Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline

The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-Väisälä frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-Väisälä frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline.     

Circulation and boundary layers in differentially heated rotating stratified fluid

Recent laboratory experiments with rotating stratified water in a cylinder have revealed many of the predictions of linearized, analytic theory. Earlier measurements of the velocity field generated in a cylinder by top heating compared well with theory. Large stratification clearly suppressed Ekman pumping so that the interior velocity field (primarily azimuthal) responded by satisfying no-slip top and bottom boundary conditions without the need for Ekman layers. This interior flow also occupied a boundary layer of greater thickness than the Ekman layer under some conditions. Theory and experiments have now been conducted for sidewall heating. As before, experiment and theory agree well over some parameter ranges. But for some parameters, the flow is unstable. The exact nature of the instability remains poorly understood. The size of one combination of both vertical and horizontal boundary layers is governed by the Rossby radius of deformation multiplied by the square root of the Prandtl number. Sidewall boundary layers and their scales will be reviewed with the present results in mind.     

Wave/wave interaction producing horizontal mean flows in stably stratified fluids

We show that internal wave/wave interactions in stratified fluids are able to produce strong horizontal mean currents. A simple analytical model allows us to estimate the amplitude of the time-periodic horizontal mean flow induced by the interaction of two monochromatic waves. This model shows that in some cases, the mean flow velocity can overgo a threshold beyond which critical layers and intense energy transfers from the waves to the mean flow are expected. This prediction is confirmed by direct pseudo-spectral simulations of the Navier–Stokes equations under the Boussinesq approximation. Such interactions may help to further understand the presence of strong vertical shear observed in the final stage of stratified flows in oceans and atmospheres.     

Experiments with density currents on a sloping bottom in a rotating fluid

The behaviour of a density current on a sloping bottom in a rotating system is investigated by laboratory experiments. The main result is that the dense bottom outflow induces cyclonic vortices in the upper fluid layer, which are formed periodically and move to the west parallel to coast. Two regimes of vortex formation have been identified. For strong density currents and weak rotation, vortices are formed by stretching of the upper layer near the source as found also in the experiments by Lane-Serff and Baines (1998) [Lane-Serff, G.F., Baines, P.G., 1998. Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229–253]. For weak density currents and strong rotation vortices are due to instability of the bottom plume itself as found in the numerical simulations of Jiang and Garwood (1996) [Jiang, L., Garwood, W. Jr., 1996. Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1224–1233].     

A note on circulation in differentially heated rotating stratified fluid and other elliptic problems

This note relates to the paper Circulation and boundary layers in differentially heated rotating stratified fluid by Whitehead and Pedlosky [Whitehead, J.A., Pedlosky, J., 2000. Circulation and boundary layers in differentially heated rotating stratified fluid. Dyn. Atmos. Ocean. 31, 1–21]. Here, we describe an alternative method of solution for the theoretical model developed therein, and provide a comparison with the original method used in the paper.     

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.     

Laboratory experiments on along-slope flows in homogeneous and stratified rotating fluids

Laboratory experiments have been carried out for the flow along isobaths of simulated shelf-continental slope geometry. Cases of both homogeneous and linearly stratified fluids are considered and the background flows are sufficiently strong to have the flow near the bottom boundary range from transitional to fully turbulent. The background motions are impulsively started and flows with a coast on the right (spin-down) and on the left (spin-up) are considered. The homogeneous spin-down and spin-up processes are smooth in the sense that no vortical structures were found to be of the order of the slope width or larger. Flows reach equilibrium more quickly for spin-down cases, and this is attributed to secondary flows forced by the basin geometry. All of the stratified experiments exhibited large-scale instabilities as evidenced by the generation of slope and basin scale eddy structures and a much slower decay than their homogeneous counterparts.     

Investigating a Hierarchy of Eulerian Closure Models for Scalar Transfer Inside Forested Canopies

Modelling the transfer of heat, water vapour, and CO₂ between the biosphere and the atmosphere is made difficult by the complex two-way interaction between leaves and their immediate microclimate. When simulating scalar sources and sinks inside canopies on seasonal, inter-annual, or forest development time scales, the so-called well-mixed assumption (WMA) of mean concentration (i.e. vertically constant inside the canopy but dynamically evolving in time) is often employed. The WMA eliminates the need to model how vegetation alters its immediate microclimate, which necessitates formulations that utilize turbulent transport theories. Here, two inter-related questions pertinent to the WMA for modelling scalar sources, sinks, and fluxes at seasonal to inter-annual time scales are explored: (1) if the WMA is to be replaced so as to resolve this two-way interaction, how detailed must the turbulent transport model be? And (2) what are the added predictive skills gained by resolving the two-way interaction vis-à-vis other uncertainties such as seasonal variations in physiological parameters. These two questions are addressed by simulating multi-year mean scalar concentration and eddy-covariance scalar flux measurements collected in a Loblolly pine (P. taeda L.) plantation near Durham, North Carolina, U.S.A. using turbulent transport models ranging from K-theory (or first-order closure) to third-order closure schemes. The multi-layer model calculations with these closure schemes were contrasted with model calculations employing the WMA. These comparisons suggested that (i) among the three scalars, sensible heat flux predictions are most biased with respect to eddy-covariance measurements when using the WMA, (ii) first-order closure schemes are sufficient to reproduce the seasonal to inter-annual variations in scalar fluxes provided the canonical length scale of turbulence is properly specified, (iii) second-order closure models best agree with measured mean scalar concentration (and temperature) profiles inside the canopy as well as scalar fluxes above the canopy, (iv) there are no clear gains in predictive skills when using third-order closure schemes over their second-order closure counterparts. At inter-annual time scales, biases in modelled scalar fluxes incurred by using the WMA exceed those incurred when correcting for the seasonal amplitude in the maximum carboxylation capacity (V _{cmax, 25}) provided its mean value is unbiased. The role of local thermal stratification inside the canopy and possible computational simplifications in decoupling scalar transfer from the generation of the flow statistics are also discussed.

“The tree, tilting its leaves to capture bullets of light; inhaling, exhaling; its many thousand stomata breathing, creating the air”. Ruth Stone, 2002, In the Next Galaxy

     

分层气流条件下地形降水的二维理想数值试验

利用WRF v3.5中尺度数值模式,在条件不稳定层结下,针对分层气流(基本气流风速和大气湿浮力频率呈二层均匀分布)过山时,地形对降水的影响进行了多组二维理想数值试验,以研究不同高度、尺度山脉和不同方向基本气流对降水形态和分布的影响。模拟结果表明,地形重力波触发对流是地形降水的主要机制之一,地形波的特征(波长、振幅)和传播均受到地形和基本气流的影响,其中,强基本气流流经高而陡峭的山脉时,更容易在其背风坡捕捉到重力波,地形降水呈现多种模态,反之亦然;当改变基本气流与山脉交角时,主要通过影响地形强迫抬升速度、基流对波动稳定性发展来进一步影响地形降水的强度和分布。     

Current Observations of Internal Tides and Parametric Subharmonic Instability in Luzon Strait

Acoustic Doppler Current Profiler (ADCP) measurements of the velocity structure in the thermocline in Luzon Strait are presented. The statistics for current, vertical variation of the inertia-gravity waveband, parametric subharmonic instability (PSI), and current shear are analyzed. It was found that 1) barotropic flow primarily consists of a nearly circular mixed tide. Diurnal tides are strongest and show smooth variance with a fortnightly spring-neap cycle, indicative of the astronomical tide-generating force. However, the semi-diurnal band power exhibits a high-frequency oscillation as a result of non-linear interactions. The high-frequency band power with high values during the spring tide oscillates with the tidal cycle. Near-inertial wave motions showing random variance may be caused by changes in the wind forcing at the sea surface or by random forcing. 2) Baroclinic velocities exhibit strong shear structure. The observed large changes in the amplitude of the baroclinic velocity and the limited vertical extent of the high-velocity cores may be interpreted as internal wave beams that pass through the observed water column. Semi-diurnal tides are dominant in the baroclinic velocity. Kinetic energy spectra also revealed that additional peaks were centred at sum-tidal-inertial interaction frequencies (such as M₂ ?+?f) and difference-interaction frequencies (such as M₂ ???f). The spectral exponent of the baroclinic velocity is ω^?α (1?<?α?<?3). 3) Strong non-linear interactions among internal waves exist, and the semi-diurnal (M₂) component plays a key role in these interactions. Bicoherence analysis showed that M₂/2 waves were non-linearly coupled with the dominant M ₂ internal tide. 4) The polarization relations were used to diagnose observational internal tidal motions. Diurnal waves propagate to the east-northeast, and the semi-diurnal–diurnal waves propagate westward. In the case of diurnal tides, the minor to major axis ratio is different from the expected value of f/ω_{K 1} because of the deviation of inclinations, whereas, for semi-diurnal tides, it is close to the expected value of f/ω _M2 at depths from 30 to 150 m.

RÉSUMÉ?[Traduit par la rédaction] Nous présentons les mesures de la structure des vitesses dans la thermocline faites par profileur de courant à effet Doppler (ADCP) dans le détroit de Luçon. Nous analysons les statistiques sur le courant, la variation verticale de la gamme d'ondes d'inertie-gravité, l'instabilité subharmonique paramétrique (PSI) et le cisaillement du courant. Il ressort que 1) l’écoulement barotrope consiste principalement en une marée mixte presque circulaire. Les marées diurnes sont les plus fortes et présentent une variance régulière dans un cycle vives-eaux mortes-eaux de deux semaines qui révèle la nature astronomique de la force qui produit les marées. Cependant, la puissance de bande semi-diurne affiche une oscillation de haute fréquence causée par des interactions non linéaires. La puissance de bande de haute fréquence avec des valeurs élevées durant les vives-eaux oscille avec le cycle des marées. Les mouvements des ondes quasi inertielles affichant une variance aléatoire peuvent être dus à des variations dans le forçage par le vent à la surface de la mer ou à un forçage aléatoire. 2) Les vitesses baroclines exhibent une structure fortement cisaillée. Les changements marqués observés dans l'amplitude des vitesses baroclines et l'extension verticale limitée des c?urs de vitesse élevée peuvent être interprétés comme des faisceaux d'ondes internes qui traversent la colonne d'eau observée. Les marées semi-diurnes sont dominantes dans les vitesses baroclines. Les spectres d’énergie cinétique ont aussi révélé que des crêtes additionnelles étaient centrées aux fréquences d'interaction cumulative marée-inertie (comme à M₂ ?+?f) et aux fréquences d'interaction différentielle (comme à M₂ ???f). L'exposant spectral de la vitesse barocline est ω^?α (1?<?α?<?3). 3) Il existe de fortes interactions non linéaires entre les ondes internes et la semi-diurne (M₂) joue un rôle clé dans ces interactions. L'analyse de bicohérence a montré que les ondes M₂/2 étaient non-linéairement couplées avec la marée interne dominante M₂ . 4) Nous avons utilisé les relations de polarisation pour diagnostiquer les mouvements de marée internes déduits des observations. Les ondes diurnes se propagent vers l'est-nord-est et les ondes semi-diurnes se propagent vers l'ouest. Dans le cas des marées diurnes, le rapport de l'axe secondaire à l'axe principal diffère de la valeur attendue (f/ω_{K 1} ) à cause de l’écart des inclinaisons alors que pour les marées semi-diurnes, il est proche de la valeur attendue (f/ω _M2 ) à des profondeurs de 30 à 150 m.     

华北盛夏暴雨过程的能量特征分析

本文利用实况资料和T213输出资料,对发生在2005年8月16日～17日的华北暴雨过程进行了能量学特征分析,结果表明:暴雨前24h～36h,对流层上下层有暖湿空气同时发展,是暴雨发生的重要动力机制;强的干、湿静力能锋区稳定维持是这次大范围暴雨产生的能量基础,中低层湿静力能差值大于0,且数值很大,说明对流不稳定层结很强,暴雨发生在高能、高不稳定度的条件下;水汽的充足补给作用,是这次暴雨过程能量转换的基础。     

Evolution of instability before and during a torrential rainstorm in North China

NCEP-NCAR reanalysis data were used to analyze the characteristics and evolution mechanism of convective and symmetric instability before and during a heavy rainfall event that occurred in Beijing on 21 July 2012.Approximately twelve hours before the rainstorm,the atmosphere was mainly dominated by convective instability in the lower level of 900-800 hPa.The strong southwesterly low-level jet conveyed the moist and warm airflow continuously to the area of torrential rain,maintaining and enhancing the unstable energy.When the precipitation occurred,unstable energy was released and the convective instability weakened.Meanwhile,due to the baroclinicity enhancement in the atmosphere,the symmetric instability strengthened,maintaining and promoting the subsequent torrential rain.Deriving the convective instability tendency equation demonstrated that the barotropic component of potential divergence and the advection term played a major role in enhancing the convective instability before the rainstorm.Analysis of the tendency equation of moist potential vorticity showed that the coupled term of vertical vorticity and the baroclinic component of potential divergence was the primary factor influencing the development of symmetric instability during the precipitation.Comparing the effects of these factors on convective instability and symmetric instability showed some correlation.     

川东北一次西北气流型强冰雹天气的成因分析

利用常规气象资料和NCEP／NCAR 1°×1° 6h再分析资料,从大气环流形势、物理量场等方面对2007年4月29日发生在川东北地区的一次强冰雹天气过程的成因进行了分析。结果表明：此次西北气流型冰雹天气是在低能量环境场条件下发生的;冰雹天气发生前12h内降雹区的对流有效位能激增、午后下垫面强烈加热对大气不稳定性增强的作用显著;大气层结对流不稳定、湿对称不稳定、充足的水汽以及干线（露点锋）的存在为此过程提供了有利条件。     

2003年一次梅雨大暴雨成因的动力学研究

运用中尺度非静力模式MN5对2003年梅雨期一次大暴雨天气进行数值模拟，在降雨模拟基本正确的基础上分析暴雨发生原因。结果表明：该次梅雨大暴雨属于切变类暴雨，对流层低层有能量锋区、高层有惯性不稳定活动，暴雨区位于低空急流的左前方、高空急流的右前方。暴雨中心物理量要素的时间一高度演变显示：低层正涡度、辐合，高层负涡度、辐散，深厚的上升运动，等相当位温线抬升，湿位涡及其正、斜压分量3者负值加大均有利于降雨加强；暴雨减弱阶段，这些要素一般向相反方向转变。该次大暴雨的直接影响系统具有明显的中尺度时、空特点，大暴雨的发生与高层惯性不稳定和低层对流不稳定有关。     

河西走廊中西部一次特强沙尘暴的对称不稳定诊断分析

2007年4月13日在河西走廊中西部发生了特强沙尘暴,极大风速25m/s,最小能见度50m。用风云2号卫星红外云图对下沉急流云头进行跟踪,并用NCEP(1°×1°)6h再分析数据对高速下沉急流到达冷锋云带前后的静力不稳定、条件不稳定、条件对称不稳定等进行了诊断分析。结果表明:这次强沙尘暴由高速下沉急流引起,急流头部触发了锋区附近强对流发生;凝结潜热释放先在对流层中层发生,然后向下发展,使对流层中下部转为条件不稳定层,700hPa附近的条件不稳定能量释放使边界层对流环流迅速增强,引发了这次特强沙尘暴。     

一次华北锋面带状降水过程中的对流-对称不稳定诊断分析

本文用GRAPES_Meso中尺度区域模式模拟了2015年8月2—4日的一次华北锋面带状降水过程,在模拟结果与实况比较吻合的情况下,用高分辨率模式输出资料对降水过程中的对流稳定度、惯性稳定度和条件性对称不稳定(CSI)进行了分析,并诊断出降水过程中的条件性对称不稳定区域。个例分析的结果表明:(1)带状降水过程中CSI的发展伴随着对流不稳定的减弱和惯性不稳定的增强。(2)根据不稳定量的变化情况,把降水过程分为3个阶段:在第一个阶段,降水区域上空-?θ_e/?p0,降水主要受对流不稳定的影响;在第二个阶段,对流不稳定、惯性不稳定与CSI发展增强,此阶段的降水受3种不稳定量的影响;在第三个阶段,3种不稳定能量均逐渐减弱,但仍然影响着降水的持续。(3)发展旺盛阶段的CSI在平面上呈带状分布,与雨带、对流不稳定区域平行,在剖面上CSI主要活跃在对流层低层。(4)用湿位涡结合对流稳定度与惯性稳定度诊断CSI区域的方法比M-θ_e剖面图方法更准确有效。     

陕西东南部一次伴有雷暴的暴雪天气分析

利用常规观测、多普勒天气雷达和ERA—Interim再分析资料(0.25°×0.25°),对2016年11月22日陕西东南部地区一次伴有雷暴的暴雪天气过程进行诊断分析。结果表明:(1)此次暴雪是在低层东路回流冷空气与中层暖湿气流共同作用下形成的,700 hPa存在强的风向风速辐合,辐合区前部16 m/s的西南急流,为暴雪产生提供了有利的动力和水汽条件。急流加强是降雪增幅的主要原因。(2)冷季、强的锋区和低空急流、冷垫、逆温层、锋区之上湿的中性到条件不稳定层结、强切变低CAPE、雷达带状回波是此类天气预报中需要关注的特征。(3)整体层状云降水中,局地对流性云团旺盛发展,是此次暴雪的云系特征,暴雪发生在对流云团加强西伸、移速减缓的时段;与本地暖季相比,暴雪对流云团的面积较小,最大反射率因子所在的高度较高。(4)由动力锋生产生的次级环流上升支促使冷垫之上的暖湿气流快速上升,触发条件对称不稳定能量释放,使气块在逆温层之上获得正浮力,是暴雪发生并伴有雷暴的主要物理机制。     

WAVE-CISK对称不稳定谱点分布的半圆定理

采用滞弹性近似研究了WAVE-CISK下对称性扰动的谱点分布,得到了WAVE-CISK下对称不稳定扰动谱点分布的半圆定理,用其可估计该对称不稳定增长率的上界.发现存在WAVE-CISK时加热反馈和层结参数对该不稳定的增长率均有重要影响.WAVE-CISK加热反馈越强、基流的垂直切变越大,扰动的垂直结构越简单则该不稳定增长率的上界就越大.存在WAVE-CISK时滞弹性近似下的对称不稳定发生的条件也较Boussinesq近似下的更苛刻.