Instabilities in hurricane-like boundary layers

Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers.The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear.     

副高外围对流雨带中的对流—对称不稳定及锋生的诊断分析

对2009年8月25日西太平洋副热带高压（简称副高）西北外围对流雨带的云图特征进行了分析,利用WRF3.3中尺度模式对对流雨带的发生发展进行了数值模拟,在模拟较成功的基础上,利用模式输出结果分析了对流雨带发生时的对称不稳定、对流不稳定、惯性不稳定以及锋生等。结果表明：副高外围对流雨带由若干具有一定间隔的对流单体构成,单体在随对流层中层气流的移动中逐渐发展直至消亡。对流雨带的西北侧为宽广的带状斜压云系,东南侧为副高控制的晴空区。对流雨带发生于对流层低层（700 hPa以下）的对称不稳定区,700～500 hPa存在对流不稳定和弱的惯性不稳定。随着对流的发展,700～500 hPa的对流不稳定度明显减弱,而惯性不稳定明显加强。对流层低层为倾斜上升区,中高层为垂直上升区,左侧对应下沉气流,呈现明显的倾斜对流和垂直对流的混和特征,体现了对流—对称不稳定的作用。对流层低层（750 hPa以下）锋生的存在提供了对流—对称不稳定能量释放的有利条件。对流雨带与500～800 hPa等厚度线基本平行,而与500 hPa等高线存在明显的交角,雨带中的对流单体随环境气流移动,雨带符合与对称不稳定相联系的带状降水特征。上述结论对实际预报副高外围对流雨带的位置和走向具有指示意义。     

Substructure layers and modes in the stratified boundary layer

Geophysical flows include small-scale substructures that support shear instabilities where the smoothed mean profiles indicate only stability. The substructures must draw their energy from the mean flow, probably through wave interactions, and it is shown that the substructures themselves give rise to a type of mode that is well suited for nonlinear interactions with the flow in and around them. The study indicates that substructures and their associated modes form a dynamically interacting system that may contribute to the chaotic nature of a stably stratified region.     

一次华北强降雪过程的湿对称不稳定性研究

运用湿球位涡和倾斜有效位能的概念从条件性对称不稳定（ＣＳＩ）和局地对称不稳定（ＬＳＩ）这两个侧面计算了一次华北强降雪过程的湿对称不稳定的水平分布和垂直分布状况，并比较详细地讨论了湿对称不稳定对１９８６年１１月２２—２３日发生在内蒙古河套地区和林东、林西地区附近的一条狭长的强降雪带的可能作用以及湿对称不稳定与基本气流走向、风垂直切变和水汽的关系，发现：这条降雪带与雪区附近低层的湿球位涡负值区走向大体平行；在降雪带中分别位于呼和浩特、东胜地区和林东、林西地区的强降雪中心有着不同的动力学机制，前者主要为在暖区具有弱的对称不稳定的情形下锋生强迫作用所致，后者则是由明显的湿对称不稳定所致。     

热带海气耦合Kelvin波的弱相互作用

本文在简单的热带海气耦合方程组中 ,引进基本风场和平均海流的作用以后 ,对热带海气耦合 Kelvin波的不稳定性进行了讨论 ,得到其耦合不稳定的判据条件 ,并且分析了它的传播结构特征。     

Boundary-Layer Stress Instabilities in Neutral,Rotating Turbulent Flows

Boundary-layer instabilities are studied by analyzing the results of laboratory simulations of wall turbulence in a shear-driven rotating flow. The experiments were carried out in the Turin University Laboratory rotating water tank, where a circular flow was generated by either increasing (spin-up) or decreasing (spin-down) the rotation speed of the platform. The flow was measured using a Particle Image Velocimetry technique and the developed turbulence analyzed. Two cases were accounted for, in the former the measurements were performed over a smooth surface (bottom of the tank), while in the latter a rough-to-smooth transition was considered. The turbulent boundary layer developed inside the tank is analyzed by means of vertical profiles of mean and turbulent quantities and on the basis of drag coefficients. Then turbulent structures developed in the different cases are shown and discussed in terms of the vorticity fields. Finally, an analysis based on the concept of swirling strength was carried out to select among the vortex extremes those associated with a coherent structure.     

Modeling large-scale instabilities in the Kuroshio extension

Large-scale instabilities of mid-latitude jets (with continuous horizontal and vertical shear) are studied using a long wave approximation, which is valid for disturbances of length scales greater than the internal Rossby radius of deformation. These large-scale instabilities are abundant in the Kuroshio Extension according to observations. Results show westward propagation if the total transport is westward (although the jet near surface is eastward). Large-scale instabilities gain energy from the release of available potential energy, but lose part of the gain to the mean flow by reinforcing the eastward jet near surface. The Reynolds stress tends to be positive north of the jet and negative south of the jet through all depths, which is consistent with observations.     

Some effects of truncation on topographic instability

Abstract

The topographic stability of forced planetary waves in α β‐channel is investigated using a barotropic model. The equilibrium forced waves are the result of the interaction of a constant mean zonal wind over finite‐amplitude surface orography. Small‐amplitude perturbations of the equilibrium flows are considered that have a wavy part with the same zonal wavenumber as the forcing but an arbitrary meridional structure. The mean zonal part of the perturbations is also taken to be arbitrary. This configuration allows us to (1) isolate those instabilities that depend crucially on topography through form drag and (2) investigate non‐topographic effects on topographic instability that arise from the convergence of Reynolds stresses. A numerical stability analysis is then performed wherein the effects of truncation are emphasized.

This numerical approach casts doubts about the results obtained from some earlier studies involving various ad hoc assumptions. We find, in particular, that unstable long waves (i.e. waves with the zonal wavelength greater than the meridional wavelength) exist under superresonant conditions. This contradicts some previous results that suggest long waves are unstable only when the flow is subresonant. Further, our model reveals the existence of some interesting travelling instabilities. The latter are shown to depend on both form drag and Reynolds stresses in that these two mechanisms alternate in time in supplying the perturbation with the required energy to maintain the exponential growth.     

Steering of upper ocean currents and fronts by the topographically constrained abyssal circulation

A two-layer theory is used to investigate (1) the steering of upper ocean current pathways by topographically constrained abyssal currents that do not impinge on the bottom topography and (2) its application to upper ocean – topographic coupling via flow instabilities where topographically constrained eddy-driven deep mean flows in turn steer the mean pathways of upper ocean currents and associated fronts. In earlier studies the two-layer theory was applied to ocean models with low vertical resolution (2–6 layers). Here we investigate its relevance to complex ocean general circulation models (OGCMs) with high vertical resolution that are designed to simulate a wide range of ocean processes. The theory can be easily applied to models ranging from idealized to complex OGCMs, provided it is valid for the application. It can also be used in understanding some persistent features seen in observed ocean frontal pathways (over deep water) derived from satellite imagery and other data. To facilitate its application, a more thorough explanation of the theory is presented that emphasizes its range of validity. Three regions of the world ocean are used to investigate its application to eddy-resolving ocean models with high vertical resolution, including one where an assumption of the two-layer theory is violated. Results from the OGCMs with high vertical resolution are compared to those from models with low vertical resolution and to observations. In the Kuroshio region upper ocean – topographic coupling via flow instabilities and a modest seamount complex are used to explain the observed northward mean meander east of Japan where the Kuroshio separates from the coast. The Japan/East Sea (JES) is used to demonstrate the impact of upper ocean – topographic coupling in a relatively weak flow regime. East of South Island, New Zealand, the Southland Current is an observed western boundary current that flows in a direction counter to the demands of Sverdrup flow and counter to the direction simulated in nonlinear global flat bottom and reduced gravity models. A model with high vertical resolution (and topography extending through any number of layers) and a model with low vertical resolution (and vertically compressed but otherwise realistic topography confined to the lowest layer) both simulate a Southland Current in the observed direction with dynamics depending on the configuration of the regional seafloor. However, the dynamics of these simulations are very different because the Campbell Plateau and Chatham Rise east and southeast of New Zealand are rare features of the world ocean where the topography intrudes into the stratified water column over a relatively broad area but lies deeper than the nominal 200 m depth of the continental shelf break, violating a limitation of the two-layer theory. Observations confirm the results from the high vertical resolution model. Overall, the model simulations show increasingly widespread upper ocean – topographic coupling via flow instabilities as the horizontal resolution of the ocean models is increased, but fine resolution of mesoscale variability and the associated flow instabilities are required to obtain sufficient coupling. As a result, this type of coupling is critical in distinguishing between eddy-resolving and eddy-permitting ocean models in regions where it occurs.     

Risø 1978: Further investigations into the effects of local terrain irregularities on tower-measured wind profiles

Observations of flow over complex terrain taken at Risø during June–July 1978 and numerical studies confirm earlier findings that small variations in surface elevation have significant effects on mean wind profiles. Measured shear stresses in the nonequilibrium region of the flow are consistent with theory but quite different from those obtained assuming simple flux-profile relationships. These findings imply that flux-profile relationships can be quite complicated over other than simple homogeneous terrain.     

Steering of upper ocean currents and fronts by the topographically constrained abyssal circulation

A two-layer theory is used to investigate (1) the steering of upper ocean current pathways by topographically constrained abyssal currents that do not impinge on the bottom topography and (2) its application to upper ocean – topographic coupling via flow instabilities where topographically constrained eddy-driven deep mean flows in turn steer the mean pathways of upper ocean currents and associated fronts. In earlier studies the two-layer theory was applied to ocean models with low vertical resolution (2–6 layers). Here we investigate its relevance to complex ocean general circulation models (OGCMs) with high vertical resolution that are designed to simulate a wide range of ocean processes. The theory can be easily applied to models ranging from idealized to complex OGCMs, provided it is valid for the application. It can also be used in understanding some persistent features seen in observed ocean frontal pathways (over deep water) derived from satellite imagery and other data. To facilitate its application, a more thorough explanation of the theory is presented that emphasizes its range of validity. Three regions of the world ocean are used to investigate its application to eddy-resolving ocean models with high vertical resolution, including one where an assumption of the two-layer theory is violated. Results from the OGCMs with high vertical resolution are compared to those from models with low vertical resolution and to observations. In the Kuroshio region upper ocean – topographic coupling via flow instabilities and a modest seamount complex are used to explain the observed northward mean meander east of Japan where the Kuroshio separates from the coast. The Japan/East Sea (JES) is used to demonstrate the impact of upper ocean – topographic coupling in a relatively weak flow regime. East of South Island, New Zealand, the Southland Current is an observed western boundary current that flows in a direction counter to the demands of Sverdrup flow and counter to the direction simulated in nonlinear global flat bottom and reduced gravity models. A model with high vertical resolution (and topography extending through any number of layers) and a model with low vertical resolution (and vertically compressed but otherwise realistic topography confined to the lowest layer) both simulate a Southland Current in the observed direction with dynamics depending on the configuration of the regional seafloor. However, the dynamics of these simulations are very different because the Campbell Plateau and Chatham Rise east and southeast of New Zealand are rare features of the world ocean where the topography intrudes into the stratified water column over a relatively broad area but lies deeper than the nominal 200 m depth of the continental shelf break, violating a limitation of the two-layer theory. Observations confirm the results from the high vertical resolution model. Overall, the model simulations show increasingly widespread upper ocean – topographic coupling via flow instabilities as the horizontal resolution of the ocean models is increased, but fine resolution of mesoscale variability and the associated flow instabilities are required to obtain sufficient coupling. As a result, this type of coupling is critical in distinguishing between eddy-resolving and eddy-permitting ocean models in regions where it occurs.     

Comparison Between Large-Eddy Simulation and Reynolds-Averaged Navier–Stokes Computations for the MUST Field Experiment. Part I: Study of the Flow for an Incident Wind Directed Perpendicularly to the Front Array of Containers

The large-eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methodologies are used to simulate the air flow inside the container’s array geometry of the Mock Urban Setting Test (MUST) field experiment. Both tools are assessed and compared in a configuration for which the incident wind direction is perpendicular to the front array. The assessment is carried out against available wind-tunnel data. Effects of including small geometrical irregularities present in the experiments are analysed by considering LES and RANS calculations on two geometries: an idealized one with a perfect alignment and an identical shape of the containers, and a second one including the small irregularities considered in the experiment. These effects are assessed in terms of the local time-mean average and as well in terms of spatial average properties (relevant in atmospheric modelling) given for the velocity and turbulent fields. The structural flow properties obtained using LES and RANS are also compared. The inclusion of geometrical irregularities is found significant on the local time-mean flow properties, in particular the repeated flow patterns encountered in a perfect regular geometry is broken. LES and RANS provide close results for the local mean streamwise velocity profiles and shear-stress profiles, however the LES predictions are closer to the experimental values for the local vertical mean velocity. When considering the spatial average flow properties, the effects of geometrical irregularities are found insignificant and LES and RANS provide similar results.     

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.) Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer / Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. The diffusion and convection of turbulence kinetic energy not accounted for in the Prandtl mixing-length concept cause departures of the mean wind profiles from those previously computed, primarily in the regions of strong pressure gradients. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.     

Local advection of momentum,heat, and moisture in micrometeorology

The local advection of momentum, heat and moisture in micrometeorology due to a horizontal inhomogeneity in surface conditions is numerically investigated by a higher-order turbulence closure model which includes equations for the mean quantities, turbulent fluxes, and the viscous dissipation rate. The application of the two-dimensional model in this paper deals with the simulation of the flow from an extensive smooth dry area to a grassy wet terrain. The mean wind speed, temperature, and humidity distributions in the resulting internal boundary layer downstream of the surface discontinuity are determined such that the energy and moisture balances at the Earth's surface are satisfied.Numerical calculations of the mean temperature and humidity profiles are compared with available observed ones. The results include the advective effects on turbulent flux distributions, surface energy balance, evaporation rate, and Bowen ratio. The sensitivity of the predicted mean profiles and turbulent flux distributions to the surface relative humidity, thermal stratification, and the roughness change is discussed.NRC-NAS Resident Research Associate at AFCRL.     

Mean Flow and Turbulence Characteristics in an Urban Roughness Sublayer

In this study, a detailed model of an urban landscape has been re-constructed inthe wind tunnel and the flow structure inside and above the urban canopy has beeninvestigated. Vertical profiles of all three velocity components have been measuredwith a Laser-Doppler velocimeter, and an extensive analysis of the measured meanflow and turbulence profiles carried out. With respect to the flow structure inside thecanopy, two types of velocity profiles can be distinguished. Within street canyons,the mean wind velocities are almost zero or negative below roof level, while closeto intersections or open squares, significantly higher mean velocities are observed.In the latter case, the turbulent velocities inside the canopy also tend to be higherthan at street-canyon locations. For both types, turbulence kinetic energy and shearstress profiles show pronounced maxima in the flow region immediately above rooflevel.Based on the experimental data, a shear-stress parameterization is proposed, inwhich the velocity scale, u_s, and length scale, z_s, are based on the level and magnitude of the shear stress peak value. In order to account for a flow region inside the canopy with negligible momentum transport, a shear stress displacement height, d_s, is introduced. The proposed scaling and parameterization perform well for the measured profiles and shear-stress data published in the literature.The length scales derived from the shear-stress parameterization also allowdetermination of appropriate scales for the mean wind profile. The roughnesslength, z₀, and displacement height, d₀, can both be described as fractions of the distance, z_s - d_s, between the level of the shear-stress peak and the shear-stress displacement height. This result can be interpreted in such a way that the flow only feels the zone of depth z_s - d_s as the roughness layer. With respect to the lower part of the canopy (z < d_s) the flow behaves as a skimming flow. Correlations between the length scales z_s and d_s and morphometric parameters are discussed.The mean wind profiles above the urban structure follow a logarithmic windlaw. A combination of morphometric estimation methods for d₀ and z₀ with wind velocity measurements at a reference height, which allow calculation of the shear-stress velocity, u_*, appears to be the most reliable and easiest procedure to determine mean wind profile parameters. Inside the roughnesssublayer, a local scaling approach results in good agreement between measuredand predicted mean wind profiles.     

A nonstationary nocturnal drainage flow model

The evolution and structure of the steady state of an idealized nocturnal drainage flow over a large uniformly-sloping surface are studied using a nonstationary model with a height-dependent eddy diffusivity profile and a specified surface cooling rate. The predicted mean velocity and temperature profiles are compared with Prandtl's stationary analytical solutions based on the assumption of a constant eddy diffusivity in the drainage layer. The effects of important physical parameters, such as the slope angle, surface cooling, atmospheric stability, and surface roughness, on the steady drainage flow are investigated.Affiliated with Oak Ridge Associated Universities (ORAU).     

Turbulent mechanisms in stratified fluids

Probability distribution of basic instabilities appearing in stratified flows and point density fluctuations have been studied. Various parameters of the mixing process have been changed in the experiments, to investigate mixing. Detailed flow visualization as well as density measurements have been used in zero-mean-flow laboratory experiments involving grid-stirred turbulent mixing across a density interface and bubble-induced mixing. The overall mixing efficiency of the processes depends on the local Richardson number as well as on the local vorticity. Parameter distributions of low and high mixedness corresponding to different instabilities are presented, showing that dipolar vortices penetrating the interface are the most efficient mixing instabilities.     

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.     

EFFECT OF THE LINEAR BETA TERM ON MOVEMENT AND DEVELOPMENT OF TROPICAL CYCLONE

The dynamics of tropical cyclone is investigated in a nondivergent,barotropic model with nobasic flow.The effect of linear beta term on the movement and development of tropical cyclone isemphatically demonstrated.The streamfunction tendency due to the symmetric component of linearbeta term appears in a dipole-like pattern with an east-west symmetry,which maintains andintensifies the large-scale beta gyres and causes the tropical cyclone to have a westerly movingcomponent.The streamfunction tendency due to the asymmetric component of linear beta termarises in an ellipse pattern with a north-south major axis,which weakens the tropical cyclone.Thestreamfunction tendency due to the asymmetric component of linear beta term and the intensity oflarge-scale cyclonic beta gyre synchronously vary in a fluctuating manner with time.     

The turbulent wind flow over an embankment

Under neutral conditions and with low winds, profiles of mean and turbulent wind components have been measured at various points across an embankment with aspect ratio 0.3. These measurements have been compared with and related to those of undisturbed flow in a horizontal homogeneous area on the windward side. The speed-up ratio, the turbulent and mean kinetic energy and the turbulent shear stress are examined. It is found that the flow stagnates on the windward side, accelerates above the crest, and separates behind the crest. The results show a remarkable dependence on the angle of attack. With an angle smaller than 90 °, the influence of the embankment on the mean wind field is reduced but is increased on the turbulent part, as lateral gustiness components are amplified. With the incoming flow normal to the embankment, maximum turbulence is found on the top of the ridge near the surface but at greater heights farther downwind. The same is true for the shear stress, but only for oblique flow, whereas for normal flow a minimum is found above the crest and a maximum on the windward side. Therefore, with varying angle of attack the embankment acts in different ways on mean wind, turbulent kinetic energy, and turbulent stress. Although the winds were low, all effects are clearly evident in the data.