Monin-Obukhov Scaling Research Articles

Evaluating Monin–Obukhov Scaling in the Unstable Oceanic Surface Layer

AbstractMonin–Obukhov similarity theory (MOST) provides important scaling laws for flow properties in the surface layer of the atmosphere and has contributed to most of our understanding of the near-surface turbulence. The prediction of near-surface vertical mixing in most operational ocean models is largely built upon this theory. However, the validity of MOST in the upper ocean is questionable due to the demonstrated importance of surface waves in the region. Here we examine the validity of MOST in the statically unstable oceanic surface layer, using data collected from two open ocean sites with different wave conditions. The observed vertical temperature gradients are found to be about half of those predicted by MOST. We hypothesize this is attributable to either the breaking of surface waves, or Langmuir turbulence generated by the wave–current interaction. Existing turbulence closure models for surface wave breaking and for Langmuir turbulence are simplified to test these two hypotheses. Although both models predict reduced temperature gradients, the simplified Langmuir turbulence model matches observations more closely, when appropriately tuned.

Numerical study of aircraft wake vortex evolution near ground in stable atmospheric boundary layer

The evolutions of aircraft wake vortices near ground in stable atmospheric boundary layer are studied by Large Eddy Simulation (LES). The sensitivity of vortex evolution to the Monin-Obukhov (M-O) scale is studied for the first time. The results indicate that increasing stability leads to longer lifetimes of upwind vortices, while downwind vortices will decay faster due to a stronger crosswind shear under stable conditions. Based on these results, an empirical model of the vortex lifetime asa function of 10-m-high crosswind and the M-O scale is summarized. This model can provide an estimate of the upper boundary of the vortex lifetime according to the real-time crosswind and atmospheric stability. In addition, the lateral translation of vortices is also inspected. The results show that vortices can travel a furthest distance of 722m in the currently-studied parameter range. This result is meaningful to safety analysis of airports that have parallel runways.

What can be measured by the temperature profiler

The ability of the ground-based microwave temperature profiler to retrieve the lapse rates in the lower part of the atmospheric boundary layer is verified by analyzing the long-term observation series. It is demonstrated that if the stratification of the whole boundary layer is either unstable or sufficiently homogeneous, measured and retrieved with a mast lapse rates are quite similar. If the stratification is stable, the retrieval algorithms require correction. Demonstrated is the potential for the more accurate retrieving of the temperature gradient over the surface layer by means of the angular scanning. This enables using the data of temperature profilers for estimating the boundary layer stability and the Monin-Obukhov scale.

Influence of advection on the characteristics of turbulence over uneven surface in the oasis and the Gobi Desert

Utilizing experimental data of the atmospheric surface layer in the Gobi Oasis of Jinta in a comparative study, we demonstrate that under the condition of unstable stratification, the normalization variances of temperature in the oasis and Gobi Desert meet φ θ (z/Λ) = α θ (−z/Λ)−1/3 while normalization variances of both humidity and CO2 in the oasis meet φ s (z/Λ) = α s (1−α s z/Λ)−1/3; the normalization variance of temperature in the oasis is large due to disturbance by advection, whereas variance of CO2 in the Gobi Desert has certain degree of deviation relative to Monin-Obukhov (M-O) scaling, and humidity variance completely deviates from variance M-O scaling. The above result indicates that under the condition of advection, humidity variance meets the relation σ m 2 = D 2 σ A 2 + σ B 2 and it is determined by relative magnitude of scalar variance of advection transport. Our study reveals that, if the scalar variance of humidity or CO2 transported by advection is much larger than local scalar variance, observation value of scalar variance will deviate from M-O scaling; when scalar variance of advection transport is close to or less than local scalar variance, the observation value of scalar variance approximately meets M-O scaling.

Hans A. Panofsky’s Integral Similarity Function—At Fifty

Fifty years ago, Hans A. Panofsky published a paper entitled Determination of stress from wind and temperature measurements. In his famous paper, he presented a new profile function for the mean horizontal wind speed under the condition of diabatic stratification that includes his integral similarity function. With his integral similarity function, he opened the door for Monin-Obukhov scaling in a wide range of micrometeorological and microclimatological applications. In a historic survey ranging from the sixties of the past century down to the present days, we present integral similarity functions for momentum, sensible heat, and water vapor for both unstable and stable stratification, where on the one hand free convection condition and on the other hand strongly stable stratification are addressed.

Turbulence spectra measured during fire front passage

Four field experiments were conducted over various fuel and terrain to investigate turbulence generation during the passage of wildland fire fronts. Our results indicate an increase in horizontal mean winds and friction velocity, horizontal and vertical velocity variances as well as a decreased degree of anisotropy in TKE during fire front passage (FFP) due to fire-induced winds. Vertical velocity and temperature variances observed during FFP approached the local free convection prediction when represented as a function of stability parameter z/L under very unstable conditions. The results of our wavelet spectral analysis show increased energy in velocity and temperature spectra at high frequency during FFP for all four cases; we hypothesize this is caused by the shedding of small eddies generated from the fire front. Additionally, spectral energy of velocity components at low frequencies may be affected by cross-flow intensity, topography, presence of canopy layer, and degree of fire–atmosphere coupling. When the velocity spectra are normalized using the friction velocity u* following Monin–Obukhov scaling, the velocity spectra observed during the FFP collapsed into a fairly narrow band in the inertial subrange, suggesting that as far as inertial range is concerned, the friction velocity u* is a valid scaling parameter that can be used for wildfire application. When the temperature spectra are normalized by T*, the temperature spectra observed during the FFP did not show any systematic behaviors predicted by the similarity scaling due to the extreme surface heating environment of fires.

On total turbulent energy and the passive and active role of buoyancy in turbulent momentum and mass transfer.

Measurements of turbulent fluctuations of horizontal and vertical components of velocity, salinity and suspended particulate matter are presented. Turbulent Prandtl numbers are found to increase with stratification and to become larger than 1. Consequently, the vertical turbulent mass transport is suppressed by buoyancy forces, before the turbulent kinetic energy (TKE) and vertical turbulent momentum exchange are inhibited. With increasing stratification, the buoyancy fluxes do not cease, instead they become countergradient. We find that buoyantly driven motions play an active role in the transfer of mass. This is in agreement with trends derived from Monin–Obukhov scaling. For positive Richardson flux numbers (Rif), the log velocity profile in the near-bed layer requires correction with a drag reduction. For negative Rif, the log velocity profile should be corrected with a drag increase, with increasing |Rif|. This highlights the active role played by buoyancy in momentum transfer and the production of TKE. However, the data do not appear to entirely follow Monin–Obukhov scaling. This is consistent with the notion that the turbulence field is not in equilibrium. The large stratification results in the decay of turbulence and countergradient buoyancy fluxes act to restore equilibrium in the energy budget. This implies that there is a finite adjustment timescale of the turbulence field to changes in velocity shear and density stratification. The energy transfers associated with the source and sink function of the buoyancy flux can be modeled with the concept of total turbulent energy.

On Monin–Obukhov Scaling in and Above the Atmospheric Surface Layer: The Complexities of Elevated Scintillometer Measurements

In scintillometry Monin–Obukhov similarity theory (MOST) is used to calculate the surface sensible heat flux from the structure parameter of temperature \({(C_{T^2})}\) . In order to prevent saturation a scintillometer can be installed at an elevated level. However, in that case the observation level might be located outside the atmospheric surface layer (ASL) and thus the validity of MOST questioned. Therefore, we examine two concepts to determine the turbulent surface sensible heat flux from the structure parameter at elevated levels with data obtained at 60-m height on the Cabauw tower (the Netherlands). In the first concept (MOSTs) \({C_{T^2}}\) is still scaled with the surface flux, whereas in the second (MOSTl) \({C_{T^2}}\) is scaled with the local sensible heat flux. The \({C_{T^2}}\) obtained from both concepts is compared with direct observations of \({C_{T^2}}\) using a sonic anemometer/thermometer. In the afternoon (when the measurement height is located within the ASL) both concepts give results that are comparable to the directly observed values of \({C_{T^2}}\) . In the morning (data outside the ASL), our data do not unequivocally support either of the two concepts. First, the peak in \({C_{T^2}}\) that occurs when the measurement height is located in the entrainment zone disqualifies the use of MOST. Second, during the morning transition, local scaling shows the correct pattern (zero flux and a minimum in \({C_{T^2}}\)) but underestimates \({C_{T^2}}\) by a factor of ten. Third, from the best linear fit a we found that the slope of MOSTl gave better results, whereas the offset is closer to zero for MOSTs. Further, the correlation between the direct observations and MOST-scaled results is low and similar for the two concepts. In the end, we conclude that MOST is not applicable for the morning hours when the observation level is above the ASL.

The energy and dissipation of turbulent fluctuations of wind velocity and temperature in the boundary layer of the atmosphere

The relationships between the energy of small-scale turbulence and its dissipation rate are studied based on the data of long-term high-frequency measurements of temperature and wind velocity fluctuations in urban area. It is shown that the energy of wind velocity turbulent fluctuations is linearly related to the dissipation rate ɛ. The proportionality coefficient between turbulent kinetic energy (TKE) and ɛ is dimensional and does not depend on the stratification of the atmosphere, the Richardson number, or the Monin-Obukhov scale. Measurements in different seasons show that this coefficient can be related to the mean velocity of adiabatic motions (sound speed or air temperature), which enables one to select a more universal constant, γ. A linear relationship between the temperature fluctuations variance (the characteristic of the inner energy of turbulence) and their dissipation rate is also shown. The revealed proportionality is confirmed by measurements in urban and forest conditions, as well as in the surface layer over a flat desert terrain.

Observational Study of Marine Atmospheric Boundary Layer Characteristics during Swell

Abstract By combining simultaneous data from an instrumented Air–Sea Interaction Spar (ASIS) buoy and a 30-m tower, profiles of wind and turbulence characteristics have been obtained at several heights from about 1 to 30 m above the water surface during swell conditions. Five cases formed as averages over time periods ranging from 2.5 to 9.5 h, representing quasi-steady conditions, have been selected. They represent a range of typical wave age and include wind-following swell cases and cross-swell cases. For relatively large wave age, the wind profile exhibits a well-defined maximum in the height range 5–10 m; for more modest wave age, this maximum turns into a sharp “knee” in the wind profile. Below the maximum (or knee), the wind increases rapidly with height; above that point the wind is very nearly constant up to the highest measuring level on the tower, 30 m. Analysis of balloon data from one day with swell indicates that the layer with constant wind in fact extends to the top of the boundary layer, in this case ∼200 m. Analysis of the complete swell dataset from the 45 days of the 2003 Baltic Swell experiment shows that the results concerning wind profile shape obtained from the selected cases are generally valid in this experiment. Analysis of the nondimensional wind profile ϕm shows that Monin–Obukhov scaling is not valid during swell. Wind and turbulence characteristics are found not to vary to a significant degree with the wind/swell angle within the range of angles encountered, ±90°.

Similarity Hypotheses for the Atmospheric Surface Layer Expressed by Non-Dimensional Characteristic Invariants – A Review

In this paper, similarity hypotheses for the atmospheric surface layer (ASL) are reviewed using nondimensional characteristic invariants, referred to as π-numbers. The basic idea of this dimensional π-invariants analysis (sometimes also called Buckingham’s π-theorem) is described in a mathematically generalized formalism. To illustrate the task of this powerful method and how it can be applied to deduce a variety of reasonable solutions by the formalized procedure of non-dimensionalization, various instances are represented that are relevant to the turbulence transfer across the ASL and prevailing structure of ASL turbulence. Within the framework of our review we consider both (a) Monin- Obukhov scaling for forced-convective conditions, and (b) Prandtl-Obukhov-Priestley scaling for free-convective conditions. It is shown that in the various instances of Monin-Obukhov scaling generally two π-numbers occur that result in corresponding similarity functions. In contrast to that, Prandtl-Obukhov-Priestley scaling will lead to only one π number in each case usually considered as a non-dimensional universal constant. Since an explicit mathematical relationship for the similarity functions cannot be obtained from a dimensional π- invariants analysis, elementary laws of π-invariants have to be pointed out using empirical or/and theoretical findings. To evaluate empirical similarity functions usually considered within the framework flux-profile relationships, so-called integral similarity functions for momentum and sensible heat are presented and assessed on the basis of the friction velocity and the vertical component of the eddy flux densities of sensible and latent heat directly measured during the GREIV I 1974 field campaign.

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 wind profile up to 300 meters over flat terrain

Analysis of profiles of meteorological measurements from a 160 m high mast at the National Test Site for wind turbines at Høvsøre (rural, Denmark) shows that the wind profile based on surface-layer theory and Monin-Obukhov scaling is valid up to a height of 50 to 80 m. At higher levels deviations from the measurements progressively occur. The measurements also indicated that the height of the boundary layer influences the wind profile even in the lowest hundreds of meters. A parameterization of the wind profile for the entire boundary layer is formulated, with emphasis on the lowest 200 - 300 meters.

On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer

Analysis of profiles of meteorological measurements from a 160 m high mast at the National Test Site for wind turbines at Hovsore (Denmark) and at a 250 m high TV tower at Hamburg (Germany) shows that the wind profile based on surface-layer theory and Monin-Obukhov scaling is valid up to a height of 50–80 m. At higher levels deviations from the measurements progressively occur. For applied use an extension to the wind profile in the surface layer is formulated for the entire boundary layer, with emphasis on the lowest 200–300 m and considering only wind speeds above 3 m s−1 at 10 m height. The friction velocity is taken to decrease linearly through the boundary layer. The wind profile length scale is composed of three component length scales. In the surface layer the first length scale is taken to increase linearly with height with a stability correction following Monin-Obukhov similarity. Above the surface layer the second length scale (L MBL ) becomes independent of height but not of stability, and at the top of the boundary layer the third length scale is assumed to be negligible. A simple model for the combined length scale that controls the wind profile and its stability dependence is formulated by inverse summation. Based on these assumptions the wind profile for the entire boundary layer is derived. A parameterization of L MBL is formulated using the geostrophic drag law, which relates friction velocity and geostrophic wind. The empirical parameterization of the resistance law functions A and B in the geostrophic drag law is uncertain, making it impractical. Therefore an expression for the length scale, L MBL , for applied use is suggested, based on measurements from the two sites.

Atmospheric surface layer spectra over a tropical desert station during Indian summer monsoon

Characteristics of turbulence have been studied using the observations of wind components (u, v and w) and temperature (T) collected by fast response sensor the sonic anemometer (8.33 Hz) during the Monsoon Trough Boundary Layer Experiment in 1990. The analysis showed that the spectra of wind and temperature obeyed the Monin-Obukhov scaling. The spectral curve showed a slope of –2/3 in high frequency portion which indicated the existence of inertial subrange. The diurnal variation in the eddy sizes were brought out.

Concerning the influence of wave breaking on Monin-Obukhov similarity theory

This analytical study is concerned with assessing the impact of wave breaking on the similarity structure in the oceanic surface layer. This is accomplished by casting a Mellor-Yamada turbulence closure scheme in nondimensional form using Monin-Obukhov scaling. The effects of wave breaking are imposed on these equations according to Craig and Banner [1], and the behavior of the resulting similarity structure is investigated. The results obtained suggest that a significant departure from the familiar Monin-Obukhov similarity structure observed in the atmospheric surface layer is possible. An obstacle in this analysis lies in prescribing the roughness length.

Surface layer turbulence spectra and dissipation rates during low winds in tropics

Spectral characteristics of surface layer turbulence in an urban atmosphere are investigated. The observations used for this purpose represent low wind conditions in the tropics. The normalized power spectral shapes exhibit the usual characteristics in the inertial subrange and obey Monin-Obukhov scaling. However, the low-frequency behaviours do not conform to the previous observed relations. For horizontal components, large energy is contained in the low frequencies in contrast to the vertical component where roll-off to zero frequency is faster. The turbulent kinetic energy dissipation rate estimated from the spectra using Kolmogorov's inertial subrange law is found to be isotropic unlike the velocity variances. The expressions for the dimensionless dissipation rate do not seem to work well in low winds in an urban atmosphere. For the data considered, the dissipation rate exhibits a power law relationship with the mean windspeed and the friction velocity.

Methodology for bulk approximation of the wind profile power-law exponent under stable stratification

The variation of the wind profile power-law exponent (p) with respect to changes in atmospheric stability is depicted using the formulation of Ku et al. (1987) for specifying the Monin-Obukhov scaling length (L) under stable atmospheric conditions. The theoretical estimates for the bulk approximation of p as a function of L under stable conditions compare well with power-law exponent data from various sources and the theoretical analysis from Irwin (1979).

Theoretical investigation of coherent structures in stratified turbulent channel flow

A theoretical model is constructed of turbulent stratified flow in a flat horizontal channel with allowance for coherent structures that arise in it. The ordered part is separated from the turbulence of the flow and to describe the Reynolds-type equations are derived. The remaining part of the turbulence is taken into account parametrically in the form of an effective exchange coefficient. The flow is divided into a core, in which the ordered structures are manifested quite clearly, and wall regions, in which ordered large-scale structures are weakly manifested. To study the coherent structures in the core of the flow, an approach analogous to one already used to model ordered structures in open flows [4] is used. Monin-Obukhov scaling theory is used to describe the turbulence in the wall region.

Wind fluctuations in stable air at the boulder tower

Spectra and variances of velocity components and pressure in stable air were analyzed at the 300 m tower of the BAO. Spectra in very stable air in light winds usually contain low-frequency fluctuations of large magnitude, and high-frequency fluctuations with considerably less energy, separated by a gap. The wave-length of the gap follows Monin-Obukhov scaling. The high-frequency portion of the spectra has characteristics of turbulence. The low-frequency energy is almost certainly due to gravity waves, since there is coherence between vertical velocities and temperatures, and since surface pressure time series resemble time series of velocity components at the higher levels on the tower. Variances of surface pressure changes appear to be positively correlated with variances of vertical velocity above 100 m, and also to some extent, with horizontal velocity components at all levels. Those results have applications to diffusion estimates from continuous elevated sources, but need confirmation on the basis of measurements elsewhere and additional analyses at BAO.