The wind in the willows: flows in forest canopies in complex terrain

Forest canopies are important components of the terrestrial carbon budget, which has motivated a worldwide effort, FLUXNET, to measure CO2 exchange between forests and the atmosphere. These measurements are difficult to interpret and to scale up to estimate exchange across a landscape. Here we review the effects of complex terrain on the mean flow, turbulence, and scalar exchange in canopy flows, as exemplified by adjustment to forest edges and hills, including the effects of stable stratification. We focus on the fundamental fluid mechanics, in which developments in theory, measurements, and modeling, particularly through large-eddy simulation, are identifying important processes and providing scaling arguments. These developments set the stage for the development of predictive models that can be used in combination with measurements to estimate exchange at the landscape scale.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

Wind observations above an urban river using a new lidar technique, scintillometry and anemometry

Flow along rivers, an integral part of many cities, might provide a key mechanism for ventilation – which is important for air quality and heat stress. Since the flow varies in space and time around rivers, there is limited utility in point measurements. Ground-based remote sensing offers the opportunity to study 3D flow in locations which are hard to observe. For three months in the winter and spring of 2011, the atmospheric flow above the River Thames in central London was observed using a scanning Doppler lidar, a dual-beam scintillometer and sonic anemometry. First, an inter-comparison showed that lidar-derived mean wind-speed estimates compare almost as well to sonic anemometers (root-mean-square error (rmse) 0.65–0.68 m s–1) as comparisons between sonic anemometers (0.35–0.73 m s–1). Second, the lidar duo-beam scanning strategy provided horizontal transects of wind vectors comparison with scintillometer rmse 1.12–1.63 m s–1) which revealed mean and turbulent flow across the river and surrounds; in particular: chanelling flow along the river and turbulence changes consistent with the roughness changes between built to river environments. The results have important consequences for air quality and dispersion around urban rivers, especially given that many cities have high traffic rates on bankside roads.

Passive urban ventilation by combined buoyancy-driven slope flow and wall flow: Parametric CFD studies on idealized city models

This paper reports the results of a parametric CFD study on idealized city models to investigate the potential of slope flow in ventilating a city located in a mountainous region when the background synoptic wind is absent. Examples of such a city include Tokyo in Japan, Los Angeles and Phoenix in the US, and Hong Kong. Two types of buoyancy-driven flow are considered, i.e., slope flow from the mountain slope (katabatic wind at night and anabatic wind in the daytime), and wall flow due to heated/cooled urban surfaces. The combined buoyancy-driven flow system can serve the purpose of dispersing the accumulated urban air pollutants when the background wind is weak or absent. The microscopic picture of ventilation performance within the urban structures was evaluated in terms of air change rate (ACH) and age of air. The simulation results reveal that the slope flow plays an important role in ventilating the urban area, especially in calm conditions. Katabatic flow at night is conducive to mitigating the nocturnal urban heat island. In the present parametric study, the mountain slope angle and mountain height are assumed to be constant, and the changing variables are heating/cooling intensity and building height. For a typical mountain of 500 m inclined at an angle of 20° to the horizontal level, the interactive structure is very much dependent on the ratio of heating/cooling intensity as well as building height. When the building is lower than 60 m, the slope wind dominates. When the building is as high as 100 m, the contribution from the urban wall flow cannot be ignored. It is found that katabatic wind can be very beneficial to the thermal environment as well as air quality at the pedestrian level. The air change rate for the pedestrian volume can be as high as 300 ACH.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.

Internal wave drag in stratified flow over mountains on a beta plane

The impact of the variation of the Coriolis parameter f on the drag exerted by internal Rossby-gravity waves on elliptical mountains is evaluated using linear theory, assuming constant wind and static stability and a beta-plane approximation. Previous calculations of inertia-gravity wave drag are thus extended in an attempt to establish a connection with existing studies on planetary wave drag, developed primarily for fluids topped by a rigid lid. It is found that the internal wave drag for zonal westerly flow strongly increases relative to that given by the calculation where f is assumed to be a constant, particularly at high latitudes and for mountains aligned meridionally. Drag increases with mountain width for sufficiently wide mountains, reaching values much larger than those valid in the non-rotating limit. This occurs because the drag receives contributions from a low wavenumber range, controlled by the beta effect, which accounts for the drag amplification found here. This drag amplification is shown to be considerable for idealized analogues of real mountain ranges, such as the Himalayas and the Rocky mountains, and comparable to the barotropic Rossby wave drag addressed in previous studies.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

The effect of wind shear and curvature on the gravity wave drag produced by a ridge

The analytical model proposed by Teixeira, Miranda, and Valente is modified to calculate the gravity wave drag exerted by a stratified flow over a 2D mountain ridge. The drag is found to be more strongly affected by the vertical variation of the background velocity than for an axisymmetric mountain. In the hydrostatic approximation, the corrections to the drag due to this effect do not depend on the detailed shape of the ridge as long as this is exactly 2D. Besides the drag, all the perturbed quantities of the flow at the surface, including the pressure, may be calculated analytically.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.

Surrounding buildings and wind pressure distribution on a high-rise building

The effect of the surrounding lower buildings on the wind pressure distribution on a high-rise building is investigated by computational fluid dynamics (CFD). When B/H=0.1, it is found that the wind pressure on the windward side was reduced especially on the lower part, but for different layers of surrounding buildings, there was no great difference, which agrees with our previous wind tunnel experiment data. Then we changed the aspect ratio from 0.1 to 2, to represent different airflow regimes: skimming flow (SF), and wake interference (WI). It shows that the average Cp increases when B/H increases. For different air flow regimes, it is found that insignificant difference exists when the number of the building layers is more than 2. From the engineering point of view, it is sufficient to only include the first layer for natural ventilation design by using CFD simulation or wind tunnel experiment.

Influence of the Antarctic ozone hole on the polar mesopause region as simulated by the Canadian Middle Atmosphere Model

It is well established that variations in polar stratospheric winds can affect mesospheric temperatures through changes in the filtering of gravity wave fluxes, which drive a residual circulation in the mesosphere. The Canadian Middle Atmosphere Model(CMAM) is used to examine this vertical coupling mechanism in the context of the mesospheric response to the Antarctic ozone hole. It is found that the response differs significantly between late spring and early summer, because of a changing balance between the competing effects of parametrised gravity wavedrag (GWD)and changes in resolved wave drag local to the mesosphere. In late spring, the strengthened stratospheric westerlies arising from the ozone hole lead to reduced eastward GWD in the mesosphere and a warming of the polar mesosphere, just as in the well known mesospheric response to sudden stratospheric warmings, but with an opposite sign.In early summer, with easterly flow revailing over most of the polar stratosphere,the strengthened easterly wind shear within the mesosphere arising from the west ward GWD anomaly induces a positive resolved wave drag anomaly through baroclinic instability. The polar cooling induced by this process completely dominates the upper mesospheric response to the ozone hole in early summer. Consequences for the past and future evolution of noctilucent clouds are discussed

Wind gust estimation for Mid-European winter storms: towards a probabilistic view

Three wind gust estimation (WGE) methods implemented in the numerical weather prediction (NWP) model COSMO-CLM are evaluated with respect to their forecast quality using skill scores. Two methods estimate gusts locally from mean wind speed and the turbulence state of the atmosphere, while the third one considers the mixing-down of high momentum within the planetary boundary layer (WGE Brasseur). One hundred and fifty-eight windstorms from the last four decades are simulated and results are compared with gust observations at 37 stations in Germany. Skill scores reveal that the local WGE methods show an overall better behaviour, whilst WGE Brasseur performs less well except for mountain regions. The here introduced WGE turbulent kinetic energy (TKE) permits a probabilistic interpretation using statistical characteristics of gusts at observational sites for an assessment of uncertainty. The WGE TKE formulation has the advantage of a ‘native’ interpretation of wind gusts as result of local appearance of TKE. The inclusion of a probabilistic WGE TKE approach in NWP models has, thus, several advantages over other methods, as it has the potential for an estimation of uncertainties of gusts at observational sites.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted