Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves

Summary In this study, the response of a dynamically unstable shear flow with a critical level to periodic forcing is presented. An energy argument is proposed to explain the upshear tilt of updrafts associated with disturbances in two-dimensional stably stratified flows. In a dynamically unstable flow, the energy equation requires an upshear tilt of the perturbation streamfunction and vertical velocity whereU _z is positive. A stability model is constructed using an iteration method. An upshear tilt of the vertical velocity and the streamfunction fields is evident in a dynamically unstable flow, which is required by energy conversion from the basic shear to the growing perturbation wave energy according to the energy argument. The momentum flux profile indicates that the basic flow is decreased (increased) above (below) the critical level. Thus, the shear instability tends to smooth the shear layer. Following the energy argument, a downshear tilt of the updraft is produced in an unstably stratified flow since the perturbation wave energy is negative. The wave energy budget indicates that the disturbance is caused by a thermal instability modified by a shear flow since the potential energy grows faster than the kinetic energy.With 4 Figures     

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves part II: Nonlinear response

Summary The nonlinear response of a dynamically unstable shear flow with critical level to an initial temperature anomaly is investigated using a nonlinear numerical model. Both nonconstant and constant shear profiles of the basic flow are considered. Effects of the solid lower boundary on the dynamically unstable, nonlinear flow are also studied. It is found that in a dynamically unstable, linear flow with a hyperbolic tangent wind profile, the updraft is tilted upshear. The result in consistent with that of a linear stability model (LC). The upshear tilt can be explained by the Orr mechanism (1907) and the energy argument proposed by LC. In a dynamically unstable, nonlinear flow, the updrafts produced by a sinusoidal initial temperature perturbation are stronger in the lower layer and are more compact and located further apart compared to the corresponding linear flow. In addition, the perturbed wave energy is slightly smaller than the linear case. It is found that the growth rate is smaller during the early stage and much larger during the later stage. For a localized initial temperature perturbation in a dynamically unstable flow, a stronger updraft with two compensated downdrafts are produced. Gravity waves are produced in a dynamically stable flow with both a hyperbolic tangent wind profile and a linear wind profile. For a linear shear flow with Richardson number less than 1/4, the disturbance grows in the early stage and then decays algebraically at later times, similar to that found in other linear theoretical studies. The influence of the solid lower boundary is to suppress the shear instability in a nonlinear flow with a hyperbolic tangent wind profile ofRi<1/4.With 9 Figures     

三维非静力平衡大气中平行切变流上重力内波的不稳定及半椭圆定理

本文应用守恒型非弹性模式研究了三维非静力平衡大气中平行切变流上重力内波的不稳定，推广了Miles定理和半圆定理，得到了有限深度气层的半椭圆定理。该定理指出不稳定波的复波速被限制在相速复平面上一个内接于霍华德（Howard）半圆的半椭圆内。该半椭圆长轴重合于半圆的直径，而短轴则取决于最小Ri数、波长、波宽等因素。     

重力波与对流耦合作用在一次山地突发性暴雨触发中的机理分析

利用欧洲中期天气预报中心（ECMWF）开发的新一代ERA5再分析资料、中国自动站与CMORPH降水产品融合的逐小时降水资料以及国家卫星气象中心FY-2G卫星云图资料,对2018年5月21～22日发生在四川盆地西南部的一次山地突发性暴雨过程中的重力波特征进行天气动力学分析。得到以下结果:此次山地突发性暴雨受到了波长约为150 km,周期为5 h的重力波活动的影响,是典型的β中尺度天气系统诱发的暴雨事件。此过程中的重力波主要是在地形和切变不稳定的共同作用下触发的。切变不稳定先于重力波的传播出现在下游降水区域,可表征切变不稳定的理查逊数对重力波传播方向及降水落区有很好指示作用。此次暴雨发生前,重力波中的上升支气流输送低层水汽到高空助力对流发展,而下沉支气流使得低层不稳定能量不断累积。随着东北低空急流的发展,在大气低层（700～800 hPa）东西风切变的过渡带内形成临界层,临界层不断吸收高空波动能量造成重力波能量下传,触发低层不稳定能量释放,促使对流不断加强,最终引发此次山地突发性暴雨。     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

Daily and annual cycle of CO2 concentration near the surface depending on boundary layer structure at a rural site in Spain

CO₂ in the rural atmosphere is related to respiration–photosynthesis processes, although the evolution of the low atmosphere is also a determinant factor. CO₂ concentrations were measured at surface and meteorological variables obtained from a radio acoustic sounding system sodar at a flat rural site during a 3-year campaign. Yearly and daily cycles of CO₂ were described. Maxima were observed in spring and autumn during the night. Wind speed and thermal structure of the lower atmosphere were analysed. Low level jets were observed during the night, their core proving lower in summer. Surface inversions observed with low winds reached up to 100 m. The turbulence layer which developed during the day extended up to 300–400 m and was capped by a stable layer. Median vertical wind speed reached 1 m s^?1 in super-adiabatic conditions in summer. Determination of decoupled low level jets proved difficult with the device used and corresponding concentrations were slightly higher than medians calculated with all the observations. The bulk Richardson number was calculated in the lower atmosphere and four intervals were considered: drainage, transitional, shear flows and unstable conditions. Median CO₂ concentrations were split according to these intervals. Higher values corresponded to drainage flow, which was associated to more stable conditions being less frequent and lower values to shear flow and unstable conditions, revealing a satisfactory link between the bulk Richardson number as a turbulence indicator in the low atmosphere and CO₂ surface concentrations.     

洱海盆地一次冬季大风演变特征及其机制模拟分析

利用WRF模式耦合Noah陆面模式和CLM湖泊模式,对2015年1月23日大理地区洱海盆地的大风天气进行模拟,对大风的发展期、强盛期和减弱期的三维动力热力结构特征进行分析,并得出了洱海盆地大风形成机制:在洱海盆地大风发展期,高空以西风为主,盆地中部上空1km高度处出现局地小气旋,地面以偏东风为主,高空偏西气流翻越苍山形成波动扰动,在背风坡侧形成空腔区和二次涡,低层形成了波不稳定区域,波不稳定区域发生波破碎,波破碎区域湍流运动活跃,把上层的能量往下传播。大风强盛期,盆地南北侧高空为两支西风气流控制,中部变为弱的辐散场,造成高空扰动,苍山东侧近地面浅薄逆温层消失,低空逆温层之上温度廓线几乎垂直上升,大气层结处于不稳定状态,有利于高空动量向下输送。大风减弱期,高空西风减弱,扰动消失,湍流动能耗散,地面风速逐渐减小。     

The instability of a horizontal five-layer jet

The instability of a symmetric jet moving horizontally, in which two shear layers with opposite shear of the same strength are separated by a central irrotational layer and are adjoined by unbounded, irrotational outer layers, is studied.First, the fluid is assumed to be homogeneous. Two unstable modes are found, the central wave one-quarter wave length out of phase with the outer wave. Mode I consists of central waves being in phase and outer waves being in phase. Mode II consists of central waves being in opposite phase and outer waves being in opposite phase. For a given width of the jet, the thicker the central irrotational layer, the stronger the shear of the shear layers, the stronger the instability. For a fixed ratio of the thickness of central layer to that of the shear layers, mode I is more unstable than mode II.Next, a density jump across the outer interface levels and another density jump across the central interface levels are introduced. The effect of these density jumps on mode I is to reduce the growth of the wave. The wave with equal density jump across every interface level grows somewhat slower than the waves with the entire density jump across outer or central interface levels. For an idealized velocity profile with isentropic layers with an overall Richardson number of 4.9, the linear theory predicts that the amplitude of the wave doubles in about 5 min and the wave-length is 241 m, which compares favorably with 320m obtained in the boundary layer by Gossard et al. (1970). For atmospheric parameters with an overall Richardson number of unity, linear theory predicts that the amplitude of the wave doubles in about % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmamaale% aaleaacaaIXaaabaGaaG4maaaaaaa!383C!\[2{\textstyle{1 \over 3}}\] min and the wave-length is about 510 m, which is only slightly larger than the width of the jet.A physical argument is invoked to explain the evolution of finite-amplitude waves.     

The linear steady response of a stratified baroclinic atmosphere to elevated diabatic forcing

Abstract

A parameter study is presented of the linear steady response to an elevated diabatic forcing in a Boussinesq baroclinic atmosphere. The model is two‐dimensional on the vertical plane; the basic wind is perpendicular to this plane with horizontal and vertical shear. The intensity of the circulation is sensitive to the strength of the baroclinic zone only for weak static stability. A scale analysis supports this conclusion: the importance of baroclinic effects depends on the ratio of the aspect ratio of the circulation to the aspect ratio of the baroclinic basic state. Baroclinicity also leads to a tilt of the circulation due to enhanced horizontal temperature advection, and the corresponding vertical flux of horizontal momentum. The magnitude of the latter can be large when the Richardson number approaches its critical value from above, i.e. for slightly symmetrically stable basic flows; this is true even with viscosity. The resonant limit where the Richardson number approaches the critical value for symmetric instability is also examined. For non‐zero dissipation, the critical value is smaller than that of the inviscid limit.     

The stability analysis of an inflexion-free velocity profile and its application to the night-time boundary layer in the atmosphere

The characteristics of waves excited in a stratified shear flow with a velocity profile monotonically increasing above the ground are calculated numerically. It is shown that unstable modes exist when the Brunt-Väisälä frequency of the ambient atmosphere decreases sufficiently fast with height. Their growth rates as a function of the horizontal wavelength and the local Richardson number are given, and a comparison between them and experimental data obtained for the night-time-boundary layer of the Earth's atmosphere is carried out. Finally, the characteristics of the singular neutral modes that the system can support are presented.On a Fellowship from the National Research Council of Italy.     

水汽空间分布对大气船舶重力波影响的数 值试验

利用中尺度数值模式ARPS模拟研究了水汽在山脉重力波和大气船波的产生和演变中的作用。研究发现水汽和非绝热效应对大气船波的影响与水汽的空间分布有关,大气船波的产生和演变对水汽的空间分布具有极端的敏感性,在一定条件下水汽的引入有可能减少大气船波的活动。对于3层模式结构的气流过山而言,如果初始的水汽分布在中层大气,则水汽和非绝热效应对大气船波的影响较小,而如果初始的水汽分布在中下层大气,则引入水汽后减少了大气船波的强度,但是如果初始的水汽分布在整个模式大气层,则水汽的引入减少了大气船波的活动。     

亚——非季风区非绝热加热与夏季环流关系的诊断研究

基于热力适应理论,本文利用 ＮＣＥＰ／ ＮＣＡＲ再分析资料对撒哈拉沙漠、青藏高原和孟加拉湾地区的非绝热加热与夏季环流进行了诊断研究。在非洲撒哈拉沙漠地区,以感热输送为主的加热仅局限于近地面层,边界层以上的大气则以辐射冷却占优势。因而除了边界层内存在着浅薄的正涡度和微弱的上升运动以外,整个对流层几乎都维持负涡度并盛行下沉运动。对于青藏高原地区,强大的表面感热通量引起的垂直扩散是近地面大气加热的主要分量,与大尺度上升运动相关的凝结潜热对低层大气的加热也有一定的贡献。长波辐射造成的对流层中、上层大气的冷却则主要由深对流潜热释放来补偿。夏季高原地区总非绝热加热是正值,且最大加热率出现在边界层内。低空大气辐合产生正涡度,而中、高层大气辐散伴有较强的负涡度。因而高原盛行上升运动,最大上升运动位于近地面层。夏季孟加拉湾地区的深对流凝结潜热释放远大于长波辐的冷却作用,因而整个对流层几乎都保持较强的非绝热加热。４００ｈＰａ层附近的最大加热率引起３００－４００ｈＰａ最强的上升运动。对流层上层是负涡度区,而中、低层为正涡度区。结果还表明,垂直和水平辐散环流与大气的热源和热汇区密切相联：在高层,辐散气流从热源区流向热汇区;在低层则相     

Midlatitude unstable air-sea interaction with atmospheric transient eddy dynamical forcing in an analytical coupled model

While recent observational studies have shown the critical role of atmospheric transient eddy (TE) activities in midlatitude unstable air-sea interaction, there is still a lack of a theoretical framework characterizing such an interaction. In this study, an analytical coupled air-sea model with inclusion of the TE dynamical forcing is developed to investigate the role of such a forcing in midlatitude unstable air-sea interaction. In this model, the atmosphere is governed by a barotropic quasi-geostrophic potential vorticity equation forced by surface diabatic heating and TE vorticity forcing. The ocean is governed by a baroclinic Rossby wave equation driven by wind stress. Sea surface temperature (SST) is determined by mixing layer physics. Based on detailed observational analyses, a parameterized linear relationship between TE vorticity forcing and meridional second-order derivative of SST is proposed to close the equations. Analytical solutions of the coupled model show that the midlatitude air-sea interaction with atmospheric TE dynamical forcing can destabilize the oceanic Rossby wave within a wide range of wavelengths. For the most unstable growing mode, characteristic atmospheric streamfunction anomalies are nearly in phase with their oceanic counterparts and both have a northeastward phase shift relative to SST anomalies, as the observed. Although both surface diabatic heating and TE vorticity forcing can lead to unstable air-sea interaction, the latter has a dominant contribution to the unstable growth. Sensitivity analyses further show that the growth rate of the unstable coupled mode is also influenced by the background zonal wind and the air–sea coupling strength. Such an unstable air-sea interaction provides a key positive feedback mechanism for midlatitude coupled climate variabilities.

     

The transmission of spatially-compact internal wave packets through a critical level

Results are presented from numerical simulations of the incidence of a spatially-compact beam of internal waves on a shear layer containing a critical level. It is found that a significant fraction of the energy of the incident beam is transmitted across the critical level when the packet is narrow in physical space and when the energy density of the packet is not too high so that nonlinear effects are weak. As either the packet width or its energy density increases, the presence of a critical level renders the shear layer increasingly opaque to the transmission of energy. The familiar exponentially small value of the transmission coefficient is recovered as the spatial width of the packet exceeds (roughly) eight to ten wave lengths.     

Shear instability and gravity wave saturation in an asymmetrically stratified jet

Motivated by the mean current and stratification structure associated with the equatorial undercurrent (EUC), we examine the stability and wave propagation characteristics of a highly idealized model flow: the asymmetrically stratified jet. This is a parallel shear flow in which the depth-varying current has the sech² form of a Bickley jet. The stratification has a step function structure: the buoyancy frequency takes uniform values above and below the center of the jet, with the larger value occurring below. The spectrum contains three classes of unstable normal modes. Two are extensions of the sinuous and varicose modes of the unstratified Bickley jet; the third has not been described previously. The asymmetric stratification structure allows instabilities to radiate gravity wave energy from the upper flank of the jet to the lower flank, where it encounters a critical layer. From here, wave energy may be reflected, absorbed or transmitted. Absorption results in wave saturation and momentum transfer to the mean flow, in close analogy with the breaking of orographic gravity waves in the middle atmosphere. Transmission beyond the lower flank may partly account for wave signals observed in the deep equatorial oceans. All of these processes exert zonal forces on the jet that alter its speed and shape. The wave structures and associated fluxes developed by the idealized model are compared with observations of the EUC.     

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.     

Spectral features of the energy transfer between internal waves and a larger-scale shear flow

Internal waves propagating in a larger-scale shear flow slowly change their amplitudes and wavenumbers. For moderate shear flows the secular effect of these changes reduces to a diffusion of wave action in wavenumber space. The diffusion coefficients are derived under the assumption that relaxation processes exist within the internal wave field. Associated with the diffusion of wave action is an energy transfer between the mean flow and the wave field. The wavenumber—frequency dependence of this energy transfer is evaluated for the Garrett and Munk (1975) spectral model. For this spectrum the transfer shows a characteristic +—+ signature with a weak source of internal wave energy at near-inertial frequencies, a weak sink at medium frequencies, and a strong source at high frequencies. The integrated energy transfer is from the mean flow to the internal wave field.     

2009年4月下旬蒙古气旋型大范围沙尘暴天气过程的诊断分析

本文利用卫星资料、加密实况观测资料、NCEP再分析资料分析了2009年4月下旬我国北方地区大范围沙尘天气过程的成因,并对热力、动力及不稳定层结等条件作了物理量诊断,得到了以下主要结论：贝加尔湖阻塞高压、高空冷涡及蒙古气旋是造成此次大范围沙尘天气的有利环流形势,其中蒙古气旋是关键影响系统;干暖舌位置对于沙尘落区有一定指示意义,沙尘暴落区与干暖舌的位置及移动方向一致;高空急流的发展演变与此次沙尘天气密切相关,沙尘天气主要发生在高空急流入口右侧,高空急流加强东移南压对应着沙尘天气东扩南压加强;螺旋度反映出沙尘暴过程中气旋区旋转上升明显,且螺旋度大值区后倾;理查逊数下降并维持低值、风垂直切变增大,大气层结不稳定,易激发沙尘暴发生和向下游传输。     

Simulating tropical instability waves in the equatorial eastern Pacific with a coupled general circulation model

Satellite observations of SSTs have revealed the existence of unstable waves in the equatorial eastern Pacific and Atlantic oceans. These waves have a 20-40-day periodicity with westward phase speeds of 0.4-0.6 m s-1 and wavelengths of 1000-2000 km during boreal summer and fall. They are generally called tropical instability waves (TIWs). This study investigates TIWs simulated by a high-resolution coupled atmosphere-ocean general circulation model (AOGCM). The horizontal resolution of the model is 120 km in...