Rapid vertical sampling in stably stratified turbulent shear flows

A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Re_λ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Ri_g=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (E_k) grows. In case 2, Ri_g=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Ri_g=0.25 and E_k decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, L_O=(ε/N³)^1/2 and the overturn scale, L_t=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.     

Efficiency of mixing by a turbulent jet in a stably stratified fluid

Mixing in a two-layer stably stratified fluid by a turbulent jet was studied by a laboratory experiment. A non-swirling jet was discharged vertically downwards in a confined fluid system consisting initially of a top layer of fresh water and a bottom layer of salt water. In total, 16 experimental cases were considered, where the diameter and exit velocity of the jet were varied together with the density difference between the top and bottom layer. Vertical density profiles were determined from conductivity measurements. A three-layer density structure developed in all cases with an intermediate layer that grew in size with time elapsed as fresh and salt water were mixed. The mixing efficiency, defined as the percentage of the supplied kinetic jet energy that is used for increasing the potential energy of the fluid system, was related to a densimetric Froude number based on the intermediate layer depth. Overall, the calculated jet mixing efficiency displayed higher values than comparable efficiencies for destratification with air-bubble plumes.     

Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state,homogeneous regimes

We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. Instead of the critical value of Richardson number separating—as is usually assumed—the turbulent and the laminar regimes, the suggested model reveals a transitional interval, , which separates two regimes of essentially different nature but both turbulent: strong turbulence at ; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at . Predictions from this model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulation and large-eddy simulation.     

A numerical study of second-order turbulent moments in the stably stratified nocturnal boundary layer

The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.     

Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer

In this paper we revise the similarity theory for the stably stratified atmospheric boundary layer (ABL), formulate analytical approximations for the wind velocity and potential temperature profiles over the entire ABL, validate them against large-eddy simulation and observational data, and develop an improved surface flux calculation technique for use in operational models.     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

Retrieval of eddy thermal conductivity in the weakly nonlinear Prandtl model for katabatic flows

Because the nonlinearity of actual physical processes can be expressed more precisely by the introduction of a nonlinear term, the weakly nonlinear Prandtl model is one of the most effective ways to describe the pure katabatic flow (no background flow). Features of the weak nonlinearity are reflected by two factors: the small parameter ε and the gradually varying eddy thermal conductivity. This paper first shows how to apply the Wentzel–Kramers–Brillouin (WKB) method for the approximate solution of the weakly nonlinear Prandtl model, and then describes the retrieval of gradually varying eddy thermal conductivity from observed wind speed and perturbed potential temperature. Gradually varying eddy thermal conductivity is generally derived from an empirical parameterization scheme. We utilize wind speed and potential temperature measurements, along with the variational assimilation technique, to derive this parameter. The objective function is constructed by the square of the differences between the observation and model value. The new method is validated by numerical experiments with simulated measurements, revealing that the order of the root mean squre error is 10^–2 and thus confirming the method’s robustness. In addition, this method is capable of anti-interference, as it effectively reduces the influence of observation error.     

中尺度降水集合预报随机参数扰动方法敏感性试验

中尺度降水模式预报具有很大的不确定性,为更好地描述与模式降水预报密切相关的物理过程关键参数的不确定性,基于中国气象局GRAPES（Global/Regional Assimilation and Prediction System）中尺度区域集合预报模式,从对模式降水预报不确定性有较大影响的积云对流、云微物理、边界层及近地面层等4个参数化方案中选取了18个关键参数,设计了一种随机参数扰动方案（Stochastically Perturbed Parameterization,SPP）,并通过2015年6—7月总计10 d的随机扰动集合预报试验,对比分析了SPP方案对不同物理过程参数扰动敏感性、随机场时、空尺度敏感性、能量变化特征及其集合预报效果。结果显示,对所选择的任一物理过程参数化方案增加SPP扰动后,降水及等压面要素的概率预报技巧优于无SPP扰动的预报,而扰动积云对流和边界层过程中的参数较扰动云微物理过程中的参数影响更显著,且同时扰动积云对流、云微物理、边界层及近地面层参数化方案中的18个参数的集合预报效果优于扰动任何单一物理过程中的部分参数,表明SPP方案能够有效地提高中尺度降水概率预报技巧;从能量变化特征可知,不同物理过程的参数扰动对动能、内能和总能量的影响层次和特征有所不同,但总体而言,扰动前后各项能量基本相同;随机场时、空尺度敏感性试验发现,SPP扰动随机场时间、空间相关尺度对集合预报效果有明显影响,当扰动随机场选用12 h抗相关时间及截断波数20时,集合预报结果最优。上述结果表明,SPP随机参数扰动方案不仅能够有效提高集合概率预报效果,还能够提高集合降水概率预报技巧,具有良好的业务应用与发展前景。      

A modified turbulent energy model for geophysical flows: Influence of the ground proximity

A modified form of the turbulent energy model for geophysical flows is presented, in which the effect of the proximity of the ground on the pressure redistribution terms is accounted for. The new form of the model retains the simplicity and the capabilities of the original form, but at the same time differentiates between the vertical and lateral components of turbulent energy in boundary layers as well as between free and near-wall turbulence.     

A non-linear extension of the mixed spectral finite difference model for neutrally stratified turbulent flow over topography

A non-linear extension of the mixed spectral finite difference model for neutrally stratified surface-layer flow over complex terrain is developed. The non-linear terms are treated as additional source terms in the present model. The solution is calculated iteratively in spectral space, while the source terms are evaluated in physical space (at each iteration step) with the help of a Fast Fourier Transform algorithm.Results for simple 2D sinusoidal topography are shown to compare well with full non-linear finite difference results. The method, compared to conventional finite difference methods, has the advantage of rapid convergence and substantial savings in computer time.     

层结流体中具有纬向基本剪切流的Rossby波振幅的mKdV方程

In this paper,modified Korteweg-de Vries (mKdV) equations for the amplitude of solitary Rossby waves in stratified fluids with a zonal shear flow are derived by using a weakly nonlinear method.It is found that the coefficients of mKdV equations depend not only on the β effect and the Visl-Brunt frequency,but also on the basic shear flow.     

Evaluation of an alternative method for numerically modeling nonhydrostatic flows over irregular terrain

Modeling nonhydrostatic atmospheric flow requires the solution of the vertical equation of motion and a prognostic or diagnostic equation for pressure. If the nonhydrostatic components of the flow are relatively small, they can be approximated and incorporated into a purely hydrostatic model, which usually is conceptually simpler and computationally more efficient. A method to do this for a linear model of local thermally-induced circulations is further developed and adapted to a non-linear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasi-nonhydrostatic version were used to simulate neutral flow over simple terrain features. One set of observations taken over a simple change in roughness and another set taken over a change in both roughness and terrain were simulated by both models to assess the capabilities of the quasi-nonhydrostatic technique.It is found that (as expected) the pressure deviation from the hydrostatic state is negligible for the roughness change, but it is an important aspect of neutral flow over terrain. Thus, for flow encountering a simple roughness change, the hydrostatic approximation is good, even for small horizontal scales. However, the quasi-nonhydrostatic model qualitatively produces the features in the observations for flow over a terrain change that the hydrostatic model cannot produce.Journal Paper No. J-12737 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

A study of turbulent energy over complex terrain (STATE, 1978)

The complex structure of the earth's surface influenced atmospheric parameters pertinent to modeling the diffusion process during the 1978 ‘STATE’ field study. The Information Theory approach of statistics proved useful for analyzing the complex structures observed in the radiometric surface temperature signals as measured from an aircraft. Results show that regardless of their complexities, these temperature processes are well approximated as Gaussian processes. Turbulent kinetic energy is shown to increase as the surface temperature signals become more complex. The nature of these variations is examined for five different categories of agricultural land as defined by percent cultivation and percent forestation.     

Evaluation of MM5 mesoscale model at local scale for air quality applications over the Swedish west coast: Influence of PBL and LSM parameterizations

Summary The performance of MM5 mesoscale model (Version 3.6.3) using different planetary boundary layer (PBL) and land surface model (LSM) parameterizations is evaluated and compared using high temporal and spatial resolution G?TE2001 campaign data at local scale (a few kilometers) over the Greater G?teborg area along the Swedish west coast during 7–20 May 2001. The focus is on impact of PBL and LSM parameterizations on simulated meteorological variables important for air quality applications such as global radiation, diurnal cycle of near-surface air temperature and wind, diurnal cycle intensity, near-surface vertical temperature gradient, nocturnal temperature inversion, boundary layer height, and low-level jet (LLJ). The model performance for daytime and nighttime and under different weather conditions is also discussed. The purpose is to examine the performance of the model using different PBL and LSM parameterizations at local scale in this area for its potential applications in air quality modeling. The results indicate that the influence of PBL and LSM parameterizations on simulated global radiation, diurnal cycle of near-surface air temperature and wind speed, diurnal cycle intensity, vertical temperature gradient, nocturnal temperature inversion and PBL heights, which are critical parameters for air quality applications, is evident. Moreover, the intensity and location of LLJ are simulated well by all schemes, but there also exist some differences between simulated results by using different PBL and LSM schemes. Therefore, the choice of PBL and LSM parameterizations is important for MM5 applications to air quality studies. Correspondence: Junfeng Miao, Department of Earth Sciences, G?teborg University, P.O. Box 460, 405 30 G?teborg, Sweden     

Classification of the stratified atmospheric boundary layers at Molve (Croatia) based on the similarity theory

Summary The stability parameter μ is suggested as the one which is determinable with satisfying accuracy for routine application by means of commonly accessible meteorological data at the Molve location (Croatia). The similarity functions applied for vertical wind speed simulation in the planetary boundary layer (PBL) at Molve were useful for the determination of local stability classes. Universal similarity functions were applied for unstable and neutral stability, whereas local similarity functions were established for stable stratification. Wind speed simulations were performed using two types of wind models. The Monin-Obukhov similarity theory was included in both types. However, it turned out that for the operative determination of the stability of the 35 m deep lowest layer, the stability parameter μ was locally a better stability parameter than the Monin-Obukhov parameter z/L. That was possibly because 35 m deep lowest layer sometimes (depending upon stability) includes a large proportion of the Ekman layer and parameter μ is originally designed for the deeper part of PBL than z/L that is originally designed for the surface layer. At Molve, the input data for local wind models as well as for the stability parameter μ were wind speed at 35 m and temperature at 2 and 35 m above the ground.     

An observational study of radiative and turbulent cooling in the nocturnal boundary layer (ECLATS experiment)

The contribution of radiative and turbulent processes to nocturnal atmospheric cooling has been studied using the experimental data of the ECLATS experiment which took place in the African Sahel; the radiative and turbulent fluxes were determined taking thermal advection into account. The turbulent cooling rate is predominant; it decreases strongly with altitude at the beginning of the night, which is the main cause of inversion formation.     

Evaluation of Two Initialization Schemes for Simulating the Rapid Intensification of Typhoon Lekima(2019)

Two different initialization schemes for tropical cyclone(TC) prediction in numerical models are evaluated based on a case study of Typhoon Lekima(2019). The first is a dynamical initialization(DI) scheme where the axisymmetric TC vortex in the initial conditions is spun up through the 6-h cycle runs before the initial forecast time. The second scheme is a bogussing scheme where the analysis TC vortex is replaced by a synthetic Rankine vortex. Results show that although both initialization schem...