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

2011 ◽  
Vol 671 ◽  
pp. 96-120 ◽  
Author(s):  
J. C. R. HUNT ◽  
D. D. STRETCH ◽  
S. E. BELCHER
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Lower Layer ◽  
Coupling Mechanism ◽  
Viscous Layer ◽  
Viscous Coupling ◽  
Viscous Effects ◽  
Horizontal Structure ◽  
Velocity Fluctuations ◽  
Viscous Boundary

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.

scholarly journals Tidal rectification in lateral viscous boundary layers of a semi-enclosed basin

1987 ◽  
Vol 184 ◽  
pp. 381-397 ◽  
Author(s):  
H. E. De Swart ◽  
J. T. F. Zimmerman
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Boundary ◽  
Stokes Number ◽  
Residual Current ◽  
Residual Flow ◽  
Oscillatory Boundary Layer ◽  
Tidal Rectification ◽  
Vorticity Flux ◽  
Viscous Boundary

The rectified flow, induced by divergence of the vorticity flux in lateral oscillatory viscous boundary layers along the sidewalls of a semi-enclosed basin, is studied as a function of the Strouhal number, k, equivalent to the Reynolds number of the viscous inner oscillatory boundary layer, and of the Stokes number. The squared ratio of these numbers defines another Reynolds number, measuring the strength of the self-advection by the residual flow. For strong self-advection the residual current decays to zero in an outer boundary, its width being large compared to the width of the inner layer. The regimes of small, moderate and strong self-advection are analysed.

scholarly journals Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

2007 ◽  
Vol 579 ◽  
pp. 1-28 ◽  
Author(s):  
N. HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
High Speed ◽  
Large Scale ◽  
Sonic Anemometer ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Wall Region ◽  
Velocity Fluctuations ◽  
Near Wall

A regime of very long meandering positive and negative streamwise velocity fluctuations, that we term ‘superstructures’, are found to exist in the log and lower wake regions of turbulent boundary layers. Measurements are made with a spanwise rake of 10 hot-wires in two separate facilities (spanning more than a decade of Reτ) and are compared with existing PIV and DNS results. In all cases, we note evidence of a large-scale stripiness in the streamwise velocity fluctuations. The length of these regions can commonly exceed 20δ. Similar length scales have been previously reported for pipes and DNS channel flows. It is suggested that the true length of these features is masked from single-point statistics (such as autocorrelations and spectra) by a spanwise meandering tendency. Support for this conjecture is offered through the study of a synthetic flow composed only of sinusoidally meandering elongated low- and high-speed regions. From detailed maps of one-dimensional spectra, it is found that the contribution to the streamwise turbulence intensities associated with the superstructures appears to be increasingly significant with Reynolds number, and scales with outer length variables (δ). Importantly, the superstructure maintains a presence or footprint in the near-wall region, seeming to modulate or influence the near-wall cycle. This input of low-wavenumber outer-scaled energy into the near-wall region is consistent with the rise in near-wall streamwise intensities, when scaled with inner variables, that has been noted to occur with increasing Reynolds number. In an attempt to investigate these structures at very high Reynolds numbers, we also report on recent large-scale sonic anemometer rake measurements, made in the neutrally stable atmospheric surface layer. Preliminary results indicate that the superstructure is present in the log region of this atmospheric flow at Reτ = 6.6×105, and has a size consistent with outer scaling.

Large-amplitude acoustic streaming

2014 ◽  
Vol 744 ◽  
pp. 329-351 ◽  
Author(s):  
G. P. Chini ◽  
Z. Malecha ◽  
T. D. Dreeben
Keyword(s):  
Boundary Layers ◽  
High Frequency ◽  
Large Amplitude ◽  
Acoustic Streaming ◽  
Ideal Gas ◽  
Mean Flow ◽  
Viscous Effects ◽  
Viscous Boundary ◽  
Streaming Flows ◽  
Hid Lamps

AbstractA mechanism is proposed for the generation of large-amplitude acoustically-driven streaming flows in which time-mean flow speeds are comparable to the instantaneous speed of fluid particles in a high-frequency sound-wave field. Motivated by streaming observed in high-intensity discharge (HID) lamps, two-dimensional flow of a density-stratified ideal gas in a channel geometry is analysed in the asymptotic limit of high-frequency acoustic-wave forcing. Predictions of streaming flow magnitudes based on classical arguments invoking Reynolds stress divergences originating in viscous boundary layers are orders of magnitude too small to account for the observed mean flows. Moreover, classical ‘Rayleigh streaming’ theory cannot account for the direction of the cellular mean flows often observed in HID lamps. In contrast, the mechanism proposed here, which invokes fluctuating baroclinic torques away from viscous boundary layers and thus is largely independent of viscous effects, can account both for the magnitude and the orientation of the observed streaming flows.

scholarly journals Rayleigh-Taylor Instability with Finite Skin Depth

2018 ◽  
Vol 5 (3) ◽  
pp. 95-98
Author(s):  
F. E. M. Silveira
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Scaling Laws ◽  
Geometric Mean ◽  
Skin Depth ◽  
Taylor Instability ◽  
Fluid Viscosity ◽  
Viscous Effects ◽  
Rayleigh Taylor Instability ◽  
Viscous Boundary

In this work, the Rayleigh-Taylor instability is addressed in a viscous-resistive current slab, by assuming a finite electron skin depth. The formulation is developed on the basis of an extended form of Ohm’s law, which includes a term proportional to the explicit time derivative of the current density. In the neighborhood of the rational surface, a viscous-resistive boundary-layer is defined in terms of a resistive and a viscous boundary layers. As expected, when viscous effects are negligible, it is shown that the viscous-resistive boundary-layer is given by the resistive boundary-layer. However, when viscous effects become important, it is found that the viscous-resistive boundary-layer is given by the geometric mean of the resistive and viscous boundary-layers. Scaling laws of the time growth rate of the Rayleigh-Taylor instability with the plasma resistivity, fluid viscosity, and electron number density are discussed.

DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality

2018 ◽  
Vol 842 ◽  
pp. 428-468 ◽  
Author(s):  
Christoph Wenzel ◽  
Björn Selent ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Scaling Laws ◽  
Scaling Law ◽  
Turbulent Boundary Layers ◽  
Wake Region ◽  
Mean Flow ◽  
Number Range ◽  
Velocity Fluctuations

A direct-numerical-simulation study of spatially evolving compressible zero-pressure-gradient turbulent boundary layers is presented for a fine-meshed range of Mach numbers from 0.3 to 2.5. The use of an identical set-up for all subsonic and supersonic cases warrants proper comparability and allows a highly reliable quantitative evaluation of compressible mean-flow scaling laws and the settlement on a commonly accepted compressible mean-flow velocity profile in the considered Mach and Reynolds number range. All data are compared to the literature data-base where significant data scattering can be observed. The skin-friction distribution was found in excellent agreement with the prediction by the van Driest-II transformation. Contrary to the prevailing appraisal, the wake region of the mean-velocity profile is observed to scale much better with the momentum-thickness Reynolds number calculated with the far-field-viscosity than with the wall-viscosity. The time-averaged velocity fluctuations, density-scaled according to Morkovin’s hypothesis, are found to be noticeably influenced by compressibility effects in the inner layer as well as in the wake region. Allowing wall-temperature fluctuations affects neither the density nor velocity fluctuations.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

Vortex reynolds number in turbulent boundary layers

1995 ◽  
Vol 7 (2) ◽  
pp. 101-117 ◽  
Author(s):  
P. R. Bandyopadhyay ◽  
R. Balasubramanian
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Turbulent Boundary Layers

Aero-optics of subsonic turbulent boundary layers

2012 ◽  
Vol 696 ◽  
pp. 122-151 ◽  
Author(s):  
Kan Wang ◽  
Meng Wang
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Dominant Role ◽  
Elevation Angle ◽  
Turbulent Boundary Layers ◽  
Density Field ◽  
Small Scale ◽  
Number Range ◽  
Scale Turbulence

AbstractCompressible large-eddy simulations are carried out to study the aero-optical distortions caused by Mach 0.5 flat-plate turbulent boundary layers at Reynolds numbers of ${\mathit{Re}}_{\theta } = 875$, 1770 and 3550, based on momentum thickness. The fluctuations of refractive index are calculated from the density field, and wavefront distortions of an optical beam traversing the boundary layer are computed based on geometric optics. The effects of aperture size, small-scale turbulence, different flow regions and beam elevation angle are examined and the underlying flow physics is analysed. It is found that the level of optical distortion decreases with increasing Reynolds number within the Reynolds-number range considered. The contributions from the viscous sublayer and buffer layer are small, while the wake region plays a dominant role, followed by the logarithmic layer. By low-pass filtering the fluctuating density field, it is shown that small-scale turbulence is optically inactive. Consistent with previous experimental findings, the distortion magnitude is dependent on the propagation direction due to anisotropy of the boundary-layer vortical structures. Density correlations and length scales are analysed to understand the elevation-angle dependence and its relation to turbulence structures. The applicability of Sutton’s linking equation to boundary-layer flows is examined, and excellent agreement between linking equation predictions and directly integrated distortions is obtained when the density length scale is appropriately defined.

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