using a complete sample of LGRBs

Long gamma-ray bursts (LGRBs) and superluminous supernovae (SLSNe) are both explosive transients with very massive progenitor stars. Clues about the nature of the progenitors can be found by investigating environments in which such transients occur. While studies of LGRB host galaxies have a long history, dedicated observational campaigns have only recently resulted in a high enough number of photometrically and spectroscopically observed SLSN hosts to allow statistically significant analysis of their properties. In this paper we make a comparison of the host galaxies of hydrogen-poor (H-poor) SLSNe and the Swift/BAT6 sample of LGRBs. In contrast to previous studies we use a complete sample of LGRBs and we address a special attention to the comparison methodology and the selection of SLSN sample whose data have been compiled from the available literature. At intermediate redshifts (0.3 < z < 0.7) the two classes of transients select galaxies whose properties (stellar mass, luminosity, star-formation rate, specific star-formation rate and metallicity) do not differ on average significantly. Moreover, the host galaxies of both classes of objects follow the fundamental metallicity relation and the fundamental plane of metallicity. In contrast to previous studies we show that at intermediate redshifts the emission line equivalent widths of the two populations are essentially the same and that the previous claims regarding the higher fraction of SLSN hosts among the extreme emission line galaxies with respect to LGRBs are mostly due to a larger fraction of strong-line emitters among SLSN hosts at z < 0.3, where samples of LGRB hosts are small and poorly defined.Comment: 7 pages, 4 figures, accepted to Astronomy & Astrophysic