Flow visualization experiments on stably stratified flow over ridges and valleys

Summary Flow visualization experiments on stably stratified flow over ridges and valleys formed by a pair of ridges were conducted in a large towing tank filled with stratified salt water. The ambient flow was normal to the axis of the ridges. Three experimental parameters were varied during the study: the steepness of the ridges, the separation distance between the ridges and the Froude number. The flow field in the valley was strongly influenced by flow separation from the lee side of the upstream ridge. For the gentle and intermediate ridges with maximum slopes of 13° and 27°, this separation was controlled by the lee waves when their wavelength was less than or equal to the width of the ridge. The flow field in the valley was similar to that downstream of a single ridge. For the steep ridge with a maximum slope of 40°, separation from the lee side of the upstream ridge and the flow field in the valley were influenced significantly by the presence of the downstream ridge.With 13 FiguresOn assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.     

Acceleration effects for linearly-stratified flow over long ridges

Summary The time-dependent motion of long ridges through a linearly stratified fluid otherwise at rest is investigated in a series of laboratory experiments. Similarity conditions for relating such flows to the atmosphere are deduced from the equations of motion and boundary conditions for the respective systems.Experiments concerning end-wall effects in towing experiments with linearly stratified fluid systems are conducted. For obstacles extending across the entire width of the tow tank it is shown that the upstream conditions are continually changing so that a final steady state motion may never be realized. Isolated topographies are shown to induce significantly less effect on the far upstream fluid motions. Case studies for the flow past long ridges for which the motion at large times is to be that of single, double and triple mode lee-waves and breaking lee vortices are conducted for impulsively started and uniformly accelerated and decelerated obstacle transverses. The final flow configuration under certain situations is shown to be relatively insensitive to the starting conditions. In other cases the final flow can be highly dependent on the time history of the ridge traverse through the tank. For example, for the case in which a breaking lee vortex is expected as the final flow, small initial uniform accelerations from a zero velocity lead to the formation of a strong rotor along the free surface of the tank and in the lee of the obstacle. This rotor is maintained in an approximate equilibrium position as the ridge speed reaches a value for which a breaking lee vortex (having no rotor) should be expected; i.e., the type of flow obtained for impulsively started or rapidly accelerating ridges, other parameters being fixed.The phenomenon of the oscillation of the structure of the wake flow between a relatively smooth laminar lee-wave pattern and lee waves that break into turbulence is investigated for impulsively started ridges. By defining the parameterN _w as the number of waves downstream of the first trough that are clearly identifiable it is shown that the tendency for wake breakdown into turbulence increases with increasing internal Froude number, other parameters being fixed. No definitive period was found relating the alternating nature of the wake between breakdown, into turbulence, relaminarization and so on.With 20 Figures     

Stratified flow over three-dimensional topography

In order to investigate flows over topography in an atmospheric context, we have studied experimentally the wake structure of axi-symmetric Gaussian obstacles towed through a linearly stratified fluid. Three dimensionless parameters govern the flow dynamics: F, the Froude number based on the topography height h; Re, the Reynolds number and the aspect ratio r = h/L, where L is the topography horizontal scale. Two-dimensional (2-D), saturated lee wave (SLW) and three-dimensional (3-D) regimes, as defined in Chomaz et al. (1993), are found to be functions of F and r only (Fig. 1) as soon as Re is larger than Re_c ≈ 2000. For F < 0.7 the flow goes around the obstacle and the motion in the wake is quasi-two-dimensional. This 2-D layer is topped by a region affected by lee wave motions with amplitude increasing with r and F. For 0.7 < F < 1/r, the flow is entirely dominated by a lee wave of saturated amplitude which suppresses the separation of the boundary layer from the obstacle. Above the critical value 1/r, the lee wave amplitude decreases with F and a recirculating zone appears behind the obstacle. Simultaneously, coherent large-scale vortices start to be shed periodically from the wake at a Strouhal number which decreases as 1/F until it reaches its neutral asymptotic value.     

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.     

Airflow patterns over and around a large three-dimensional hill

Summary Surface wind patterns and air flows within the planetary boundary layer over a large three-dimensional hill of moderate slope are grouped according to Froude number classes. An evolution of flow patterns is shown to occur as the Froude number increases.Separation of the surface flow begins at the base of the lee side of the mountain near the centerline, moving upward on the lee slope as the Froude number increases. Recirculating eddies follow the separation of the lee flow. Eventually the separation line moves forward to the windward side as the Froude number becomes very large. The recirculating eddy becomes unsteady, with indication of an intermittent counterrolating eddy near the lee surface in neutral flow. The lee-side turbulence is enhanced with respect to the windward side due to the large eddies in high Froude number regimes.The concept of a critical height for the approach flow is generally supported. The integral form of the Froude number does not appear to be superior to a bulk Froude calculation in representing a particular airflow pattern.With 6 FiguresDeceased.     

大地形背风波的转槽实验研究

文中利用转槽在相似定律及动力无量纲数的控制下,对旋转层结流越过大地形产生的背风波做了一系列的实验.实验及分析结果表明,无量纲数中Froude数是最重要的参数,发现在层结适当时背风波同旋涡结构在山的下风方同时出现.在无旋转情况下,在Froude数适当时仍然存在着明显的背风波,但旋转的作用能增加背风波的波动幅度,特别是起着引发下坡流的作用.文中最后还讨论了背风波在季风区内对低层涡旋发展的驱动作用及有待进一步研究的问题.     

On atmospheric vortex streets in the wake of large islands

Summary Results from laboratory experiments on stably stratified flows over three-dimensional obstacles are related to atmospheric vortex streets formed in the lee of large islands. A quasi horizontal flow around the island can be expected if stable stratification favours the formation of a so-called dividing streamline below the islands top. The subsequent shedding of vortices with vertical axis from islands may then be due to viscous boundary layer separation, but also other possible mechanisms of vortex shedding in stably stratified flows are discussed.With 6 Figures     

Prediction Errors Associated with Sparse Grid Estimates of Flows over Hills

Numerical simulations of geophysical flows have to be done on very sparse grids. Nevertheless, flows over moderately sloped hills can be predicted quite accurately as long as the near ground vertical resolution is reasonably dense. Recirculation flows behind steeper hills are associated with slow convergence towards grid independent integrations, but even then moderately stratified flows of this type can be predicted usefully accurately. For better horizontal grids than about half the hill-height Δx ₁/H ≈ 0.5 or so, separation and recirculating domains are predicted with an error factor comparable to 0.3. The characteristic wavelength of lee waves is predicted more accurately while the lee wave amplitude and the maximum turbulence intensity in recirculating domains are underestimated by factors comparable to 0.3. Strongly stratified flows may be associated with hydraulic transitions and even this is predicted on quite coarse grids, up to say Δx ₁/H ≈ 0.5. However, the details of such flows turn out to be predicted with considerable errors also on high-resolution grids. Inaccurate modelling of stratified turbulence is a main contributor to this error.     

Numerical modeling studies of lee mesolows,mesovortices and mesocyclones with application to the formation of Taiwan mesolows

Summary Numerical experiments are performed for inviscid flow past an idealized topography to investigate the formation and development of lee mesolows, mesovortices and mesocyclones. For a nonrotating, low-Froude number flow over a bell-shaped moutain, a pair of mesovortices form on the lee slope move downstream and weaken at later times. The advection speed of the lee vortices is found to be about two-thirds of the basic wind velocity, which is due to the existence of a reversed pressure gradient just upstream of the vortices. The lee vortices do not concur with the upstream stagnation point in time, but rather form at a later time. It is found that a pair of lee vortices form for a flow withFr=0.66, but take a longer time to form than in lower-Froude number flows. Since the lee vortices are formed rather progressively, their formation may be explained by the baroclinically-induced vorticity tilting as the mountain waves become more and more nonlinear.A stationary mesohigh and mesolow pressure couplet forms across the mountain and is produced in both high and low-Froude number flows. The results of the high Froude number simulations agree well with the classical results predicted by linear, hydrostatic mountain wave theory. It is found that the lee mesolow is not necessarily colocated with the lee vortices. The mesolow is formed by the downslope wind associated with the orographically forced gravity waves through adiabatic warming. The earth's rotation acts to strengthen (weaken) the cyclonic (anticyclonic) vortex and shifts the lee mesolow to the right for an observer facing downstream. The cyclonic vortex then develops into a mesocyclone with the addition of planetary vorticity at later times. For a flow over a steeper mountain, the disturbance is stronger even though the Froude number is kept the same.For a southwesterly flow past the real topography of Taiwan, there is no stagnation point or lee vortices formed because the impinging angle of the flow is small. A major mesoscale low forms to the southeast of the Central Mountain Range (CMR), while a mesohigh forms upstream. For a westerly flow past Taiwan, a stagnation point forms upstream of the mountain and a pair of vortices form on the lee and move downstream at later times. The cyclonic vortex then develops into a mesocyclone. A mesolow also forms to the southeast of Taiwan. For a northeasterly flow past Taiwan, the mesolow forms to the northwest of the mountain. Similar to flows over idealized topographies, the Taiwan mesolow is formed by the downslope wind associated with mountain waves through adiabatic warming. A conceptual model of the Taiwan southeast mesolow and mesocyclone is proposed.With 16 Figures     

Early-Morning Flow Transition in a Valley in Low-Mountain Terrain Under Clear-Sky Conditions

We investigate the evolution of the early-morning boundary layer in a low-mountain valley in south-western Germany during COPS (convective and orographically induced precipitation study) in summer 2007. The term low-mountain refers to a mountainous region with a relief of gentle slopes and with an absolute altitude that remains under a specified height (usually 1,500 m a.s.l.). A subset of 23 fair weather days from the campaign was selected to study the transition of the boundary-layer flow in the early morning. The typical valley atmosphere in the morning hours was characterized by a stable temperature stratification and a pronounced valley wind system. During the reversal period—called the low wind period—of the valley wind system (duration of 1–2 h), the horizontal flow was very weak and the conditions for free convection were fulfilled close to the ground. Ground-based sodar observations of the vertical wind show enhanced values of upward motion, and the corresponding statistical properties differ from those observed under windless convective conditions over flat terrain. Large-eddy simulations of the boundary-layer transition in the valley were conducted, and statistical properties of the simulated flow agree with the observed quantities. Spatially coherent turbulence structures are present in the temporal as well as in the ensemble mean analysis. Thus, the complex orography induces coherent convective structures at predictable, specific locations during the early-morning low wind situations. These coherent updrafts, found in both the sodar observations and the simulation, lead to a flux counter to the gradient of the stably stratified valley atmosphere and reach up to the heights of the surrounding ridges. Furthermore, the energy balance in the surface layer during the low wind periods is closed. However, it becomes unclosed after the onset of the valley wind. The partition into the sensible and the latent heat fluxes indicates that missing flux components of sensible heat are the main reason for the unclosed energy balance in the considered situations. This result supports previously published investigations on the energy balance closure.     

Topographic and stratification effects on shelf edge flows

Results are presented from two sets of laboratory model experiments on the effects of an isolated seamount upon the flow of an intermediate-water slope current along a continental shelf. The experimental results for initial ambient conditions of respectively two-layer and linearly stratified fluids show that the structure of such a boundary current depends primarily on the values of the appropriate set of dimensionless dynamical parameters (namely the Burger (Bu), Ekman (Ek) and Rossby (Ro) numbers), as well as the dimensionless lateral separation of the seamount and shelf and the proportional height of the seamount relative to the distance from the bottom at which the intermediate-water flows. Comparisons of the present results with those from a previous two-layer fluid study with no obstacle present reveals that the presence of the obstacle does not alter significantly the stability of the current even when situated close to the shelf. However, for such configurations, the density, velocity and vorticity fields in the local zone of interaction between the current and the obstacle are distorted significantly by the presence of the obstacle, provided that the summit of the obstacle penetrates the level of current flow. Measurements of density, velocity and vorticity fields show no significant dependence of the flow interaction upon the detailed bathymetry of the shelf-slope. For stable intermediate-water slope currents, the nature of the interaction with the obstacle is determined primarily by (i) the lateral separation of the obstacle and the shelf edge and (ii) the Ro of the flow. For sufficiently low values of the former and high values of the latter, the interaction results in a splitting of the incident flow around the obstacle, with cyclonic and anticyclonic eddy pairs being generated in the lee. Geostrophic equilibrium is seen to be maintained in the current, even in the near wake of the obstacle. For cases in which the summit of the seamount is below the initially-undisturbed intermediate water level, no Taylor column-like division of the slope current occurs and no significant distortion of the current structure (velocity and density) occurs for the parameter ranges investigated. For linearly stratified cases, measurements show that no significant local elevation or depression of the density interfaces is observed in the interaction zone. The distributions of the local buoyancy frequencies calculated from the density profiles reveal that the minimum value of the frequency upstream of the obstacle is smaller than that downstream, indicating that the flow interactions generate local mixing downstream, with consequent erosion of the density interfaces.     

A nonhydrostatic model for simulation of airflow over mesoscale bell-shaped ridges

This paper describes a nonhydrostatic and incompressible mesoscale model formulation using a terrain-following coordinate system. A tensor transformation procedure is used to derive a diagnostic equation for the nonhydrostatic pressure field. The model features a simplified second-order turbulence closure scheme. The two-dimensional version of the nonhydrostatic model, as well as the corresponding hydrostatic model, are applied to simulate stably stratified airflow over mesoscale bell-shaped mountain ridges. The results show that the nonhydrostatic model is capable of simulating nonhydrostatic dynamics of mesoscale lee wave systems such as the trapped wave phenomenon.     

条件不稳定湿大气中三维理想地形上空对流的动力学特征

条件不稳定湿大气情况下,气流经过三维地形可以形成不同性质的对流系统以及不同特征的地形流结构,其对流系统、地形流的性质主要取决于地形上空的对流触发、对流-地形流-重力波三者之间的相互作用,同样这些过程对于地形降水的性质、分布起重要的作用.根据不同湿Fr数(Froude number),湿条件不稳定大气经过三维小尺度山地上空时其对流和地形流动存在4种不同的流域(flow regirnes):(1)下游传播对流模态;(2)上游传播和下游传播共存对流模态;(3)山峰附近准静止和下游传播共存对流模态;(4)下坡稳定和下游传播对流共存模态.地形上空对流系统主要可以通过两种不同机制形成:(1)地形直接的抬升或减速作用;(2)在地形流形成后,由于地形流本身特性(如上游分离、背风涡旋和下坡重力波破碎)触发.在较大的Fr数情况下,地形上空对流生成后反过来可以破坏上、下游的地形流结构,但对背风坡的重力波破碎影响较小.不同初始对流有效位能(CAPE)不仅可以影响对流系统的传播、发展,而且可以影响整体地形流性质.较低的初始CAPE有利于地形流的形成,此时对流对地形流结构特征的影响相对较小,其流场性质与低Fr数流域性质相似.     

Influence of the Amur River runoff on the hydrological conditions of the Amur Liman and Sakhalin Bay (Sea of Okhotsk) during the spring-summer flood

Hydrographic and satellite observation data obtained in June 2007 enabled to study the influence of the Amur River runoff on the hydrological conditions of the Amur Liman and the Sea of Okhotsk during the spring-summer flood. Salt waters from the Sea of Japan and fresh Amur River waters mix in the estuary (the Amur Liman). Freshened waters flow from the estuary into the Sea of Okhotsk as a jet-like flow drift, which forms a recirculating anticyclonic gyre in the Sakhalin Bay. The coastal current associated with the Amur River flow was obserwed near Sakhalin Island coast. The computed values of dynamic parameters (Kelvin number K=2, Froude number F = 0.4) showed that the Earth rotation and stratification are important factors in the dynamical balance of the Amur River plume during the spring-summer flood event.     

Directional Shear in the Nocturnal Atmospheric Surface Layer

Stratified nocturnal flow above and within a small valley of approximately 12-m depth and a few hundred metres width is examined as a case study, based on a network of 20 sonic anemometers and a central 20-m tower with eight levels of sonic anemometers. Several regimes of stratified flow over gentle topography are conceptually defined for organizing the data analysis and comparing with the existing literature. In our case study, a marginal cold pool forms within the shallow valley in the early evening but yields to larger ambient wind speeds after a few hours, corresponding to stratified terrain-following flow where the flow outside the valley descends to the valley floor. The terrain-following flow lasts about 10 h and then undergoes transition to an intermittent marginal cold pool towards the end of the night when the larger-scale flow collapses. During this 10-h period, the stratified terrain-following flow is characterized by a three-layer structure, consisting of a thin surface boundary layer of a few metres depth on the valley floor, a deeper boundary layer corresponding to the larger-scale flow, and an intermediate transition layer with significant wind-directional shear and possible advection of lee turbulence that is generated even for the gentle topography of our study. The flow in the valley is often modulated by oscillations with a typical period of 10 min. Cold events with smaller turbulent intensity and duration of tens of minutes move through the observational domain throughout the terrain-following period. One of these events is examined in detail.     

Upstream stagnation points in stratified flow past obstacles

An experimental study has been made of stagnation points and flow splitting on the upstream side of obstacles in uniformly stratified flow. A range from small to large values of Nh/U (where N is the buoyancy frequency, h_m is the maximum obstacle height and U is the undisturbed fluid velocity) has been covered, for three obstacle shapes which are, respectively, axisymmetric, and elongated in the across-stream and in the downstream directions. Upstream stagnation for the first two of these models does not occur until Nh_m/U > 1.05, where it occurs at z ≈ h_m/2. On the central line below this point the flow descends and diverges, and we term this ‘flow splitting’. For the third model (elongated in the downstream direction), stagnation upstream first occurs at Nh_m/U ≈ 1.43, at z ≈ 0. Results for this obstacle are not consistent with the ‘Sheppard criterion’, and this upstream flow stagnation is not apparently related to lee wave overturning, in contrast to flow over two-dimensional obstacles.     

Regional effects of large-scale extreme wind events over orographically structured terrain

Summary ?Above orographically structured terrain considerable differences of the regional wind field may be identified during large-scale extreme wind events. So far, these regional differences could not be resolved by climate models. To determine the relationships between large-scale atmospheric conditions, the influence of orography, and the regional wind field, data measured in the upper Rhine valley within the framework of the REKLIP Regional Climate Project were analyzed and calculations were made using the KAMM mesoscale model. In the area of the upper Rhine valley, ratios of the wind velocity in the Rhine valley at 10 m above ground level, ν_val, and the large-scale flow velocity, ν_lar, are between ν_val/ν_lar ≈ 0.1 and ν_val/ν_lar ≈ 1. The ν_val/ν_lar ratio exhibits a strong dependence on thermal stratification, δ, and decreases from ν_val/ν_lar ≈ 1 at δ = 0 K m⁻¹ to ν_val/ν_lar ≈ 0.2 at δ = 0.0075 K m⁻¹. In areas, where the lateral mountainous border of the Rhine valley is interrupted, the ν_val/ν_lar ratio increases again with increasing stability or decreasing Froude number. This is obviously due to flow around the Black Forest under stable stratification. It is demonstrated by model calculations that a complex wind field develops in the Rhine valley at small Froude numbers (Fr < 1) irrespective of the direction of large-scale flow. The ν_val/ν_lar ratio is characterized by small values in the direct lee side (ν_val/ν_lar ≈ 0.2) and high values on the windward side of the lateral mountainous border of the Rhine valley (ν_val/ν_lar ≈ 0.8). Received October 22, 2001; revised June 18, 2002; accepted June 23, 2002     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

Observations of Boundary-Layer Wind-Tunnel Flow over Isolated Ridges of Varying Steepness and Roughness

Boundary-layer wind-tunnel flow is measured over isolated ridges of varyingsteepness and roughness. The steepness/roughness parameter space is chosento produce flows that range from fully attached to strongly separated. Measurementsshow that maximum speedup at the hill crest is significantly lower than predictedby linear theory and that recovery in the lee of the hill is much slower for stronglyseparated flow over steep terrain. The measurements also show that behaviour ofthe mean and turbulent components of the flow on the downwind side of the ridgeis fundamentally different between separated and non-separated flows. This suggeststhe dominance of much increased turbulence time and length scales in the lee of thehill in association with a production mechanism that scales with the hill length ratherthan the proximity to the surface as on the windward side of the hill crest.     

Numerical Simulation of Strongly Stratified Flow Over a Three-Dimensional Hill

A numerical study of stably stratified flow over a three-dimensional hill is presented. Large-eddy simulation is used here to examine in detail the laboratory experimental flows described in the landmark work of Hunt and Snyder about stratified flow over a hill. The flow is linearly stratified and U/Nh is varied from 0.2 to 1.0. Here N and U are the buoyancy frequency and freestream velocity respectively, and h is the height of the hill. The Reynolds number based on the hill height is varied from 365 to 2968. The characteristic flow patterns at various values of U/Nh have been obtained and they are in good agreement with earlier theoretical and experimental results. It is shown that the flow field cannot be predicted by Drazin's theory when recirculation exists at the leeside of the hill even at UNh 1. The wake structure agrees well with a two-dimensional wake assumption when U/Nh 1 but lee waves start to influence the wake structure as U/Nh increases. The dividing-streamline heights obtained in the simulation are in accordance with experimental results and Sheppard's formula. The energy loss along the dividing streamline due to friction/turbulence approximately offsets the energy gained from pressure field. When lee waves are present, linear theory always underestimates the amplitude and overestimates the wavelength of three-dimensional lee waves. The simulated variations of drag coefficients with the parameterK (=ND/ U) are qualitatively consistent with experimental data and linear theory. Here D is the depth of the tank.