Two phenomenological constants explain similarity laws in stably stratified turbulence

Katul, Gabriel G.; Porporato, Amilcare; Shah, Stimit; Bou‐Zeid, Elie

doi:10.1103/physreve.89.023007

Cited by 61 publications

(121 citation statements)

References 60 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…This approach has also been used to explain macroscopic relations between the turbulent Prandtl number, Monin-Obukhov stability parameter, and Richardson number in the stratified ASL. [19][20][21] The modeled MVP in KM14 matches experimental observations well in the logarithmic region (see also Ref. 22) and the viscous sublayer, where turbulent stresses are small.…”

Section: )supporting

confidence: 66%

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

et al. 2016

Self Cite

View full text Add to dashboard Cite

A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the “law of the wall”. While the approach reasonably models the MVP’s logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the “missing” curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the “spectral link” between Fvv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.

show abstract

Section: )supporting

confidence: 66%

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

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…With a higher Reynolds number (Re f = 600), the surface Richardson number Ri 0,0 where this intermittent behaviour in TKE is seen increases to around 0.005, while for Ri 0,0 = 0.010 the flow laminarizes almost completely. At Re f = 900, the flow remains fully and steadily turbulent up to Ri 0,0 = 0.005; therefore, the hypothesized increase in the critical Richardson number with increasing Reynolds number (Schlichting 1979;Katul et al 2014) is further supported by these findings.…”

Section: Physical Parameterssupporting

confidence: 60%

“…For example, some studies (see Canuto 2002, and references therein) indicate that Ri c may be as large as one or beyond, and some argue that a critical limit does not exist at all (Monin & Yaglom 1975;Yamamoto 1975;Lettau 1979;Galperin, Sukoriansky & Anderson 2007). Other arguments suggest that laminarization would happen when the characteristic length of the large eddies (estimated as the Obukhov scale in Flores & Riley (2011) and the Ozmidov scale in Katul et al (2014)), which is reduced by buoyancy, approaches some multiple of the Kolmogorov scale, the ratio of the two scales effectively becoming proportional to Re 3/4 . Chung & Matheou (2012) also argue in their analysis of stationary homogeneous stratified turbulence that the Richardson number is not sufficient to determine the state of the flow; a measure of the scale separation (given by the Reynolds number) is also needed.…”

Section: Profiles Of the Gradient Richardson Number Tke And Stressmentioning

confidence: 94%

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Shah

Bou‐Zeid

2014

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

Direct numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin-Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress-strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

show abstract

“…For example, in the University of Washington moist turbulence scheme in CAM5 [ Bretherton and Park , ; Park and Bretherton , ], which is a turbulent kinetic energy closure scheme, uses the moist gradient Richardson number to diagnose the vertical extent and stability characteristics of all turbulent layers in a model grid column. Flux Richardson number is often used in observational and theoretical studies [ Yamada , ; Grachev et al , ; Katul et al , ]. It is particularly pointed out that the “ critical bulk Richardson number” used in our study is different from the “ critical gradient Richardson number” often associated with the Miles‐Howard theory on the stability of laminar boundary layers whose value is about 0.25 [ Miles , ].…”

Section: Introductionmentioning

confidence: 81%

Sensitivity of a global climate model to the critical Richardson number in the boundary layer parameterization

et al. 2015

View full text Add to dashboard Cite

The critical bulk Richardson number (Ri cr ) is an important parameter in planetary boundary layer (PBL) parameterization schemes used in many climate models. This paper examines the sensitivity of a global climate model, the Beijing Climate Center atmospheric general circulation model, to Ri cr . The results show that the simulated global average of PBL height increases nearly linearly with Ri cr , with a change of about 114 m for a change of 0.5 in Ri cr . The surface sensible (latent) heat flux decreases (increases) as Ri cr increases. The influence of Ri cr on surface air temperature and specific humidity is not significant. The increasing Ri cr may affect the location of the Westerly Belt in the Southern Hemisphere. Further diagnosis reveals that changes in Ri cr affect stratiform and convective precipitations differently. Increasing Ri cr leads to an increase in the stratiform precipitation but a decrease in the convective precipitation. Significant changes of convective precipitation occur over the Intertropical Convergence Zone, while changes of stratiform precipitation mostly appear over arid land such as North Africa and Middle East.

show abstract

Two phenomenological constants explain similarity laws in stably stratified turbulence

Cited by 61 publications

References 60 publications

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

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

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

Sensitivity of a global climate model to the critical Richardson number in the boundary layer parameterization

Contact Info

Product

Resources

About