Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

Quart J Royal Meteoro Soc

et al. 2017

Self Cite

While the breakdown in similarity between turbulent transport of heat and momentum (or Reynolds analogy) is not disputed in the atmospheric surface layer (ASL) under unstably stratified conditions, the causes of this breakdown are still debated. One reason for the breakdown is differences between how coherent structures transport heat and momentum, and their differing responses to increasing instability. Monin—Obukhov Similarity Theory (MOST), which hypothesizes that only local length‐scales play a role in ASL turbulent transport, implicitly assumes that large‐scale structures are inactive, despite their large energy content. Widely adopted mixing‐length models also rest on this assumption in the ASL. The difficulty of characterizing low‐wavenumber turbulent motions with field measurements motivates the use of high‐resolution Direct Numerical Simulation (DNS), which is free from subgrid‐scale parametrizations and adhoc assumptions near the boundary. Despite the low Reynolds number and idealized geometry of the DNS, DNS‐estimated MOST functions are consistent with ASL field experiments, as are low‐frequency features of the spectra. Parsimonious spectral models for MO stability correction functions for momentum (φm) and heat (φh) are derived, based on idealized vertical velocity variance and buoyancy variance spectra fit to the corresponding DNS spectra. For φm, a spectral model, based only on local length‐scales, matches DNS and field measurements well. In contrast, for φh, the model is substantially biased unless contributions from larger length‐scales are also included. These results are supported by sensitivity analyses based on field measurements that are independent of the DNS. They show that ASL heat transport is not MO‐similar, even under mild stratification, and in the absence of entrainment, non‐stationarity and canopy effects. It further suggests that the breakdown of the Reynolds analogy is at least partially caused by the influence of large eddies on turbulent heat transport.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Role of large eddies in the breakdown of the Reynolds analogy in an idealized mildly unstable atmospheric surface layer

McColl

Heerwaarden

Quart J Royal Meteoro Soc

et al. 2017

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“…where S is the mean streamwise velocity gradient along the vertical direction, A UU is a parameter in the gradient diffusion model for the flux transfer term, A U is the Rotta parameter associated with the slow-component of ⇡ uw , 29 whereas the (3/5)P uw term is associated with the fast-component (wall blocking is ignored at z sufficiently far from the boundary for reasons discussed elsewhere 30 ), and ⌧(k) = ✏ 1/3 k 2/3 is a wavenumber-dependent relaxation time scale derived from K41 dimensional considerations 31 where ✏ is the mean TKE dissipation rate. In statistical mechanics, the relaxation time scale measures the time required for a perturbed system to go back to an equilibrium state.…”

Section: Theorymentioning

confidence: 99%

On the linkage between the k−5/3 spectral and k−7/3 cospectral scaling in high-Reynolds number turbulent boundary layers

2017

Physics of Fluids

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Connections between the " 5/3" spectral and " 7/3" cospectral scaling exponents characterizing the inertial subranges of the wall-normal energy spectrum and the turbulent momentum flux cospectrum are explored in the equilibrium layer of high-Reynolds number turbulent boundary layers. Previous laboratory experiments and field measurements featured here in the atmospheric boundary layer show that the " 7/3" scaling in the momentum flux cospectrum F uw (k) commences at lower wavenumbers (around kz = 3) than the " 5/3" scaling in the wall-normal energy spectrum E ww (k) (around kz = 6), where k is the streamwise wavenumber and z is the distance from the surface. A satisfactory explanation as to why F uw (k) attains its " 7/3" inertial subrange scaling earlier than E ww (k) in wavenumber space remains elusive. A cospectral budget (CSB) model subject to several simplifications and closure schemes offers one viewpoint. In its simplest form, the CSB model assumes a balance at all k between the production term and a Rotta-like pressure decorrelation term with a prescribed wavenumberdependent relaxation time scale. It predicts the " 7/3" scaling for F uw (k) from the " 5/3" scaling in E ww (k), thereby recovering earlier results derived from dimensional considerations. A finite flux transfer term was previously proposed to explain anomalous deviations from the " 7/3" cospectral scaling in the inertial subrange using a simplified spectral diffusion closure. However, this explanation is not compatible with an earlier commencement of the " 7/3" scaling in F uw (k). An alternative explanation that does not require a finite flux transfer is explored here. By linking the relaxation time scale in the slow-component of the Rotta model to the turbulent kinetic energy (TKE) spectrum, the earlier onset of the " 7/3" scaling in F uw (k) is recovered without attainment of a " 5/3" scaling in E ww (k). The early onset of the " 7/3" scaling at smaller k is related to a slower than k 5/3 decay in the TKE spectrum at the crossover from production to inertial scales.

“…Despite the maximum simplicity of this approach relative to the original derivation in Brutsaert [], the proposed structure function approach suffers from a number of limitations. To begin with, it is known that near roughness elements, production, and dissipation of TKE are not in balance and production may be up to 1.7 times larger than ϵ [ Pope , ] even for very high Reynolds numbers and close to the surface at

z u_{*} / ν \approx 10

[ McColl et al ., ]. However, this imbalance may not be as detrimental given the subunity exponent dependency of k T on ϵ .…”

Section: Discussion and Study Limitationmentioning

confidence: 99%

A Kolmogorov‐Brutsaert structure function model for evaporation into a turbulent atmosphere

Water Resources Research

2017

In 1965, Brutsaert proposed a model that predicted mean evaporation rate E¯ from rough surfaces to scale with the 3/4 power law of the friction velocity ( u∗) and the square‐root of molecular diffusivity (Dm) for water vapor. In arriving at these results, a number of assumptions were made regarding the surface renewal rate describing the contact durations between eddies and the evaporating surface, the diffusional mass process from the surface into eddies, and the cascade of turbulent kinetic energy sustaining the eddy renewal process itself. The working hypothesis explored here is that trueE¯∼Dmu∗3/4 is a direct outcome of the Kolmogorov scaling for inertial subrange eddies modified to include viscous cutoff thereby bypassing the need for a surface renewal assumption. It is demonstrated that Brutsaert's model for E¯ may be more general than its original derivation implied.