scholarly journals Optimal transient growth and very large–scale structures in turbulent boundary layers

2009 ◽  
Vol 619 ◽  
pp. 79-94 ◽  
Author(s):  
CARLO COSSU ◽  
GREGORY PUJALS ◽  
SEBASTIEN DEPARDON
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Outer Region ◽  
Wall Region ◽  
Mean Flow ◽  
Large Scale Structures ◽  
Energy Growth ◽  
Scale Structures

The optimal energy growth of perturbations sustained by a zero pressure gradient turbulent boundary is computed using the eddy viscosity associated with the turbulent mean flow. It is found that even if all the considered turbulent mean profiles are linearly stable, they support transient energy growths. The most amplified perturbations are streamwise uniform and correspond to streamwise streaks originated by streamwise vortices. For sufficiently large Reynolds numbers two distinct peaks of the optimal growth exist, respectively scaling in inner and outer units. The optimal structures associated with the peak scaling in inner units correspond well with the most probable streaks and vortices observed in the buffer layer, and their moderate energy growth is independent of the Reynolds number. The energy growth associated with the peak scaling in outer units is larger than that of the inner peak and scales linearly with an effective turbulent Reynolds number formed with the maximum eddy viscosity and a modified Rotta–Clauser length based on the momentum thickness. The corresponding optimal perturbations consist of very large–scale structures with a spanwise wavelength of the order of 8δ. The associated optimal streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer, in which they are proportional to the mean flow velocity. These outer streaks protrude far into the near wall region, having still 50% of their maximum amplitude at y+ = 20. The amplification of very large–scale structures appears to be a robust feature of the turbulent boundary layer: optimal perturbations with spanwise wavelengths ranging from 4δ to 15δ can all reach 80% of the overall optimal peak growth.

Large-scale motions in a plane wall jet

2019 ◽  
Vol 877 ◽  
pp. 239-281 ◽  
Author(s):  
Ebenezer P. Gnanamanickam ◽  
Shibani Bhatt ◽  
Sravan Artham ◽  
Zheng Zhang
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Large Scale ◽  
Plane Wall ◽  
Shear Stresses ◽  
Wall Jet ◽  
Wall Region ◽  
Free Shear Layer ◽  
Large Scale Structures ◽  
Scale Structures

The plane wall jet (PWJ) is a wall-bounded flow in which a wall shear layer develops in the presence of extremely energetic flow structures of the outer free-shear layer. The structure of a PWJ, developing in still air, was studied with the focus on the large scales in the flow. Wall-normal hot-wire anemometry (HWA) measurements along with double-frame particle image velocimetry (PIV) measurements (wall-normal–streamwise plane) were carried out at streamwise distances up to $162b$, where $b$ is the slot width of the PWJ exit. The nominal PWJ Reynolds number based on exit parameters was $Re_{j}\approx 5940$. Comparisons with a zero-pressure-gradient boundary layer (ZPGBL) at nominally matched friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ were also carried out as appropriate, to highlight key features of the PWJ structure. Consistent with previous work, the PWJ showed a dependence of the peak turbulent stresses on the jet exit Reynolds number. The turbulent production showed a peak corresponding to the near-wall cycle similar to the peak seen in the ZPGBL. However, another turbulent production peak was observed in the outer free-shear layer that was an order of magnitude larger than the inner one. Along with the change in sign of the viscous and Reynolds shear stresses, the PWJ was shown to have a region of very low turbulent production between these two peaks. The dissipation rate increased over the PWJ layer with a peak also in the outer region. Visualizations of the flow and two-point correlations reveal that the most energetic large-scale structures within a PWJ are vortical motions in the wall-normal–streamwise plane similar to those structures seen in free-shear layers. These structures are referred to as J (for jet) type structures. In addition two-point correlations reveal the existence of large-scale structures in the wall region which have a signature similar to those structures seen in canonical boundary layers. These structures are referred to as W (for wall) type structures. Instantaneous PIV realizations and flow visualizations reveal that these W type large-scale features are consistent with the paradigm of hairpin vortex packets in the wall region. The J type structures were seen to intrude well into the wall region while the W type structures were also seen to extend into the outer shear layer. Further, these large-scale structures were shown to modulate the amplitude of the finer scales of the flow.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

scholarly journals Exploring the origin of ultra-diffuse galaxies in clusters from their primordial alignment

2020 ◽  
Vol 498 (1) ◽  
pp. L72-L76 ◽  
Author(s):  
Yu Rong ◽  
Pavel E Mancera Piña ◽  
Elmo Tempel ◽  
Thomas H Puzia ◽  
Sven De Rijcke
Keyword(s):  
Large Scale ◽  
High Surface ◽  
Outer Region ◽  
Major Axis ◽  
Large Scale Structures ◽  
Tidal Interactions ◽  
Angular Momenta ◽  
Cluster Environment ◽  
Scale Structures ◽  
Absolute Magnitudes

ABSTRACT We find that the minor axes of the ultra-diffuse galaxies (UDGs) in Abell 2634 tend to be aligned with the major axis of the central dominant galaxy, at a $\gtrsim 95{{\ \rm per\ cent}}$ confidence level. This alignment is produced by the bright UDGs with the absolute magnitudes Mr < −15.3 mag, and outer-region UDGs with R > 0.5R200. The alignment signal implies that these bright, outer-region UDGs are very likely to acquire their angular momenta from the vortices around the large-scale filament before they were accreted into A2634, and form their extended stellar bodies outside of the cluster; in this scenario, the orientations of their primordial angular momenta, which are roughly shown by their minor axes on the images, should tend to be parallel to the elongation of the large-scale filament. When these UDGs fell into the unrelaxed cluster A2634 along the filament, they could still preserve their primordial alignment signal before violent relaxation and encounters. These bright, outer-region UDGs in A2634 are very unlikely to be the descendants of the high-surface-brightness dwarf progenitors under tidal interactions with the central dominant galaxy in the cluster environment. Our results indicate that the primordial alignment could be a useful probe of the origin of UDGs in large-scale structures.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

scholarly journals On the decay of dispersive motions in the outer region of rough-wall boundary layers

2019 ◽  
Vol 862 ◽  
Author(s):  
Johan Meyers ◽  
Bharathram Ganapathisubramani ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Layer ◽  
Stokes Equations ◽  
Outer Region ◽  
Rough Wall ◽  
Rough Boundary ◽  
Mean Flow ◽  
Wall Boundary

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier–Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp (-kz)$ and $\exp (-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\boldsymbol{k}$, and where $K(\boldsymbol{k},Re)$ is a function of $\boldsymbol{k}$ and the Reynolds number $Re$. Moreover, for $k\rightarrow \infty$ or $k_{1}\rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp (-kz)$ and $z\exp (-kz)$, and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for $\ell _{k}/\unicode[STIX]{x1D6FF}\leqslant 0.5$, with $\unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $\ell _{k}=2\unicode[STIX]{x03C0}/k$.

A supersonic turbulent boundary layer in an adverse pressure gradient

1990 ◽  
Vol 211 ◽  
pp. 285-307 ◽  
Author(s):  
Emerick M. Fernando ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Large Scale Structures ◽  
Streamline Curvature ◽  
The Mean ◽  
Scale Structures

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.

Large-scale structures in a forced turbulent mixing layer

1985 ◽  
Vol 150 ◽  
pp. 23-39 ◽  
Author(s):  
M. Gaster ◽  
E. Kit ◽  
I. Wygnanski
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Phase Distribution ◽  
Mixing Layer ◽  
Global Scale ◽  
Travelling Wave ◽  
Mean Flow ◽  
Turbulent Mixing Layer ◽  
Large Scale Structures ◽  
Scale Structures

The large-scale structures that occur in a forced turbulent mixing layer at moderately high Reynolds numbers have been modelled by linear inviscid stability theory incorporating first-order corrections for slow spatial variations of the mean flow. The perturbation stream function for a spatially growing time-periodic travelling wave has been numerically evaluated for the measured linearly diverging mean flow. In an accompanying experiment periodic oscillations were imposed on the turbulent mixing layer by the motion of a small flap at the trailing edge of the splitter plate that separated the two uniform streams of different velocity. The results of the numerical computations are compared with experimental measurements.When the comparison between experimental data and the computational model was made on a purely local basis, agreement in both the amplitude and phase distribution across the mixing layer was excellent. Comparisons on a global scale revealed, not unexpectedly, less good accuracy in predicting the overall amplification.

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