Observational and Numerical Simulation Study of a Sequence of Eight Atmospheric Density Currents in Northern Spain

A sequence of eight atmospheric density current fronts occurred in consecutive days are identified and analyzed using micrometeorological time series and numerical simulations. Observations were collected in the context of the INTERCLE project, which took place from September 2002 to November 2003 at the CIBA (Research Centre for the Lower Atmosphere) site located over the northern Spanish plateau. Numerical simulations used the Weather Research and Forecast (WRF) model with fine horizontal resolution (1 km). Both observations and simulations agree that the arrival of the density currents are characterized by a sharp change in temperature, wind velocity, wind direction and specific humidity and a source of intermittent turbulence. However, comparison between model and observations shows that the model predicts the intrusion of the density currents earlier than is observed. In addition, wavelet techniques applied to the data help distinguish the different scales present in the events, and therefore can reveal traces of gravity waves induced by the arrival of the density currents.     

A unified linear theory of wavelike perturbations under general ocean conditions

A linearized instability analysis model with five unknowns was proposed to describe disturbance motions under general oceanic background conditions, including large-scale current shear, density stratification, frontal zone, and arbitrary topography. A unified linear theory of wavelike perturbations for surface gravity waves, internal gravity waves and inertial gravity waves was derived for the adiabatic case, and the solution was then found using Fourier integrals. In this theory, we discarded the assumptions widely accepted in the literature concerning derivations of wave motions such as the irrotationality assumption for surface gravity waves, the rigid-lid approximation for internal gravity waves, and the long-wave approximation for inertial gravity waves. Analytical solutions based on this theory indicate that the complex dispersion relationships between frequency and wave-number describing the propagation and development of the three types of wavelike perturbation motions include three components: complex dispersion relationships at the sea surface; vertical invariance of the complex frequency; and expressions of the vertical wave-number (phase). Classical results of both surface waves and internal waves were reproduced from the unified theory under idealized conditions. The unified wave theory can be applied in the dynamical explanation of the generation and propagation properties of internal waves that are visible in the satellite SAR images in the southern part of the China Seas. It can also serve as the theoretical basis for both a numerical internal-wave model and analytical estimation of the ocean fluxes transported by wavelike perturbations.     

切变流场中惯性重力内波的发展

假定背景流场为缓变的平行切变流,扰动沿基本流方向是均匀的;用WKBJ方法求解Boussinesg近似下的线性化重力波方程组,根据波作用量守恒原理,研究了流场非均匀性对重力波发展的影响。      

Atmospheric Disturbances that Generate Intermittent Turbulence in Nocturnal Boundary Layers

Using the unprecedented observational facilities deployed duringthe 1999 Cooperative Atmosphere-Surface Exchange Study (CASES-99),we found three distinct turbulent events on the night of 18October 1999. These events resulted from a density current,solitary wave, and internal gravity wave, respectively. Our studyfocuses on the turbulence intermittency generated by the solitarywave and internal gravity wave, and intermittent turbulenceepisodes associated with pressure change and wind direction shiftsadjacent to the ground. Both the solitary and internal gravitywaves propagated horizontally and downward. During the passage ofboth the solitary and internal gravity waves, local thermal andshear instabilities were generated as cold air was pushed abovewarm air and wind gusts reached to the ground. These thermal andshear instabilities triggered turbulent mixing events. Inaddition, strong vertical acceleration associated with thesolitary wave led to large non-hydrostatic pressure perturbationsthat were positively correlated with temperature. The directionaldifference between the propagation of the internal gravity waveand the ambient flow led to lateral rolls. These episodic studiesdemonstrate that non-local disturbances are responsible for localthermal and shear instabilities, leading to intermittentturbulence in nocturnal boundary layers. The origin of thesenon-local disturbances needs to be understood to improve mesoscalenumerical model performance.     

Energy- and Flux-Budget Turbulence Closure Model for Stably Stratified Flows. Part II: The Role of Internal Gravity Waves

We advance our prior energy- and flux-budget (EFB) turbulence closure model for stably stratified atmospheric flow and extend it to account for an additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant ≈0.2–0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. For heterogeneous stratification, when internal gravity waves propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. Internal gravity waves also reduce the anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, internal gravity waves generate both horizontal and vertical TKE. Internal gravity waves also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of internal gravity waves is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), internal gravity waves either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.     

热带平流层多尺度波动分离方案的研究：多站点高分辨率无线电探空联合分析

利用太平洋地区台风过境期间6个热带气象站的高分辨率无线电探空资料,结合扩展经验正交函数（EEOF）展开,对热带下平流层行星波和重力波扰动进行了分离,给出了一种热带地区提取重力波扰动的新方案。对观测数据做EEOF展开后,选择表征行星尺度波动模态的特征向量和相应权重进行气象要素场的重建。结果显示,在不同的台风过程期间,温度、纬向风和经向风的重建扰动量显示出不同的动力学偏振关系:在准两年振荡（QBO）东风位相时与赤道开尔文波的偏振关系一致,而在准两年振荡西风位相时与混合罗斯贝-重力波（MRG）的偏振关系一致。把行星尺度波动模态从原始观测中剔除,得到新的扰动廓线,对其进行重力波垂直波数谱的谱型拟合。结果发现,与以往方法提取的重力波扰动相比,新方法所得谱型参数中特征垂直波长λ*在不同时期不同站点变化很小,稳定在1.7 km左右,且低频波数段谱斜率s的数值与理论假设1十分接近。综合其研究结果可以推测,用新方法提取的热带重力波扰动更加符合当前的理论垂直波数谱模型。      

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.     

Study of Coherent Structures and Estimation of the Pressure Transport Terms for the Nocturnal Stable Boundary Layer

During the CASES-99 field experiment, three quartz-based microbarographs were installed on the 58-m main tower at the Central Site. These devices measuredabsolute pressure with temperature compensated output at a resolution better than 0.2 Pa and a sampling frequency of 2 s^-1 during the whole campaign. This sampling rate is not adequate to compute turbulent pressure fluxes with the classic averaging method, but the wavelet transform allows flux estimations at a wide range of scales. The resolution of the devices is suitable to study pressure perturbations such as internal gravity waves. The night period of the Intensive Operational Period number 6 (IOP6), where wave-like structures were present, is chosen to illustrate the method. A complete wavelet analysis of pressure recordsand data from sonic anemometers located at the same heights in the tower is performed. Wavelet methods make it possible to identify the relevant scales in the flowand to study the vertical structure of pressure perturbations, including coherent structures and small-scale motions.A study of a simplified turbulence kinetic energy budget equation is made and the contribution of the pressure terms is discussed.     

非均匀层结大气中的重力惯性波及其激发对流的物理机制

本文用WKBJ方法求解Boussinesq近似下的重力波方程,导出非均匀层结大气中重力惯性内波的一个守恒波作用量(称为广义波作用量)。根据广义波作用量守恒原理,着重讨论了重力惯性内波在发展过程中尺度变化的规律;在适当的条件下,重力波随着其尺度的变化而可能崩溃(或破碎),从而激发对流的发展。      

Estimating the Random Error in Eddy-Covariance Based Fluxes and Other Turbulence Statistics: The Filtering Method

A spatially local decomposition of turbulent fluxes based on properties of spatial filters is used to develop a new method of estimating random error in turbulent moments of any order. The proposed error estimation method does not require an estimate of the integral time scale, which can be highly sensitive to the method used to calculate it. The error estimation method is validated using synthetic flux data with a known ensemble mean and intercompared with existing methods using data from the Advection Horizontal Array Turbulence Study (AHATS). Typical errors for a 27.3-min block of data collected at a height of 8 m are found to be approximately 10% for the heat flux and 7–15% for variances. The error in the momentum flux increases rapidly with increasing atmospheric instability, reaching values of 40% or greater for unstable conditions. A new method based on filtering is also proposed to estimate integral time scales of turbulent quantities.     

The turbulent bottom boundary layer and its influence on local dynamics over the continental shelf

We report on measurements of the structure of the bottom boundary layer on the continental shelf off Vancouver Island. A time series of vertical profiles obtained with the microstructure profiler FLY II revealed large temporal variations in the dissipation rate and in the density structure. The near-bottom current structure was simultaneously measured at fixed heights with conventional current meters.The data reveal the association between the predominantly diurnal tide and the variations in the structure of the bottom boundary layer. A clear distinction appears between the turbulent bottom boundary layer (8–40 m deep in a total water depth of 138 m) and the well-mixed layer (20–40 m deep). The two layers vary independently, with horizontal advection dominating the fluctuations in the thickness of the well-mixed layer while local dissipation is more closely related to the thickness of the turbulent layer. Variations in the density structure of the bottom layer are related to the strength and direction of the vertical shear and to the regional distribution of isopycnals. Current veering is commonly concentrated above the well-mixed layer. The evolution of the characteristics of the bottom layers is followed through a tidal cycle and related to local dissipation and other variables.Microstructure measurements from six locations over the southern portion of the Vancouver Island continental shelf are used to estimate the influence of turbulent energy dissipation on regional-scale flows. That fraction of the dissipation taking place in the bottom boundary layer is attributed to barotropic tidal flows, while that occurring above it is associated with nearly geostrophic baroclinic flows. Results give a lower limit of ∼ 1070 km for the length scale of shelf wave decay, in good agreement with current models; the estimates of tidal friction based on our dissipation measurements are however much lower than required by astronomical observations. An estimate of 230 h is obtained for the spin-down time of the local Tully eddy, rather longer than the decay time of 68 h obtained from observations.     

Numerical simulation of the boundary layer above waves

A new approach to investigations of the structure of the boundary layer above waves is discussed. The approach is based on direct numerical simulation of wave motions in the boundary layer produced by a moving curved surface. Model equations are derived, which are the Reynolds equations in a curvilinear nonstationary system of co-ordinates, evolution equations for turbulent kinetic energy, and Kolmogorov's approximate similarity formulae relating the coefficient of turbulent viscosity to the dissipation of turbulent energy; the length scale is assumed to grow linearly with increasing distance from the surface. Principles of constructing the model numerical scheme are described. Results are given of modelling the structure of the boundary layer above a nonsteady surface, which, in a general case, is a superposition of progressive waves with assigned dispersion relations and amplitudes. Mechanisms of energy and momentum transfer to the surface, effects of density stratification and energy structure in the boundary layer are studied. Merits and demerits of the approach are discussed.     

Analysis of turbulent exchange and coherent structures in the stable atmospheric boundary layer based on tower observations

Using data collected at the Spanish low troposphere research centre CIBA (Centro de Investigación de la Baja Atmósfera) and at the Cabauw Experimental Site for Atmospheric Research (CESAR) in the Netherlands, we analyzed the most significant features of different coherent structures occurring in the stable atmospheric boundary layer. In particular, we used both the Reynolds and wavelet methods to analyze a solitary wave, a gravity wave, a density current and a low-level jet. For each of these structures, we found that wavelet analysis had the capacity to distinguish the different scales involved in these events due to the different timing and heights of the thermal instabilities and downdrafts associated with the disturbances. In addition, the wavelet method highlights the different roles of turbulence and coherent structures in the transfer of heat, moisture and CO₂ in the nocturnal boundary layer.     

青藏高原东部重力波过程与西南涡活动的统计关系

本文利用2012～2015年西南涡加密观测大气科学实验的剑阁、金川、九龙和名山四站探空资料,统计分析了6～7月西南涡活动期间对流层中、高层（6～12 km）的重力波过程,结果表明:青藏高原东部川西高原南部的九龙站与其余三站不同,重力波源主要来自对流层上层,波能传播方向向上,剑阁、金川和名山三站重力的波源主要来自对流层下层,波能传播方向向下。重力波过程在不同类型的西南涡活动中有明显差异,在移出型西南涡活动初期,重力波水平传播方向主要为东北向,其上传概率远大于下传概率,波动的动能和潜能较大且变化剧烈;而对应源地型西南涡,初期主要呈西北—东南向传播且重力波上传与下传概率相当,动能和潜能较小且变化相对平缓同时本次研究表明,重力波水平传播方向对西南涡的移动方向也有一定指示作用。按照发生时刻本文将重力波分为日发型重力波和夜发型重力波,在夜发型西南涡初期,重力波活动夜发（北京时20:00～08:00）的概率较大,这表明重力波的夜发性与西南涡的夜发性可能存在一定关联。     

Some aspects of internal gravity waves in the multicell-type convective system

Summary Some aspects of internal gravity waves in the multicell-type convective system are examined using a linear theory and a nonlinear numerical model. The basic-state wind is assumed to increase linearly with height and then remain constant.In the theoretical part, the two-dimensional, linear, steady-state response of a stably stratified atmosphere to specified cooling representing the evaporative cooling of falling precipitation in the subcloud layer is analytically considered. It is shown that there exist an updraft on the upstream side of the cooling and a downdraft on the downstream side. As the wind shear increases enough, the magnitude of the updraft decreases. This is because a large portion of the specified cooling is used to compensate for the positive vorticity associated with the positive wind shear and accordingly the effective cooling necessary to produce perturbations is reduced.In the numerical part, a two-dimensional version of the ARPS (Advanced Regional Prediction System) that is a nonhydrostatic, compressible model with detailed physical processes is employed. Results from the dry simulation, in which the steady cooling is specified in the model, show that the simulated quasi-steady field resembles the linear, steady-state solution field because the nonlinearity factor of thermally-induced waves in this case is small. For the moist simulation, the quasi-steady perturbations obtained from the dry simulation are used as initial conditions. It is shown that gravity waces can effectively initiate convection even with small amplitude and that updraft at the head of the density current somewhat resembles the linear, steady-state response of a stably straified flow to the specified cooling. The updraft, that is, forced internal gravity waves, at the head of the density current is responsible for the initiation of consecutive convective cells that move downstream and develop as a main convective cell. This study suggests that internal gravity waves play a major role in the initiation of consecutive convective cells in the multicell-type convective system and hence in its maintenance.     

Numerical studies on cold fronts Part I: Gravity flows in a neutral and stratified atmosphere

Summary We have used a two dimensional version of a nonhydrostatic mesoscale model to simulate atmospheric gravity currents for different thermal stratification. The horizontal and vertical grid increments are chosen such, that the major features of a current like head and elevated nose are resolvable.When the density current propagates into a neutral stratified environment it was found, that frontspeed agrees well with an empirical formula. Also characteristic length scales like depth of the head or height of the following cold air body agree well with observations found in water tank experiments.When a stable atmosphere is adopted, the front moves faster and the generated gravity waves have a significant influence on the atmospheric variables ahead of the current. This results especially in a pressure increase before the front arrives, an effect, which was found in observations, too.Finally, it is shown, that an elevated inversion, embedded in a stable layer, intensifies the vertical velocities and therefore the mesoscale heat flux, which results in a stronger entrainment. For this case a remarkable decrease of front speed is simulated with time.With 7 Figures     

An energy budget for waves and turbulence within an inversion

Several features of the maintenance of breaking gravity waves and turbulence in a marine inversion are examined. A formulation is proposed for a critical Richardson number based on a mutual response of the mean and turbulent states to a wave-like disturbance. The energy balance, based on averaged aircraft soundings, is examined to ascertain the order of magnitude of the component terms in the vicinity of a contemporaneous radar echo. Some physical mechanisms are discussed which may explain some aspects of the sustained existence of the echo layers.After preparation of this paper, a considerable number of pertinent and up-dated results bearing on waves and turbulence in stable layers were published as Volume 4 ofBoundary-Layer Meteorology, April 1973. The present discussion should be considered in relation to these papers and of Gossardet al. (1973) and Metcalf and Atlas (1973) in particular.     

Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves

An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler–Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.     

Numerical studies on cold fronts Part II: Orographic effects on gravity flows

Summary A two-dimensional nonhydrostatic numerical model was used to investigate the behaviour of a cold air gravity current, moving along complex terrain. It is found, that the model with a high horizontal and vertical resolution and with a closure scheme, using the turbulent kinetic energy, is suitable to simulate currents, which have the main features of those found in laboratory experiments.Simulations are presented for different orographic structures (mountain and valley), for varying thermal stratification of the environmental atmosphere (neutral, stable and stable with an elevated inversion) and for different heights of the cold air reservoir.The major effect of a hill on the advance of a gravity current is a reduction of the front speed upstream as well as (even stronger) downstream of the obstacle, where the amount of this decrease depends on thermal stratification. Near surface blocking of the air flow on the windward side occurs for all simulations. However, for small depths of the oncoming cold air, the current cannot surmount the hill and remains on the lee side.With 11 Figures     

Blocking in periodic valleys

Results are presented from a study of blocked flow (practically stagnant or recirculating light winds) in periodic valleys in thermally stably stratified ambient conditions. Inviscid and turbulent diffusion cases were modelled numerically to clarify the effects of turbulence on the blocking. The reflection of gravity waves from the top boundary of the hydrostatic model atmosphere was avoided by employing the radiation condition given by Klemp and Durran (1983). The dissipative numerical results are compared with new laboratory experiments which utilized the technique of Baines and Hoinka (1985) to simulate a semi-infinitely deep region.A criterion for the occurrence of blocked flow cannot be defined for the inviscid case except when the Froude number, Fr, based on the peak-to-trough ridge amplitude is less than about 0.4: then blocking is clearly identifiable before wave-breaking occurs. Breaking of waves is evident for Fr as large as 0.75, in agreement with analytical results given by Lilly and Klemp (1979).At small Froude number (Fr 0.5) in the dissipative flow simulations, blocked flow (stagnation) is present in the valleys, but a lee rotor (complete stagnation) is not evident. For order unity Froude numbers, blocking is a wave phenomenon, resulting from wave steepening and overturning or turbulent mixing. A finite thickness is brought to rest or participates in a recirculating flow when it first appears. A strong upward flow appears ahead of the rotor in the valleys, and the downslope wind over the windward side of the valleys is strengthened. Thus the present study shows that conditions for the onset of a rotor, and of stagnant flow, in periodic valleys are different.When blocked flow exists, the amplitudes of gravity waves in the upper layer are only 15% (Fr = 0.3) to 80% (Fr = 1.5) of those given by linear theory; this is supported by observations.