Obukhov Length Scale Research Articles

Influence of the Coriolis force on the formation of a seasonal thermocline

Large eddy simulation (LES) reveals that the Coriolis force plays an important role in seasonal thermocline formation. In the high-latitude ocean, a seasonal thermocline is formed at a certain depth, across which the downward transports of heat and momentum are prohibited. On the other hand, in the equatorial ocean, heat and momentum continue to propagate downward to the deeper ocean without forming a well-defined thermocline. Mechanism to clarify the latitudinal difference is suggested. The depth of a seasonal thermocline h is scaled in terms of both the Ekman length scale λ and the Monin–Obukhov length scale L, as h ≅ 0.5(Lλ)1/2, which is in contrast to the earlier suggestion as h ∝ L.

Direct numerical simulation of top-down and bottom-up diffusion in the convective boundary layer

AbstractA direct numerical simulation (DNS) of an unstably stratified convective boundary layer with system rotation was performed to study top-down and bottom-up diffusion processes. In order to better understand near-wall dynamics associated with scalar diffusion in the absence of surface roughness, direct simulation is utilized to numerically integrate the governing equations that model the atmospheric boundary layer. The ratio of the inversion height to Obukhov length scale, ${z}_{i} / L= - 49. 1$, indicates moderately strong heating for the case studied. Two passive scalars were initialized in the flow field: the first with a zero gradient at the wall (${q}_{t} $, top-down diffusion), and the second with a non-zero wall gradient and a close-to-zero gradient at the height of the temperature inversion (${q}_{b} $, bottom-up diffusion). Scalar flux, variance and covariance profiles show good agreement between the DNS and rough-wall large-eddy simulation (LES). The top-down gradient function displays a slight increase in amplitude, indicating reduced mixing efficiency for the smooth-wall, low-Reynolds-number convective boundary layer. For the bottom-up process, the gradient matches other rough-wall simulations. The only notable difference between the smooth-wall DNS data and other rough-wall simulations is an increase in the gradient function near the wall. This indicates that the bottom-up gradient functions for a rough wall and a smooth wall are nearly identical except as the viscous sublayer is approached. Finally, a new empirical model for the scalar variance of a bottom-up scalar is proposed: here, a single function replaces two piecewise relationships to accurately capture the DNS results up to the viscous sublayer. The scalar covariance between top-down and bottom-up processes agrees with rough-wall and tree-canopy LES results; this indicates that the scalar covariance is independent of both Reynolds number and surface friction.

Flow and turbulence in an industrial/suburban roughness canopy

A field study conducted to investigate the flow and turbulence structure of the urban boundary layer (UBL) over an industrial/suburban area is described. The emphasis was on morning and evening transition periods, but some measurements covered the entire diurnal cycle. The data analysis incorporated the dependence of wind direction on morphometric parameters of the urban canopy. The measurements of heat and momentum fluxes showed the possibility of a constant flux layer above the height $$z\approx 2{H}$$ , wherein the Monin-Obukhov Similarity Theory (MOST) is valid; here $$H$$ is the averaged building height. For the nocturnal boundary layer, the mean velocity and temperature profiles obeyed classical MOST scaling up to $$\sim 0.5\Lambda \left( {\sim 6{H}}\right) $$ , where $$\Lambda $$ is the Obukhov length scale, beyond which stronger stratification may disrupt the occurrence of constant fluxes. For unstable and neutral cases, MOST scaling described the mean data well up to the maximum measured height $$(\sim 6{H})$$ . Available MOST functions, however, could not describe the measured turbulence structure, indicating the influence of additional governing parameters. Alternative turbulence parameterizations were tested, and some were found to perform well. Calculation of integral length scales for convective and neutral cases allowed a phenomenological description of eddy characteristics within and above the urban canopy layer. The development of a significant nocturnal surface inversion occurred only on certain days, for which a criterion was proposed. The nocturnal UBL exhibited length scale relationships consistent with the evening collapse of the convective boundary layer and maintenance of buoyancy-affected turbulence overnight. The length and velocity scales so identified are useful in parameterizing turbulent dispersion coefficients in different diurnal phases of the UBL.

Nocturnal subcanopy flow regimes and missing carbon dioxide

Two distinct nocturnal subcanopy flow regimes are observed beneath a tall (16 m) open pine forest canopy. The first is characterized by weaker mixing, stronger stability, westerly downslope flow decoupled from the flow above the canopy and much smaller than expected ecosystem respiration from the eddy flux plus storage measurements compared to estimates based on chambers (missing carbon dioxide). The second regime is characterized by stronger mixing, weaker stability, southerly flow coupled to the flow above the canopy and good agreement between the eddy flux plus storage estimate and the chamber-based estimate of ecosystem respiration. The observations show that the inferred advection terms dominate the carbon dioxide budget in the first regime and are small relative to the eddy flux plus storage terms in the stronger mixing second regime, where the advection is estimated as a residual taking chamber-based measurements of respiration as truth. The friction velocity, standard deviation of vertical velocity, bulk Richardson number, Monin–Obukhov length scale and the subcanopy 3-m wind direction are all good indicators of missing carbon dioxide at this site.

Analysis of Turbulence Collapse in the Stably Stratified Surface Layer Using Direct Numerical Simulation

The nocturnal atmospheric boundary layer (ABL) poses several challenges to standardturbulenceanddispersionmodels,sincethestablestratificationimposedbytheradi- ative cooling of the ground modifies the flow turbulence in ways that are not yet completely understood. In the present work we perform direct numerical simulation of a turbulent open channel flow with a constant (cooling) heat flux imposed at the ground. This configuration provides a very simplified model for the surface layer at night. As a result of the ground cool- ing, the Reynolds stresses and the turbulent fluctuations near the ground re-adjust on times of the order of L/uτ ,w hereL is the Obukhov length scale and uτ is the friction velocity. For relatively weak cooling turbulence survives, but when ReL = Luτ /ν 100 turbulence collapses, a situation that is also observed in the ABL. This criterion, which can be locally measured in the field, is justified in terms of the scale separation between the largest and smallest structures of the dynamic sublayer.

Micrometeorological Conditions for Dust-Devil Occurrence in the Atacama Desert

We report on field observations in January 2009 (austral summer) of atmospheric dust devils in the northern part of the Atacama Desert in South America (≈20◦S). An extremely high level of dust-devil activity over the study site has been observed, dependent on local meteorological conditions. We found a high correlation between the dust-devil frequency of occurrence and the Obukhov length scale, L, calculated from meteorological gradient measurements, with a clear tendency for this frequency to increase with decreasing −L. The upper threshold values of −L ≈ 20–30 m, and the 2-m mean wind speed, V 2 ≈ 8m s−1, for dust-devil occurrence have been found, but the minimal V 2 threshold was not observed. Parallel routine meteorological measurements enabled us to calculate the main constituents of the surface energy balance, to obtain direct estimates of the surface albedo (α ≈ 0.21 at the solar noon) and to summarize the local conditions.

Observations of the Effects of Atmospheric Stability on Turbulence Statistics Deep within an Urban Street Canyon

Abstract Data obtained in downtown Oklahoma City, Oklahoma, during the Joint Urban 2003 atmospheric dispersion study have been analyzed to investigate the effects of upstream atmospheric stability on turbulence statistics in an urban core. The data presented include turbulent heat and momentum fluxes at various vertical and horizontal locations in the lower 30% of the street canyon. These data have been segregated into three broad stability classification regimes: stable (z/L > 0.2), neutral (−0.2 < z/L < 0.2), and unstable (z/L < −0.2) based on upstream measurements of the Monin–Obukhov length scale L. Most of the momentum-related turbulence statistics were insensitive to upstream atmospheric stability, while the energy-related statistics (potential temperatures and kinematic heat fluxes) were more sensitive. In particular, the local turbulence intensity inside the street canyon varied little with atmospheric stability but always had large magnitudes. Measurements of turbulent momentum fluxes indicate the existence of regions of upward transport of high horizontal momentum fluid near the ground that is associated with low-level jet structures for all stabilities. The turbulent kinetic energy normalized by a local shear stress velocity collapses the data well and shows a clear repeatable pattern that appears to be stability invariant. The magnitude of the normalized turbulent kinetic energy increases rapidly as the ground is approached. This behavior is a result of a much more rapid drop in the correlation between the horizontal and vertical velocities than in the velocity variances. This lack of correlation in the turbulent momentum fluxes is consistent with previous work in the literature. It was also observed that the mean potential temperatures almost always decrease with increasing height in the street canyon and that the vertical heat fluxes are always positive regardless of upstream atmospheric stability. In addition, mean potential temperature profiles are slightly more unstable during the unstable periods than during the neutral or stable periods. The magnitudes of all three components of the heat flux and the variability of the heat fluxes decrease with increasing atmospheric stability. In addition, the cross-canyon and along-canyon heat fluxes are as large as the vertical component of the heat fluxes in the lower portion of the canyon.

The low‐level katabatic jet height versus Monin–Obukhov height

AbstractIn this short note we discuss a long‐standing problem in modelling the atmospheric boundary layer (ABL) over complex terrain: namely, an excessive use of the Monin–Obukhov length scale LMO. This issue becomes increasingly relevant with the ever‐increasing resolution of numerical weather‐prediction and climate models, which typically use LMO in one way or another for parametrizing the surface layer, or at least for formulating the lower boundary conditions. Hence, inevitably, the models under‐represent a significant part of the mesoscale flow variability.We focus here on the stable ABL over land: in particular, sloped cooled flows. However, a qualitatively similar reasoning applies to the corresponding unstable ABL. We show that for sufficiently stratified flows over moderately sloped surfaces, Monin–Obukhov scaling is inadequate for describing the basic ABL dynamics, which is often governed by katabatic and drainage flows. Copyright © 2007 Royal Meteorological Society

The Scaling and Structure of the Estuarine Bottom Boundary Layer

Abstract A two-week dataset from a partially and periodically stratified estuary quantifies variability in the turbulence across the tidal and spring–neap time scales. These observations have been fit with a two-parameter model of the Reynolds stress profile, which produces estimates of the time variation of the bottom boundary layer height and the friction velocity. Conditions at the top of the bottom boundary layer indicate that the dynamics governing the development of the estuarine bottom boundary layer are different on ebb tides than on flood tides. The asymmetry in the flow is explained by consideration of the strain-induced buoyancy flux, which is stabilizing on ebb tides and destabilizing on flood tides. Based on these observations, a scaling approach to estimating estuarine bottom boundary layer parameters (height and friction velocity) is presented, which includes a modified Monin–Obukhov length scale to account for the horizontal buoyancy flux created by the sheared advection. Comparison with the observations of boundary layer height and friction velocity suggests that this approach may be successful in predicting bottom boundary layer parameters in estuaries and coastal regions with significant horizontal buoyancy fluxes. Comparison between the strain-induced buoyancy flux and shear production indicates that the straining of the density field is an important contributor to the turbulent kinetic energy budget and creates an asymmetry in turbulent energy between ebb and flood tides. It appears that the structure of the turbulence, specifically the ratio of the Reynolds stress to the turbulent energy, is also modified by tidal straining, further accentuating the ebb–flood asymmetries.

Incorporation of a high-roughness lower boundary into a mesoscale model for studies of dry deposition over complex terrain

For flow over natural surfaces, there exists a roughness sublayer within the atmospheric surface layer near the boundary. In this sublayer (typically 50 z0 deep in unstable conditions), the Monin-Obukhov (M-O) flux profile relations for homogeneous surfaces cannot be applied. We have incorporated a modified form of the M-O stability functions (Garratt, 1978, 1980, 1983) in a mesoscale model to take account of this roughness sublayer and examined the diurnal variation of the boundary-layer wind and temperature profiles with and without these modifications. We have also investigated the effect of the modified M-O functions on the aerodynamic and laminar-sublayer resistances associated with the transfer of trace gases to vegetation. Our results show that when an observation height or the lowest level in a model is within the roughness sublayer, neglect of the flux-profile modifications leads to an underestimate of resistances by 7% at the most. Central to the United States and European dry deposition monitoring programs is an inferential technique for calculating the deposition velocity 14t of various trace gases and small particles. Essentially, the method estimates "v~ by applying a 'resistance' model which makes use of measurements of selected meteorological variables (Hicks et aI., 1987). The model needs values of wind speed (u), friction velocity (~), Obukhov length scale (L), air temperature and global radiation at a level just above the zero-plane displacement. One approach to obtaining these values in complex terrain where observations are sparse, and where they are likely to show significant horizontal variation, is to predict them with a prognostic mesoscale numerical model of the atmosphere. However, the presence of a high-roughness lower boundary such as a forest must be taken into account in the mesoscale model by following one of two approaches. The first involves a detailed parameterisation of the mean flow and turbulent fluxes within the forest (e.g., Deardorff, 1978; Garrett, 1983). The second approach is simpler and basically treats the forest as a very rough surface. The first model level is above the forest top, but the presence of the forest is felt by incorporating a zero plane displacement, a relatively large value of the aerodynamic roughness length z0, and modified Monin-Obukhov (M- O) functions to take account of increased mixing arising from flow around the roughness elements (trees). In this study, we have adopted the second and simpler approach.

A numerical study of the convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio −zi/L*=26. However, when heating is more moderate (so that −zi/L*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.

Estimates of diabatic wind speed profiles from near-surface weather observations

In this paper we analyse diabatic wind profiles observed at the 213 m meteorological tower at Cabauw, the Netherlands. It is shown that the wind speed profiles agree with the well-known similarity functions of the atmospheric surface layer, when we substitute an effective roughness length. For very unstable conditions, the agreement is good up to at least 200 m or z/L≃−7(z is height, L is Obukhov length scale). For stable conditions, the agreement is good up to z/L≃1. For stronger stability, a semi-empirical extension is given of the log-linear profile, which gives acceptable estimates up to ~ 100 m. A scheme is used for the derivation of the Obukhov length scale from single wind speed, total cloud cover and air temperature. With the latter scheme and the similarity functions, wind speed profiles can be estimated from near-surface weather data only. The results for wind speed depend on height and stability. Up to 80 m, the rms difference with observations Σ is on average ≃1.1 m s−1. At 200 m, Σ ≃ 0.8 m s−1 for very unstable conditions increasing to Σ ≃ 2.1 m s−1 for very stable conditions. The proposed methods simulate the diurnal variation of the 80 m wind speed very well. Also the simulated frequency distribution of the 80 m wind speed agrees well with the observed one. It is concluded that the proposed methods are applicable up to at least 100 m in generally level terrain.

Turbulent mixing with stabilizing surface buoyancy flux

A laboratory experiment is studied with turbulence in salt water produced by an oscillating grid. A stabilizing buoyancy flux leads to a mixed layer depth that is proportional to the properly defined Monin–Obukhov length scale.