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Transition in atmospheric boundary layer turbulence structure from neutral to convective, and large-scale rolls
- Balaji Jayaraman, James G. Brasseur
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- Journal:
- Journal of Fluid Mechanics / Volume 913 / 25 April 2021
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- 02 March 2021, A42
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The three-dimensional turbulence structure of the canonical daytime atmospheric boundary layer (ABL) reflects the balance between shear and buoyancy turbulence production characterized by $-z_i/L>0$, where $z_i$ is the boundary layer height and $L<0$ is the Obukhov length. In the shear-driven neutral ABL ($-z_i/L=0$) the surface layer is characterized by coherent low-speed streaks, while the ‘moderately convective’ state ($-z_i/L\sim 1\text {--}10$) contains streamwise-elongated sheet-like updraughts. Using large-eddy simulation, we analyse the transition in ABL turbulence structure in response to systematic increases in surface heat flux and $-z_i/L$ from neutral to moderately convective. We discover a sudden change in turbulence structure at the ‘critical’ state $-z_i/L=0.433$ with nearly three-fold increase in the streamwise coherence length of ‘streaks’ at the upper surface layer and four-fold increase in the streamwise scale of updraughts in the mixed layer – as well as the initiation of spatial correlations between the two that contribute to the local generation of thermal updraughts as surface heating increases. At subcritical stability states, buoyancy impacts only the vertical thickness of the streaks. ABL receptivity to buoyancy changes when supercritical and updraughts now grow in the vertical with increasing surface heat flux; the previously amalgamated updraughts extend further in the streamwise direction. The post-critical regime is highlighted by a ‘maximum coherence state’ at $-z_i/L=1.08$ and maximally coherent ‘large-scale rolls’. At increasingly unstable states ($-z_i/L>1.08$), roll coherence decreases and the vertical scales asymptote to the canonical moderately convective ABL.
Polymer-laden homogeneous shear-driven turbulent flow: a model for polymer drag reduction
- ASHISH ROBERT, T. VAITHIANATHAN, LANCE R. COLLINS, JAMES G. BRASSEUR
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- Journal:
- Journal of Fluid Mechanics / Volume 657 / 25 August 2010
- Published online by Cambridge University Press:
- 28 June 2010, pp. 189-226
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Drag reduction (DR) under a turbulent boundary layer implies the suppression of turbulent momentum flux to the wall, a large-eddy phenomenon. Our hypothesis is that the essential mechanisms by which dilute concentrations of long-chain polymer molecules reduce momentum flux involve only the interactions among turbulent velocity fluctuations, polymer molecules and mean shear. Experiments indicate that these interactions dominate in a polymer-active ‘elastic layer’ outside the viscous sublayer and below a Newtonian inertial layer in a polymer-laden turbulent boundary layer. We investigate our hypothesis by modelling the suppression of momentum flux with direct numerical simulation (DNS) of homogeneous turbulent shear flow (HTSF) and the finite extensible nonlinear elastic with Peterlin approximation (FENE-P) model for polymer stress. The polymer conformation tensor equation was solved using a new hyperbolic algorithm with no artificial diffusion. We report here on the equilibrium state with fixed mean shear rate S, where progressive increases in non-dimensional polymer relaxation time WeS (shear Weissenberg number) or concentration parameter 1 − β produced progressive reductions in Reynolds shear stress, turbulence kinetic energy and turbulence dissipation rate, concurrent with increasing polymer stress and elastic potential energy. The changes in statistical variables underlying polymer DR with 1 − β, WeS, %DR and polymer-induced changes to spectra are similar to experiments in channel and pipe flows and show that the experimentally measured increase in normalized streamwise velocity variance is an indirect consequence of DR that is true only at lower DR. Comparison of polymer stretch and elastic potential energy budgets with channel flow DNS showed qualitative correspondence when distance from the wall was correlated to WeS. As WeS increased, the homogeneous shear flow displayed low-DR, high-DR and maximum-DR (MDR) regimes, similar to experiments, with each regime displaying distinctly different polymer–turbulence physics. The suppression of turbulent momentum flux arises from the suppression of vertical velocity fluctuations primarily by polymer-induced suppression of slow pressure–strain rate correlations. In the high-Weissenberg-number MDR-like limit, the polymer nearly completely blocks Newtonian inter-component energy transfer to vertical velocity fluctuations and turbulence is maintained by the polymer contribution to pressure–strain rate. Our analysis from HTSF with the FENE-P representation of polymer stress and its comparisons with experimental and DNS studies of wall-bounded polymer–turbulence supports our central hypothesis that the essential mechanisms underlying polymer DR lie directly in the suppression of momentum flux by polymer–turbulence interactions in the presence of mean shear and indirectly in the presence of the wall as the shear-generating mechanism.
Polymer mixing in shear-driven turbulence
- T. VAITHIANATHAN, ASHISH ROBERT, JAMES G. BRASSEUR, LANCE R. COLLINS
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- Journal:
- Journal of Fluid Mechanics / Volume 585 / 25 August 2007
- Published online by Cambridge University Press:
- 07 August 2007, pp. 487-497
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We investigate numerically the influence of polymer mixing on shear-driven turbulence. Of particular interest is the suppression of mixing that accompanies drag reduction with dilute polymer solutions. The simulations use the finite extensible nonlinear elastic model with the Peterlin closure (FENE-P) to describe the polymer stresses in the momentum equation, with polymer concentration allowed to vary in space and time. A thin slab of concentrated polymer was placed in an initially Newtonian homogeneous turbulent shear flow on a plane perpendicular to the mean velocity gradient, and allowed to mix in the gradient direction while actively altering the turbulence. The initially higher concentration of polymer near the centreplane suppressed production of turbulent kinetic energy and Reynolds stress in that region, while turbulence outside the polymer-rich region remained shear-dominated Newtonian turbulence. The rate of mixing in the shear direction was severely damped by the action of the polymer compared to a passive scalar in the corresponding Newtonian turbulent shear flow. This, in part, was a result of the same damping of vertical velocity fluctuations by the polymer that leads to the suppression of momentum flux. However, the cross-correlation between the polymer concentration and vertical velocity fluctuations was also suppressed, indicating that the explanation for the reduction in polymer mixing involves both the suppression of vertical velocity fluctuations and an alteration of turbulence structure by the polymer–turbulence interactions.
Non-steady peristaltic transport in finite-length tubes
- Meijing Li, James G. Brasseur
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- Journal of Fluid Mechanics / Volume 248 / March 1993
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- 26 April 2006, pp. 129-151
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The classical lubrication-theory model of steady peristaltic transport of periodic sinusoidal waves in infinite-length tubes (Shapiro et al. 1969) is generalized to arbitrary wave shape and wavenumber in tubes of finite length. Whereas the classical model is steady in a frame of reference moving with the peristaltic waves, peristaltic transport in a finite-length tube is inherently non-steady. It may be shown, however, that pumping performance is independent of tube length if there exists an integral number of peristaltic waves in the tube. Three particularly interesting characteristics of non-steady peristalsis are described: (i) fluctuations in pressure and shear stress arise due to a non-integral number of waves in the finite-length tube; (ii) retrograde motion of fluid particles during peristaltic transport (reflux) has inherently different behaviour with single peristaltic waves as compared to multiple ‘train waves’, and (iii) finite tube length, the number of peristaltic waves and the degree of tube occlusion affect global pumping performance. We find that, whereas significant increases in pressure and shear stress result from the tube-to-wave length ratio being non-integral, global pumping performance is only slightly degraded by the existence of a non-integral number of waves in the tube during peristaltic transport. Furthermore, the extent of retrograde motion of fluid particles is much greater with single waves than with train waves. These results suggest that in the design and analysis of peristaltic pumps attention should be paid to the unsteady effects of finite tube length and to the differences between single and multiple peristaltic waves.
Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views
- P. K. Yeung, James G. Brasseur, Qunzhen Wang
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- Journal:
- Journal of Fluid Mechanics / Volume 283 / 25 January 1995
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- 26 April 2006, pp. 43-95
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As discussed in a recent paper by Brasseur & Wei (1994), scale interactions in fully developed turbulence are of two basic types in the Fourier-spectral view. The cascade of energy from large to small scales is embedded within ‘local-to-non-local’ triadic interactions separated in scale by a decade or less. ‘Distant’ triadic interactions between widely disparate scales transfer negligible energy between the largest and smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small scales as energy moves through spectral shells from low to high wavenumbers, distant interactions redistribute energy within spectral shells in a manner that leads to anisotropic redistributions of small-scale energy and phase in response to anisotropic structure in the large scales. To study the role of long-range interactions in small-scale dynamics, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coherent narrow-band anisotropic forcing at the large scales readily interpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Because these asymptotic equations apply in the infinite Reynolds number limit, Yeung & Brasseur argued that the observed long-range effects should be applicable also at high Reynolds numbers.
We continue the analysis of forced simulations in this study, focusing (i) on the detailed three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that the three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the distant interactions alter small-scale structure in two ways: energy is redistributed anisotropically within high-wavenumber spectral shells, and phase correlations are established at the small scales by the distant interactions. In the numerical experiments, the long-range interactions create two pairs of localized volumes of concentrated energy in three-dimensional Fourier space at high wavenumbers in which the Fourier modes are phase coupled. Each pair of locally phase-correlated volumes of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating small-scale anisotropy may be described in physical space by differential advection and distortion of small-scale vorticity by the coherent large-scale energy-containing eddies, producing anisotropic alignment of small-scale vortex tubes.
Scaling arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions which increases with scale separation. Consequently, the small scales respond to forcing initially through the distant interactions. However, as energy cascades from the large-scale to the small-scale Fourier modes, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that whereas the small-scale structure is still anisotropic at these later times, the second-order velocity moment tensor is insensitive to this anisotropy. Third-order moments, on the other hand, do detect the anisotropy. We conclude that whereas a single statistical measure of anisotropy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropic. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to long-range interactions and deviations from local isotropy.
Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field
- Lian-Ping Wang, Shiyi Chen, James G. Brasseur, John C. Wyngaard
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- Journal of Fluid Mechanics / Volume 309 / 25 February 1996
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- 26 April 2006, pp. 113-156
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The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k−5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate εr, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both εr, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Reεr = ε1/3rr4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δru/(εrr)1/3 is found to be universal. Because the local Reynolds number of K62, Rεr = ε1/3rr4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number Rr = ε−1/3r4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number Rλ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε′r deviates more from a log-normal model than the full dissipation εr. The velocity increments conditioned on ε′r do not follow the refined similarity hypotheses to the same degree as those conditioned on εr.
The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids
- James G. Brasseur, Stanley Corrsin, Nan Q. Lu
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- Journal of Fluid Mechanics / Volume 174 / January 1987
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- 21 April 2006, pp. 495-519
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The analysis by Shapiro et al. (1969) of a two-dimensional peristaltic pump at small Reynolds number and with long wavelengths is extended to include a Newtonian peripheral layer adjacent to the wall to simulate the effect of a coating in physiological flows. An earlier analysis by Shukla et al. (1980) violates mass conservation because of an incorrect deduction of the interface shape. We present a detailed analysis of the effect of the peripheral layer on the fluid motions, the pumping characteristics, and the phenomena of reflux and trapping. For prescribed wall motion, a peripheral layer more viscous than the inner fluid improves pumping performance, while a less-viscous outer layer degrades performance. Even a very thin peripheral layer may substantially reduce pumping if the viscosity in this layer is very low relative to the inner region. The effects of the peripheral layer on reflux and trapping depend on the conditions which are held fixed while making the comparison. However, the general trend with decreasing peripheral-layer viscosity is towards an overall decrease in trapping, a decrease in reflux with fixed total volume flow rate, but an increase in reflux with fixed pressure head.
Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field
- LIAN-PING WANG, SHIYI CHEN, JAMES G. BRASSEUR
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- Journal of Fluid Mechanics / Volume 400 / 10 December 1999
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- 10 December 1999, pp. 163-197
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Using direct numerical simulations (DNS) and large-eddy simulations (LES) of velocity and passive scalar in isotropic turbulence (up to 5123 grid points), we examine directly and quantitatively the refined similarity hypotheses as applied to passive scalar fields (RSHP) with Prandtl number of order one. Unlike previous experimental investigations, exact energy and scalar dissipation rates were used and scaling exponents were quantified as a function of local Reynolds number. We first demonstrate that the forced DNS and LES scalar fields exhibit realistic inertial-range dynamics and that the statistical characteristics compare well with other numerical, theoretical and experimental studies. The Obukhov–Corrsin constant for the k−5/3 scalar variance spectrum obtained from the 5123 mesh is 0.87±0.10. Various statistics indicated that the scalar field is more intermittent than the velocity field. The joint probability distribution of locally-averaged energy dissipation εr and scalar dissipation χr is close to log-normal with a correlation coefficient of 0.25±0.01 between the logarithmic dissipations in the inertial subrange. The intermittency parameter for scalar dissipation is estimated to be in the range 0.43≈0.77, based on direct calculations of the variance of lnχr. The scaling exponents of the conditional scalar increment
δ rθ [mid ] χr,εr suggest a tendency to follow RSHP. Most significantly, the scaling exponent ofδ rθ [mid ] χr,εr over εr was shown to be approximately −⅙ in the inertial subrange, confirming a dynamical aspect of RSHP. In agreement with recent experimental results (Zhu et al. 1995; Stolovitzky et al. 1995), the probability distributions of the random variable βs = δrθ[mid ] χr,εr/ (χ1/2r ε−⅙rr1/3) were found to be nearly Gaussian. However, contrary to the experimental results, we find that the moments of βs are almost identical to those for the velocity field found in Part 1 of this study (Wang et al. 1996) and are insensitive to Reynolds number, large-scale forcing, and subgrid modelling.
Analysis of Monin–Obukhov similarity from large-eddy simulation
- SAMIR KHANNA, JAMES G. BRASSEUR
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- Journal:
- Journal of Fluid Mechanics / Volume 345 / 25 August 1997
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- 25 August 1997, pp. 251-286
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A detailed analysis of the predictability of observed Monin–Obukhov (MO) similarity within the near-ground region of near-neutral to moderately convective atmospheric boundary layers (ABL) from large-eddy simulation (LES) fields is reported in this work. High-resolution LES predictions of means, variances, budgets of turbulent kinetic energy and temperature variance, and the velocity and temperature spectra from three ABL states (−zi/L=0.44, 3 and 8) are analysed under MO scaling. The resolution in the near-ground region is increased by using ‘nested meshes.’ For the close-to-neutral case (−zi/L=0.44) the relative roles of grid resolution and subgrid-scale scale (SGS) parameterization on the predictability of MO-similarity are also studied. The simulated temperature field is found to satisfy the MO hypothesis and agree well with observations. The simulated velocity field, on the other hand, shows significant departures. Except for the horizontal variance, MO scales are the appropriate normalizing scales for the near-ground-layer statistics. However, the LES suggest that the boundary layer depth zi has an ‘indirect’ influence on all near-ground-layer variables except temperature, and the LES-predicted MO-scaled variables exhibit a functional dependence on both z/L and z/zi. The simulated two-dimensional spectra of velocity and temperature fluctuations, however, suggest that while large scales deviate from MO-similarity, inertial subrange scales are MO-similar. Discrepancies with field observations raise important questions of the non-dimensional depth z/zi over which MO-similarity holds for a particular variable. Surface-layer field studies generally do not document zi. It is also not clear to what extent these discrepancies are due to approximations made in LES. Measurements are needed designed specifically for comparing with LES predictions.