Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

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.

Large coherence of spanwise velocity in turbulent boundary layers

2018 ◽  
Vol 847 ◽  
pp. 161-185 ◽  
Author(s):  
Charitha M. de Silva ◽  
Kevin Kevin ◽  
Rio Baidya ◽  
Nicholas Hutchins ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Velocity Fields ◽  
Spatial Extent ◽  
Large Field ◽  
Logarithmic Region ◽  
Spanwise Velocity

The spatial signature of spanwise velocity coherence in turbulent boundary layers has been studied using a series of unique large-field-of-view multicamera particle image velocimetry experiments, which were configured to capture streamwise/spanwise slices of the boundary layer in both the logarithmic and the wake regions. The friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 2600$ was chosen to nominally match the simulation of Sillero et al. (Phys. Fluids, vol. 26 (10), 2014, 105109), who had previously reported oblique features of the spanwise coherence at the top edge of the boundary layer based on the sign of the spanwise velocity, and here we find consistent observations from experiments. In this work, we show that these oblique features in the spanwise coherence relate to the intermittent turbulent bulges at the edge of the layer, and thus the geometry of the turbulent/non-turbulent interface, with the clear appearance of two counter-oriented oblique features. Further, these features are shown to be also present in the logarithmic region once the velocity fields are deconstructed based on the sign of both the spanwise and the streamwise velocity, suggesting that the often-reported meandering of the streamwise-velocity coherence in the logarithmic region is associated with a more obvious diagonal pattern in the spanwise velocity coherence. Moreover, even though a purely visual inspection of the obliqueness in the spanwise coherence may suggest that it extends over a very large spatial extent (beyond many boundary layer thicknesses), through a conditional analysis, we show that this coherence is limited to distances nominally less than two boundary layer thicknesses. Interpretation of these findings is aided by employing synthetic velocity fields of a boundary layer constructed using the attached eddy model, where the range of eddy sizes can be prescribed. Comparisons between the model, which employs an array of self-similar packet-like eddies that are randomly distributed over the plane of the wall, and the experimental velocity fields reveal a good degree of agreement, with both exhibiting oblique features in the spanwise coherence over comparable spatial extents. These findings suggest that the oblique features in the spanwise coherence are likely to be associated with similar structures to those used in the model, providing one possible underpinning structural composition that leads to this behaviour. Further, these features appear to be limited in spatial extent to only the order of the large-scale motions in the flow.

scholarly journals Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

2009 ◽  
Vol 628 ◽  
pp. 311-337 ◽  
Author(s):  
ROMAIN MATHIS ◽  
NICHOLAS HUTCHINS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Wall Turbulence ◽  
Small Scale ◽  
Supporting Evidence ◽  
Scale Structures ◽  
Small Scale Structures ◽  
Near Wall

In this paper we investigate the relationship between the large- and small-scale energy-containing motions in wall turbulence. Recent studies in a high-Reynolds-number turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the large-scale boundary-layer motions on the small-scale near-wall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered small-scale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the large-scale log-region structures superimposing a footprint (or mean shift) on the near-wall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the small-scale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow

1995 ◽  
Vol 286 ◽  
pp. 137-171 ◽  
Author(s):  
Stephen R. Snarski ◽  
Richard M. Lueptow
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Wall Pressure ◽  
Small Scale ◽  
Fluctuating Pressure ◽  
Large Scale Structures ◽  
Transverse Curvature ◽  
Scale Structures

Measurements of wall pressure and streamwise velocity fluctuations in a turbulent boundary layer on a cylinder in an axial air flow (δ/a = 5.04, Reθ = 2870) have been used to investigate the turbulent flow structures in the cylindrical boundary layer that contribute to the fluctuating pressure at the wall in an effort to deduce the effect of transverse curvature on the structure of boundary layer turbulence. Wall pressure was measured at a single location with a subminiature electret condenser microphone, and the velocity was measured throughout a large volume of the boundary layer with a hotwire probe. Auto- and cross-spectral densities, cross-correlations, and conditional sampling of the pressure and streamwise velocity indicate that two primary groups of flow disturbances contribute to the fluctuating pressure at the wall: (i) low-frequency large-scale structures with dynamical significance across the entire boundary layer that are consistent with a pair of large-scale spanwise-oriented counter-rotating vortices and (ii) higher frequency small-scale disturbances concentrated close to the wall that are associated with the burst-sweep cycle and are responsible for the short-duration large-amplitude wall pressure fluctuations. A bidirectional relationship was found to exist between both positive and negative pressure peaks and the temporal derivative of u near the wall. Because the frequency of the large-scale disturbance observed across the boundary layer is consistent with the bursting frequency deduced from the average time between bursts, the burst-sweep cycle appears to be linked to the outer motion. A stretching of the large-scale structures very near the wall, as suggested by space-time correlation convection velocity results, may provide the coupling mechanism. Since the high-frequency disturbance observed near the wall is consistent with the characteristic frequency deduced from the average duration of bursting events, the bursting process provides the two characteristic time scales responsible for the bimodal distribution of energy near the wall. Because many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers, transverse curvature appears to have little effect on the fundamental turbulent structure of the boundary layer for the moderate transverse curvature ratio used in this investigation. From differences that exist between the turbulence intensity, skewness, and spectra of the streamwise velocity, however, it appears that transverse curvature may enhance (i.e. energize) the large-scale motion owing to the reduced constraint imposed on the flow by the smaller cylindrical wall.

Interacting oscillatory boundary layers and wall modes in modulated rotating convection

2009 ◽  
Vol 625 ◽  
pp. 75-96 ◽  
Author(s):  
A. RUBIO ◽  
J. M. LOPEZ ◽  
F. MARQUES
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Stokes Equations ◽  
Broad Band ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Rotating Convection ◽  
High Modulation ◽  
Wide Range

Thermal convection in a rotating cylinder near onset is investigated using direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation in a regime dominated by the Coriolis force. For thermal driving too small to support convection throughout the entire cell, convection sets in as alternating pairs of hot and cold plumes in the sidewall boundary layer, the so-called wall modes of rotating convection. We subject the wall modes to small amplitude harmonic modulations of the rotation rate over a wide range of frequencies. The modulations produce harmonic Ekman boundary layers at the top and bottom lids as well as a Stokes boundary layer at the sidewall. These boundary layers drive a time-periodic large-scale circulation that interacts with the wall-localized thermal plumes in a non-trivial manner. The resultant phenomena include a substantial shift in the onset of wall-mode convection to higher temperature differences for a broad band of frequencies, as well as a significant alteration of the precession rate of the wall mode at very high modulation frequencies due to the mean azimuthal streaming flow resulting from the modulations.

scholarly journals Dynamics of an Abyssal Circulation Driven by Bottom-Intensified Mixing on Slopes

2018 ◽  
Vol 48 (6) ◽  
pp. 1257-1282 ◽  
Author(s):  
Jörn Callies ◽  
Raffaele Ferrari
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Boundary Layer Theory ◽  
Internal Tides ◽  
Small Scale ◽  
Ocean Bottom ◽  
Basin Scale ◽  
Lee Waves ◽  
Abyssal Circulation

AbstractThe large-scale circulation of the abyssal ocean is enabled by small-scale diapycnal mixing, which observations suggest is strongly enhanced toward the ocean bottom, where the breaking of internal tides and lee waves is most vigorous. As discussed recently, bottom-intensified mixing induces a pattern of near-bottom up- and downwelling that is quite different from the traditionally assumed widespread upwelling. Here the consequences of bottom-intensified mixing for the horizontal circulation of the abyssal ocean are explored by considering planetary geostrophic dynamics in an idealized “bathtub geometry.” Up- and downwelling layers develop on bottom slopes as expected, and these layers are well described by boundary layer theory. The basin-scale circulation is driven by flows in and out of these boundary layers at the base of the sloping topography, which creates primarily zonal currents in the interior and a net meridional exchange along western boundaries. The rate of the net overturning is controlled by the up- and downslope transports in boundary layers on slopes and can be predicted with boundary layer theory.

scholarly journals A Combined Local and Nonlocal Closure Model for the Atmospheric Boundary Layer. Part I: Model Description and Testing

2007 ◽  
Vol 46 (9) ◽  
pp. 1383-1395 ◽  
Author(s):  
Jonathan E. Pleim
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Convective Boundary Layer ◽  
Large Scale ◽  
Eddy Diffusion ◽  
Small Scale ◽  
Convective Conditions ◽  
Convective Boundary ◽  
Scale Turbulence ◽  
Convective Model

Abstract The modeling of the atmospheric boundary layer during convective conditions has long been a major source of uncertainty in the numerical modeling of meteorological conditions and air quality. Much of the difficulty stems from the large range of turbulent scales that are effective in the convective boundary layer (CBL). Both small-scale turbulence that is subgrid in most mesoscale grid models and large-scale turbulence extending to the depth of the CBL are important for the vertical transport of atmospheric properties and chemical species. Eddy diffusion schemes assume that all of the turbulence is subgrid and therefore cannot realistically simulate convective conditions. Simple nonlocal closure PBL models, such as the Blackadar convective model that has been a mainstay PBL option in the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) for many years and the original asymmetric convective model (ACM), also an option in MM5, represent large-scale transport driven by convective plumes but neglect small-scale, subgrid turbulent mixing. A new version of the ACM (ACM2) has been developed that includes the nonlocal scheme of the original ACM combined with an eddy diffusion scheme. Thus, the ACM2 is able to represent both the supergrid- and subgrid-scale components of turbulent transport in the convective boundary layer. Testing the ACM2 in one-dimensional form and comparing it with large-eddy simulations and field data from the 1999 Cooperative Atmosphere–Surface Exchange Study demonstrates that the new scheme accurately simulates PBL heights, profiles of fluxes and mean quantities, and surface-level values. The ACM2 performs equally well for both meteorological parameters (e.g., potential temperature, moisture variables, and winds) and trace chemical concentrations, which is an advantage over eddy diffusion models that include a nonlocal term in the form of a gradient adjustment.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

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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