Molecular dissipation of turbulent fluctuations in the convective mixed layer part II: Height variations of characteristic time scales and experimental test of molecular dissipation models

Extensive turbulence measurements from the Limagne and Beauce experiments were used to compute a characteristic time scale of the turbulence field (Τ = second moment/dissipation rate) for turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance. The height variations of these time scales were analysed. The characteristic half-time scale Τ/2 of the turbulent velocity field was found, as expected, to be of the same order of magnitude as the large-eddy time scale Τ _L = Z_i/w*, showing that the turbulence structure is controlled by large eddies in the bulk of the mixed layer. The increase of Τ/2 above z/Z _i ～- 0.7 implies, however, that this time scale is no longer relevant to destruction of turbulent kinetic energy in the statically stable region with negative heat fluxes. An effective time scale Τ_eff, introduced by Zeman (1975), has been computed and its behaviour discussed. The scales for θ′ ², q′², and θ′q′ were found to be much shorter than Τ. Furthermore, a significant difference in behaviour was also revealed between the characteristic time scales of temperature and humidity fields in the stable layer. By using these experimental estimates, we tested some of the models for molecular dissipations, which are currently in use in higher order closure atmospheric boundary-layer models. The parameterized dissipation rates for θ′ ², and q′ ² agree well qualitatively with experimental estimates in the bulk of the mixed layer. In the stable layer, however, the parameterized dissipation rate ε _θ tends to become larger than the experimental ones although the parameterized dissipation rate ε _q still agrees with the experimental ones. For the molecular dissipation of θ′q′, this current model becomes physically inconsistent in the middle part of the mixed layer, because this term may become a production term for temperature-humidity covariance.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

Fractal properties of temperature fluctuations in the convective surface layer

Temperature fluctuations in a convective surface layer were investigated. Box counting analysis was performed to investigate fractal properties of surfaces of constant temperature and was performed on sets of points obtained by setting thresholds on detrended records. Results indicate that surfaces of constant temperature have fractal properties for thresholds far from the mean. Estimated fractal dimensions of one-dimensional cuts through these surfaces varied between 0.23 and 0.66, increasing with threshold value approaching the mean temperature. For thresholds close to the mean, no fractal behavior was found. Asymmetry in results for thresholds above and below the mean temperature was attributed to the asymmetry between updrafts and downdrafts in the convective surface layer.The temperature dissipation rate (TD) was also investigated. It was found to be strongly intermittent with large fluctuations of the intermittency exponent. Moments were analyzed in order to investigate multifractal properties of TD. Results indicate scaling in the range of 50–1000 (where is the Kolmogorov scale) and multifractal properties resembling those observed for passive scalar dissipation in laboratory flows.     

Characteristics of vertical turbulent velocities in the urban convective boundary layer

Turbulence measurements of the vertical velocity component were obtained by an instrumented aircraft under fair weather conditions in the St. Louis, Missouri, metropolitan area. Time series of vertical velocity fluctuations from horizontal flight segments made in the lower part of and near the middle of the convective boundary layer (CBL) over the urban area and surrounding region were subjected to various statistical and objective analyses. Higher order vertical velocity moments, and positive and negative velocity statistics, were computed. The horizontal dimensions of updrafts and downdrafts, and related properties of these turbulent eddies were derived by conditional sampling analysis. Emphasis is on a comparison of the results from urban and selected rural measurements from the lower part of the CBL.The vertical velocity probability density distribution for each segment was positively skewed and the mode was negative. The means and standard deviations of positive and negative velocity fluctuations were greater over the urban area. The urban vertical velocity variance was 50% greater than rural values, and power spectra revealed greater production of vertical turbulent energy in the urban area over a wide frequency range.The mean and maximum widths of downdrafts were generally larger than the corresponding values for updrafts. Differences between urban and rural eddy sizes were not statistically significant. The widths of the largest updraft and downdraft are comparable to the boundary-layer depth, Z _i, and the mean value of the ratio of spectral peak wavelength to Z _iwas about 1.3 and 1.1 for urban and rural areas, respectively. Convective similarity scaling parameters appeared to order both the urban and rural measurements.On assignment from the National Oceanic and Atmospheric Administration, U.S. Dept. of Commerce.     

Generation and dissipation of microwave refractive-index fluctuations in the boundary layer

The index of refraction and its short-term variations have been measured on a 152-m meteorological tower at three fixed levels and on a moveable platform. Analysis of the data reveals that the time rates of production and dissipation of refractivity fluctuations are approximately in balance under a variety of meteorological conditions, and that changes in the rate of dissipation usually coincide with comparable changes in the rate of production. Under reasonably stationary conditions, terms corresponding to the rate of change and vertical diffusion of refractivity variance are found to be negligible. Power spectral densities of the variations increase when the rate of generation (and dissipation) increase, and conversely. Comparison of the results with simultaneous acoustic sounder returns provides a valuable insight into the mechanisms responsible for changes in the rates of production and dissipation.     

A laboratory study of the turbulent velocity characteristics in the convective boundary layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.     

Micromixing modelling of concentration fluctuations in inhomogeneous turbulence in the convective boundary layer

The micromixing technique, widely used in engineering calculations of mixing and chemical reaction, is extended to atmospheric boundary-layer flows. In particular, a model based on the interaction-by-exchange-with-the-conditional-mean (IECM) micromixing approach is formulated to calculate concentration fluctuation statistics for a line source and a point source in inhomogeneous and non-Gaussian turbulence in the convective boundary layer. The mixing time scale is parameterised as a linear function of time with the intercept value determined by the source size at small times. Good agreement with laboratory data for the intensity of concentration fluctuations is obtained with a value of 0.9 for the coefficient of the linear term in the time-scale parameterisation for a line source, and a value of 0.6 for a point source. Calculation of higher-order moments of the concentration field for a line source shows that non-Gaussian effects persist into the vertically well-mixed region. The cumulative distribution function predicted by the model for a point source agrees reasonably well with laboratory data, especially in the far field. In the limit of zero mixing time scale, the model reduces to a meandering plume model, thus enabling the concentration variance to be partitioned into meandering and relative components. The meandering component is shown to be more persistent for a point source than for a line source.     

Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windu _g . The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.     

Sensitivity analysis of the equations for a convective mixed layer

Jump or slab models are frequently used to calculate the depth of the convectively mixed layer and its potential temperature during the course of a clear day. Much attention has been paid theoretically to the parameterization of the budget for turbulent kinetic energy that is required in these models. However, for practical applications the sensitivity of the solutions of the model equations to variations in the entrainment formulation and in the initial and boundary conditions is also very important. We analyzed this sensitivity on the basis of an analytical solution for the model which uses the well-known constant heat flux ratio. The initial conditions for the mixed-layer height (h) and potential temperature ( _m ) quickly lose their influence. Only the initial temperature deficit is important. The mixed-layer temperature at noon on convective days is insensitive to the entrainment coefficient c. It is governed by the integral of the heat input and by the stable lapse rate. A change in c from 0.2 to 0.5 leads to a variation of 20% in h. This is not very much considering the accuracy in the determination of h from actual observations.     

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Second order modeling of turbulent transport in the surface mixed layer

A model for the simultaneous transport of heat and water vapor is presented. In an effort to resolve the structure of the entrainment region at the inversion base, models are constructed so as to satisfy realizability as far as possible. Density anomaly and water vapor mixture fraction (specific humidity) are taken as the basic variables. Algebraic expressions for the third moments are derived from first principles, and contain no adjustable constants. Separate equations are carried for the dissipation of each variance, constructed to give rational behavior of all time scale ratios. New forms for relaxation and cross-dissipation terms are constructed in such a way as to guarantee realizability. We describe how realizability was used as a tool to construct these models. We present preliminary results without mean velocity gradients for a dry surface mixed layer leaving the land and starting over water, producing a stable internal humidity boundary layer, but with large fluxes of sensible heat and water vapor (local advection).Prepared for presentation at the 29th OHOLO Conference on Boundary Layer Structure — Modelling and Application to Air Pollution and Wind Energy, Zichron Ya'acov, Israel, March 25–28, 1984. Supported in part by the U.S. Office of Naval Research under the following programs: Physical Oceanography (Code 422PO), Power (Code 473); in part by the U.S. National Science Foundation under grant no. ATM 79-22006; and in part by the U.S. Air Force Geophysics Laboratory.     

对流边界层湍流通量及逆梯度输送参数化分析

"K"理论是众多气象预报模式中运用最广泛的湍流参数化方案之一,但无法解释"逆梯度"的输送,必须进行修正。最具代表性的修正方案有三种:方案Ⅰ(Deardroff方案)、方案Ⅱ(Holtslag和Moeng方案)和方案Ⅲ(刘烽方案)。本文利用香河的边界层观测资料对上述三种方案进行验证和比较,发现方案Ⅰ的结果在整个对流边界层(Convective Boundary Layer,CBL)呈系统性偏低,与观测不符;方案Ⅱ在CBL中上部能够再现逆梯度输送现象,基本能给出合理的湍流通量垂直分布,但在CBL的下部和上部与观测不符;方案Ⅲ的逆梯度项与高度有关,并在CBL中部达到最大,而其他两个方案中逆梯度项随高度不变。该方案不但在CBL中上部与方案Ⅱ的结果一致,并能合理表达整个CBL内的湍流通量分布,更接近观测结果。     

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Comments on the characteristics of turbulent velocity components in the surface layer under convective conditions

     

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.     

Direct measurements of radiative and turbulent flux convergences in the lowest 1000 m of the convective boundary layer

Results derived from simultaneous measurements of turbulent heat flux and radiation convergence in the daytime convective boundary layer are presented. It is found that the effects of long-wave radiation result in a warming near the surface and cooling at higher levels, in good agreement with infra-red radiative transfer models. Heating rates, roughly 30% of those produced by turbulence, are observed as a result of the absorption of short-wave radiation in the lowest 1000 m of the atmosphere.     

Detection of turbulent coherent motions in a forest canopy part I: Wavelet analysis

Turbulence measurements performed at high frequencies yield data revealing intermittent and multi-scale processes. Analysing time series of turbulent variables thus requires extensive numerical treatment capable, for instance, of performing pattern recognition. This is particularly important in the case of the atmospheric surface layer and specifically in the vicinity of plant canopies, where largescale coherent motions play a major role in the dynamics of turbulent transport processes. In this paper, we examine the ability of the recently developedwavelet transform to extract information on turbulence structure from time series of wind velocities and scalars. It is introduced as a local transform performing a time-frequency representation of a given signal by a specific wavelet function; unlike the Fourier transform, it is well adapted to studying non-stationary signals. After the principles and the most relevant mathematical properties of wavelet functions and transform are given, we present various applications of relevance for our purpose: determination of time-scales, data reconstruction and filtering, and jump detection. Several wavelet functions are inter-compared, using simple artificially generated data presenting large-scale features similar to those observed over plant canopies. Their respective behaviour in the time-frequency domain leads us to assign a specific range of applications for each.     

The turbulent characteristics in the lowest part of the sea breeze front in the atmospheric surface layer

Tower measurements for the sea breeze front in the surface layer were carried out over the Kochi plain about 2 km inland from Tosa Bay in Shikoku, Japan during the period from August 1986 to October 1987. The study shows that the penetration time of the sea breeze has an annual variation, which is around 0830 JST in summer and 12 JST in winter, and that the width of the sea breeze front depends on the ratio of the sea breeze speed and the opposing flow speed. Moreover, the frontal width also shows a seasonal variation.The characteristics of the vertical winds (w) found just before and just after the passage of the sea breeze front lead to remarkable downdrafts and updrafts, respectively, with relatively large vertical velocities. Such behaviour ofw is shown to be consistent with the flow relative to the head of the front as reviewed by Simpson (1987), influencing the magnitude of the turbulence scale and the turbulent energy dissipation near the ground surface.     

Modulating synoptic scale convective activity and boundary layer dissipation in the IPESD models of the Madden–Julian oscillation

A self-contained derivation of the IPESD models [Majda, A.J., Klein, R., 2003. Systematic multi-scale models for the tropics. J. Atmos. Sci. 60, 393–408] governing synoptic and planetary scale tropical flows is provided. This derivation demonstrates the analytic tractability of the model and the effect of zonally and meridionally tilted synoptic scale heating on the forcing of planetary scale flows through upscale momentum and temperature fluxes. Exploiting the analytic tractability of the models, different aspects of the planetary scale forcing are traced to meridional and vertical tilts in the synoptic scale heating profile. Variants of the archetypal IPESD models for the Madden–Julian oscillation (MJO) presented in Majda and Biello [Majda, A.J., Biello, J.A., 2004. A multi-scale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. 101, 4736–4741; Biello, J.A., Majda, A.J., 2005. A new multi-scale model for the Madden–Julian oscillation. J. Atmos. Sci. 62, 1694–1721] are studied. In addition to vertically tilted synoptic scale heating, the models discussed herein incorporate upscale zonal momentum flux due to meridional flux convergence arising from meridionally tilted heating. The effect of a boundary layer momentum drag at the base of the free troposphere is also systematically incorporated into the IPESD models. Both meridional tilts and lower boundary layer drag are shown to meridionally confine the MJO westerly wind burst and drive a planetary scale barotropic flow. Meridionally tilted heating can also greatly strengthen the wind burst at the base of the troposphere and modify its vertical profile. The competing effects of meridionally tilted, and off-equatorial heating can also significantly weaken the MJO winds. Appendices are provided which discuss generalizations and a solution algorithm for the IPESD models.     

An ensemble of dynamically identical thermals and vertical profiles of turbulent moments in the convective surface layer of atmosphere

An ensemble of convective thermals is distinguished from the surface layer of penetrative turbulent convection over a heated horizontally uniform surface. For an isolated convective element, an integral model of a quasi-stationary spontaneous jet is proposed which admits an exact analytical solution. A simple statistical model is constructed for an ensemble of dynamically identical thermals. In this model, convective thermals ascend in a static environment, their dynamic parameters are described by the equations of an isolated quasi-stationary jet, and their diameters are stochastic. It is shown that the ensemble of thermals rising in a horizontally homogeneous environment forms surface-layer turbulent moments. The analytical relationships for higher turbulent moments of vertical velocity and temperature are compared with experimental data from the second to the forth order inclusive.     

Probability distributions of concentration fluctuations of a weakly diffusive passive plume in a turbulent boundary layer

Results are presented from an experimental investigation of turbulent dispersion of a saline plume of large Schmidt number (Sc=830) in a turbulent boundary-layer shear flow simulated in a laboratory water channel. The dispersion measurements are obtained in a neutrally buoyant plume from an elevated point source over a range of downstream distances, where both plume meandering and fine-structure variations in the instantaneous plume are important. High-resolution measurements of the scalar fluctuations in the plume are made with a rake of conductivity probes from which probability distributions of concentration at various points throught the plume are extracted from the time series.Seven candidate probability distributions were tested, namely, the exponential, lognormal, clipped normal, gamma, Weibull, conjugate beta, andK-distributions. Using the measured values of the conditional mean concentration, , and the conditional fluctuation intensity,i _p , the Weibull distribution provided the best match to the skewness and kurtosis over all downstream fetches. The skewness and kurtosis were always overpredicted by the lognormal probability density function (pdf), and underpredicted by the gamma pdf. The conjugate beta distribution for which the model parameters are determined using a method of moments based on the fluctuation intensity,i _p , and skewness,S _p , was capable of modeling the distribution of scalar concentration over a wide range of positions in the plume.