南海台风边界层湍流小波分析

利用小波变换（WT）对香港天文台飞机观测台风“妮妲”（1604）资料进行分析,研究在不稳定、不均匀的台风边界层中湍流涡旋的垂直传输作用。在0.1~5 Hz惯性子区内横风和顺风分量功率谱密度能较好符合-5/3幂律。小波分析显示:横风的小波功率谱峰值集中在1 km之下,顺风分量的小波功率谱峰值集中在1~6 km之间;眼区动量通量的主要贡献尺度为2.3 km,眼区外主要贡献尺度在1~2 km,中低层为较小尺度（< 1.0 km）;湍流功能(TKE)的生成尺度主要集中在4 km之下。这项研究定量描述了南海北部台风边界层各个区域湍流结构的差异特征,讨论了对台风边界层通量参数化的可能影响。      

Multifractal Characteristics of Intermittent Turbulence in the Urban Canopy Layer

The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.     

Wavelet Analysis of Intermittent Turbulent Transport in the Atmospheric Surface Layer over a Monsoon Trough Region

The structure of the turbulence in the atmospheric surface layer over a monsoon trough region has been studied using structural analysis based on wavelet transform. The observational site is located at the eastern (wet) end of the monsoon trough region, characterized by high moisture in the atmospheric surface layer. On the average relative humidity varied from 70% to 100% during the experiment. The wind and temperature data, collected at Kharagpur (22°25' N, 87°18' E) at six observational hours of a day in June 1990 during the Monsoon Trough Boundary Layer Experiment (MONTBLEX), have been utilized in the study. The wind and instantaneous momentum flux time series were decomposed into 12 scales using the Haar wavelet transform. The eddies exhibited a large temporal variability generating intermittency in the energy and flux distributions. A criterion based on the isotropy has been suggested for separating the large eddies from the small eddies. At the separation scale the isotropy coefficient drops sharply. It is shown that the intermittency in the small eddies resulted from the spatial variation of energy, and deviation of velocity statistics from the Gaussian distribution known as flatness. The deviation from the -5/3 power law has been attributed to the increased mean values of, (i) the coefficient of variation of energy, and (ii) the flatness factor, in the inertial subrange. The decomposition of the instantaneous momentum flux time series reveals that the major contribution to the total flux arises from the large eddies. The quadrant analysis of the momentum flux shows that ejections and sweeps account for a substantial part of the total flux, and quantifies the relative importance of the various spatial scales that contribute to the transport of momentum.     

Large-Scale Turbulence Structures and Their Contributions to the Momentum Flux and Turbulence in the Near-Neutral Atmospheric Boundary Layer Observed from a 213-m Tall Meteorological Tower

Large-scale turbulence structures in the near-neutral atmospheric boundary layer (ABL) are investigated on the basis of observations made from the 213-m tall meteorological tower at Tsukuba, Japan. Vertical profiles of wind speed and turbulent fluxes in the ABL were obtained with sonic anemometer-thermometers at six levels of the tower. From the archived data, 31 near-neutral cases are selected for the analysis of turbulence structures. For the typical case, event detection by the integral wavelet transform with a large time scale (180 s) from the streamwise velocity component (u) at the highest level (200 m) reveals a descending high-speed structure with a time scale of approximately 100 s (a spatial scale of 1 km at the 200-m height). By applying the wavelet transform to the u velocity component at each level, the intermittent appearance of large-scale high-speed structures extending also in the vertical is detected. These structures usually make a large contribution to the downward momentum transfer and induce the enhancement of turbulent kinetic energy. This behaviour is like that of “active” turbulent motions. From the analysis of the two-point space–time correlation of wavelet coefficients for the u velocity component, the vertical extent and the downward influence of large-scale structures are examined. Large fluctuations in the large-scale range (wavelet variance at the selected time scale) at the 200-m level tend to induce the large correlation between the higher and lower levels.     

Spectrum Analysis of Wind Profiling Radar Measurements

Unlike previous studies on wind turbulence spectrum in the planetary boundary layer, this investigation focuses on high-altitude （1-5 km） wind energy spectrum and turbulence spectrum under various weather conditions. A fast Fourier transform （FFT） is used to calculate the wind energy and turbulence spectrum density at high altitudes （1-5 km） based on wind profiling radar （WPR） measurements. The turbulence spectrum under stable weather conditions at high altitudes is expressed in powers within a frequency range of 2 × 10-5-10-3 s-1, and the slope b is between -0.82 and -1.04, indicating that the turbulence is in the transition from the energetic area to the inertial sub-range. The features of strong weather are reflected less obviously in the wind energy spectrum than in the turbulence spectrum, with peaks showing up at different heights in the latter spectrum. Cold windy weather appears over a period of 1.5 days in the turbulence spectrum. Wide-range rainstorms exhibit two or three peaks in the spectrum over a period of 15-20 h, while in severe convective weather conditions, there are two peaks at 13 and 9 h. The results indicate that spectrum analysis of wind profiling radar measurements can be used as a supplemental and helpful method for weather analysis.     

The Near-Calm Stable Boundary Layer

For the near-calm stable boundary layer, nominally 2-m mean wind speed <0.5 ms⁻¹, the time-average turbulent flux is dominated by infrequent mixing events. These events are related to accelerations associated with wave-like motions and other more complex small-scale motions. In this regime, the relationship between the fluxes and the weak mean flow breaks down. Such near-calm conditions are common at some sites. For very weak winds and strong stratification, the characteristics of the fluctuating quantities change slowly with increasing scale and the separation between the turbulence and non-turbulent motions can become ambiguous. Therefore, a new analysis strategy is developed based on the scale dependence of selected flow characteristics, such as the ratio of the fluctuating potential energy to the kinetic energy. In contrast to more developed turbulence, correlations between fluctuating quantities are small, and a significant heat flux is sometimes carried by very weak vertical motions with large temperature fluctuations. The relation of the flux events to small-scale increases of wind speed is examined. Large remaining uncertainties are noted.     

The local effect of intermittency on the inertial subrange energy spectrum of the atmospheric surface layer

Orthonormal wavelet expansions are applied to atmospheric surface layer velocity measurements. The effect of intermittent events on the energy spectrum of the inertial subrange is investigated through analysis of wavelet coefficients. The local nature of the orthonormal wavelet transform in physical space makes it possible to identify a relationship between the inertial subrange slope of the local wavelet spectrum and a simple indicator (i.e. the local variance of the signal) of local intermittency buildup. The slope of the local wavelet energy spectrum in the inertial subrange is shown to be sensitive to the presence of intermittent events. During well developed intermittent events (coherent structures), the slope of the energy spectrum is somewhat steeper than -5/3, while in less active regions the slope is found to be flatter than -5/3. When the slopes of local wavelet spectra are ensemble averaged, a slope of -5/3 is recovered for the inertial subrange.     

Intermittency of Turbulence in the Atmospheric Boundary Layer: Scaling Exponents and Stratification Influence

We show the relationship between the intermittency of turbulence and the type of stratification for different atmospheric situations during the SABLES98 field campaign. With this objective, we first demonstrate the scaling behaviour of the velocity structure functions corresponding to these situations; next, we analyze the curvature of the scaling exponents of the velocity structure functions versus the order of these functions (ζ _p vs. p), where ζ _p are the exponents of the power relation for the velocity structure function with respect to the scale. It can be proved that this curve must be concave, under the assumption that the incompressible approximation does not break down at high Reynolds numbers. The physical significance of this kind of curvature is that the energy dissipation rate increases as the scale of the turbulent eddies diminishes (intermittency in the usual sense). However, the constraints imposed by stability, preventing full development of the turbulence, allow the function ζ _p versus p to show any type of curvature. In this case, waves of high frequency trapped by the stability, or bursts of turbulence caused by the breaking up of internal waves, may produce a redistribution of energy throughout the scaling range. Due to this redistribution, the variation with the scale of the energy dissipation rate may be smaller (decreasing the intermittency) and, even in more stable situations, this rate may diminish (instead of increasing) as the scale diminishes (convex form of the curve ζ _p vs. p).     

Modelling the One-Dimensional Stable Boundary Layer with an E−ℓ Turbulence Closure Scheme

The atmospheric boundary layer (ABL) model of Weng and Taylor with E−ℓ turbulence closure is applied to simulate the one-dimensional stably stratified ABL. The model has been run for nine hours from specified initial wind, potential temperature and turbulent kinetic energy profiles, and with a specified cooling rate applied at the surface. Different runs are conducted for different cooling rates, geostrophic winds and surface roughnesses. The results are discussed and compared with other models, large-eddy simulations and published field data.     

An Investigation into Ridge-Top Turbulence Characteristics During Neutral and Weakly Stable Conditions: Velocity Spectra and Isotropy

An investigation into high Reynolds number turbulent flow over a ridge top in New Zealand is described based on high-resolution in-situ measurements, using ultrasonic anemometers for two separate locations on the same ridge with differing upwind terrain complexity. Twelve 5-h periods during neutrally stratified and weakly stable atmospheric conditions with strong wind speeds were sampled at 20 Hz. Large (and small) turbulent length scales were recorded for both vertical and longitudinal velocity components in the range of 7–23 m (0.7–3.3 m) for the vertical direction and 628–1111 m (10.5–14.5 m) for the longitudinal direction. Large-scale eddy sizes scaled to the WRF (Weather Research and Forecasting) numerical model simulated boundary-layer thickness for both sites, while small-scale turbulent features were a function of the complexity of the upwind terrain. Evidence of a multi-scale turbulent structure was obtained at the more complex terrain site, while an assessment of the three-dimensional isotropy assumption in the inertial subrange of the spectrum showed anisotropic turbulence at the less complex site and evidence of isotropic turbulence at the more complex site, with a spectral ratio convergence deviating from the 4/3 or unity values suggested by previous theory and practice. Existing neutral spectral models can represent locations along the ridge top with simple upwind complexity, especially for the vertical wind spectra, but sites with more orographic complexity and strong vertical wind speeds are often poorly represented using these models. Measured spectra for the two sites exhibited no significant diurnal variation and very similar large-scale and small-scale turbulent length scales for each site, but the turbulence energy measured by the variances revealed a strong diurnal difference.     

Maximal Overlap Wavelet Statistical Analysis With Application to Atmospheric Turbulence

Statistical tools based on the maximal overlap discrete wavelet transform (MODWT) are reviewed, and then applied to a dataset of aircraft observations of the atmospheric boundary layer from the tropical eastern Pacific, which includes quasi-stationary and non-stationary segments. The wavelet methods provide decompositions of variances and covariances, e.g. fluxes, between time scales that effectively describe a broadband process like atmospheric turbulence. Easily understood statistical confidence bounds are discussed and applied to these scale decompositions, and results are compared to Fourier methods for quasi-stationary turbulence. The least asymmetric LA(8) wavelet filter yields coefficients that exhibit better uncorrelatedness across scales than the Haar filter and is better suited for decomposition of broadband turbulent signals. An application to a non-stationary segment of our dataset, namely vertical profiles of the turbulent dissipation rate, highlights the flexibility of wavelet methods.     

Structure Function Analysis of Two-Scale Scalar Ramps. Part I: Theory and Modelling

Structure functions are used to study the dissipation and inertial range scales of turbulent energy, to parametrize remote turbulence measurements, and to characterize ramp features in the turbulent field. Ramp features are associated with turbulent coherent structures, which dominate energy and mass fluxes in the atmospheric surface layer. The analysis of structure functions to identify ramp characteristics is used in surface renewal methods for estimating fluxes. It is unclear how commonly observed different scales of ramp-like shapes (i.e., smaller ramps and spikes embedded in larger ramps) influence structure function analysis. Here, we examine the impact of two ramp-like scales on structure function analysis using artificially generated data. The range of time lags in structure function analysis was extended to include time lags typically associated with isotropic turbulence to those larger than the ramp durations. The Van Atta procedure (Arch Mech 29:161–171, 1977) has been expanded here to resolve the characteristics of two-scale ramp models. This new method accurately, and in some cases, exactly determines the amplitude and duration of both ramp scales. Spectral analysis was applied to the structure functions for a broad range of time lags to provide qualitative support for the expanded Van Atta procedure results. The theory reported here forms the foundation for novel methods of analyzing turbulent coherent structures.     

The Effects of Non-stationarity on the Clustering Properties of the Boundary-layer Vertical Wind Velocity

Non-stationarity is a common feature in geophysical flows, though it still remains an open question on how the non-stationarity of flow affects its statistical structure. Using the telegraph approximation (TA) method, we quantified how non-stationarity in the measured atmospheric turbulent vertical velocity time series affects its clustering properties—one of the two main components of intermittency in turbulence. We compare different TA results between stationary and non-stationary atmospheric turbulent vertical velocity records, and find that the non-stationary data possess different cluster and intermittency exponents from stationary data. The inter-pulse period of the non-stationary records takes a near power-law distribution while the inter-pulse period of the stationary records exhibits a stretched exponential distribution. These results suggest that non-stationarity of the underlying processes can affect the statistical structure of turbulence, especially the clustering properties.     

On the Prediction of the Kurtosis of Velocity Derivatives in a Turbulent Field

The prediction of the values of non-dimensional fourth-order moment (kurtosis) of the velocity derivative in a turbulent field is made under the assumption that the values of kurtosis depend on both the turbulence Reynolds number and the intermittency factor. The method consists of modeling a suitable probability density of the variable in a given turbulence Reynolds number and the intermittency factor. A crude model of the probability density function is derived, and the numerical calculations based on the model show excellent agreement with many of the experimental data. The analysis shows that the values of kurtosis depend strongly on the intermittency factor, and that depending on the value of the intermittency factor, it is entirely possible to have values of kurtosis as low as five in a flow with a turbulence Reynolds number of 5000.     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

On the prediction of the kurtosis of velocity derivatives in a turbulent field

The prediction of the values of non-dimensional fourth-order moment (kurtosis) of the velocity derivative in a turbulent field is made under the assumption that the values of kurtosis depend on both the turbulence Reynolds number and the intermittency factor. The method consists of modeling a suitable probability density of the variable in a given turbulence Reynolds number and the intermittency factor. A crude model of the probability density function is derived, and the numerical calculations based on the model show excellent agreement with many of the experimental data. The analysis shows that the values of kurtosis depend strongly on the intermittency factor, and that depending on the value of the intermittency factor, it is entirely possible to have values of kurtosis as low as five in a flow with a turbulence Reynolds number of 5000.     

A New Method for the Determination of Area-Averaged Turbulent Surface Fluxes from Low-Level Flights Using Inverse Models

The low-level flight method (LLF) has been combined with linear inverse models (IM) resulting in an LLF+IM method for the determination of area-averaged turbulent surface fluxes. With this combination, the vertical divergences of the turbulent latent and sensible heat fluxes were calculated from horizontal flights. The statistical errors of the derived turbulent surface fluxes were significantly reduced. The LLF+IM method was tested both in numerical and field experiments. Large-eddy simulations (LES) were performed to compare ‘true’ flux profiles with ‘measurements’ of simulated flights in an idealised convective boundary layer. Small differences between the ‘true’ and the ‘measured’ fluxes were found, but the vertical flux divergences were correctly calculated by the LLF+IM method. The LLF+IM method was then applied to data collected during two flights with the Helipod, a turbulence probe carried by a helicopter, and with the research aircraft Do 128 in the LITFASS-98 field campaign. The derived surface fluxes were compared with results from eddy-covariance surface stations and with large-aperture scintillometer data. The comparison showed that the LLF+IM method worked well for the sensible heat flux at 77 and 200 m flight levels, and also for the latent heat flux at the lowest level. The model quality control indicated failures for the latent heat flux at the 200 m level (and higher), which were probably due to large moisture fluctuations that could not be modelled using linear assumptions. Finally the LLF+IM method was applied to more than twenty low-level flights from the LITFASS-2003 experiment. Comparison with aggregated surface flux data revealed good agreement for the sensible heat flux but larger discrepancies and a higher statistical uncertainty for the latent heat flux     

Turbulent Kinetic Energy Dissipation in the Surface Layer

We estimated the turbulent kinetic energy (TKE) dissipation rate for thirty-two 1-h intervals of unstable stratification covering the stability range 0.12 ≤ −z/L ≤ 43 (z/L is the ratio of instrument height to the Obukhov length), by fitting Kolmogorov’s inertial subrange spectrum to streamwise spectra observed over a desert flat. Estimated values are compatible with the existence of local equilibrium, in that the TKE dissipation rate approximately equalled the sum of shear and buoyant production rates. Only in the neutral limit was the turbulent transport term in the TKE budget measured to be small.     

不同下垫面上近地层湍流的多尺度属性研究

文中利用统计和多尺度分析方法分析了几种复杂下垫面情况下的风、温湍流脉动观测资料 ,结果表明 :下垫面结构的差异明显地影响湍流量 ,如 :戈壁地区的热力作用明显大于雪面和城郊面 ,表现在湍流时间尺度上也明显地大于雪面和城郊面。但复杂下垫面下的湍谱在惯性区仍满足“- 23”次律 ;多尺度方法研究湍流 ,可以更简捷地分析湍流的多尺度结构及其在湍流输送中的作用。由此可看出 ,多尺度方法是发展湍流统计理论的一种有效工具。