Search Results - (Author, Cooperation:M. R. Raupach)

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Electronic Resource

2015-05-23

American Association for the Advancement of Science (AAAS)

0036-8075

1095-9203

Biology

Chemistry and Pharmacology

Computer Science

Medicine

Natural Sciences in General

Physics

Atmosphere/*chemistry ; *Carbon Cycle ; Carbon Dioxide/*analysis ; *Forests ; *Grassland

1089-7666

AIP Digital Archive

Physics

Large-scale temperature discontinuities are detected in a high Reynolds number boundary layer over a slightly heated rough wall. In the streamwise and normal plane of the measurements, the discontinuities form (as for smooth wall boundary layers) the boundaries between successive spanwise vortexlike structures, flattened against the wall. The regions immediately downstream from the discontinuities are particularly important for the transport of heated, low-momentum fluid away from the wall. The proportions contributed by the detected organized motion to the velocity and temperature variances are similar to those in smooth wall boundary layers. The proportions contributed to mean products, especially to the Reynolds shear stress, are significantly higher than over smooth walls at similar Reynolds numbers. The detected organized motion in the rough wall boundary layer resembles that in a smooth wall boundary layer of similar skin friction coefficient (and hence much lower Reynolds number).

Electronic Resource

1365-2486

Blackwell Publishing Journal Backfiles 1879-2005

Biology

Energy, Environment Protection, Nuclear Power Engineering

Geography

Systematic, operational, long-term observations of the terrestrial carbon cycle (including its interactions with water, energy and nutrient cycles and ecosystem dynamics) are important for the prediction and management of climate, water resources, food resources, biodiversity and desertification. To contribute to these goals, a terrestrial carbon observing system requires the synthesis of several kinds of observation into terrestrial biosphere models encompassing the coupled cycles of carbon, water, energy and nutrients. Relevant observations include atmospheric composition (concentrations of CO2 and other gases); remote sensing; flux and process measurements from intensive study sites; in situ vegetation and soil monitoring; weather, climate and hydrological data; and contemporary and historical data on land use, land use change and disturbance (grazing, harvest, clearing, fire).A review of model–data synthesis tools for terrestrial carbon observation identifies ‘nonsequential’ and ‘sequential’ approaches as major categories, differing according to whether data are treated all at once or sequentially. The structure underlying both approaches is reviewed, highlighting several basic commonalities in formalism and data requirements.An essential commonality is that for all model–data synthesis problems, both nonsequential and sequential, data uncertainties are as important as data values themselves and have a comparable role in determining the outcome.Given the importance of data uncertainties, there is an urgent need for soundly based uncertainty characterizations for the main kinds of data used in terrestrial carbon observation. The first requirement is a specification of the main properties of the error covariance matrix.As a step towards this goal, semi-quantitative estimates are made of the main properties of the error covariance matrix for four kinds of data essential for terrestrial carbon observation: remote sensing of land surface properties, atmospheric composition measurements, direct flux measurements, and measurements of carbon stores.

Electronic Resource

1365-2486

Blackwell Publishing Journal Backfiles 1879-2005

Biology

Energy, Environment Protection, Nuclear Power Engineering

Geography

Land–air exchanges of energy and matter are modulated by several feedback processes at both small and large space and time scales, with implications for the linked carbon, water and energy cycles. This paper studies the influences of four local feedbacks, occurring at single-patch spatial scales and subdiurnal temporal scales, on the surface energy balance (SEB) and land–air carbon fluxes. The feedbacks are: (i) radiative feedback, the modulation of available energy through the effect of surface temperature, Ts, on outgoing longwave radiation; (ii) physiological feedback, the interaction between vegetation physiology and the SEB through Ts; (iii) aerodynamic feedback, the modulation of turbulent heat and moisture transfer by atmospheric stability; and (iv) Convective Boundary Layer (CBL) feedback, the coupling between the daytime evolution of the SEB and CBL through saturation deficit.It is found that radiative feedback is significant only over very smooth surfaces. Physiological feedback is positive with respect to Ts at moderate to high temperatures, pushing stomata towards complete closure and the SEB towards very low evaporation rates. The SEB is quite sensitive to whether or not such closure occurs. Aerodynamic feedback, on the other hand, is negative with respect to Ts at these temperatures, reducing Ts and attenuating the tendency for heat-induced stomatal closure. CBL feedback alone does not dampen the sensitivity of the SEB to physiological feedback and stomatal closure. However, when aerodynamic feedback is included, this sensitivity is greatly reduced.

Electronic Resource

1476-4687

Nature Archives 1869 - 2009

Biology

Chemistry and Pharmacology

Medicine

Natural Sciences in General

Physics

[Auszug] Knowledge of carbon exchange between the atmosphere, land and the oceans is important, given that the terrestrial and marine environments are currently absorbing about half of the carbon dioxide that is emitted by fossil-fuel combustion. This carbon uptake is therefore limiting the extent of ...

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract This paper considers the near-field dispersion of an ensemble of tracer particles released instantaneously from an elevated source into an adiabatic surface layer. By modelling the Lagrangian vertical velocity as a Markov process which obeys the Langevin equation, we show analytically that the mean vertical drift velocity w(t) is w(τ)=bu *(1−e −τ(1+τ)), where Τ is time since release (nondimensionalized with the Lagrangian time scale at the source), b Batchelor's constant, and u *, the friction velocity. Hence, the mean height and mean depth of the ensemble are calculated. Although the derivation is formally valid only when Τ ≪ 1, the predictions for w, mean height and mean depth are consistent in the downstream limit (Τ ≫ 1) with surface-layer Lagrangian similarity theory and with the diffusion equation. By comparing the analytical predictions with numerical, randomflight solutions of the Langevin equation, the analytical predictions are shown to be good approximations at all times, both near-field and far-field.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that: (i) The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy. (ii) In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss. (iii) In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller. (iv) Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence. (v) Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract An experiment is reported in which heat was released as a passive tracer from an elevated lateral line source within a model plant canopy, with h s = 0.85 h c (h s and h c being the source and canopy heights, respectively). A sensor assembly consisting of three coplanar hot wires and one cold wire was used to measure profiles of mean temperature % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGaeqiUdehaaiaacMcaaaa!390C!\[(\overline \theta )\], temperature variance (Σθ 2), vertical and streamwise turbulent heat fluxes, and third moments of wind and temperature fluctuations. Conclusions were: (i) Despite the very heterogeneous flow within the canopy, the observed dispersive heat flux (due to spatial correlation between time-averaged temperature and vertical velocity) was small. However, there is evidence from the plume centroid (which was lower than h s at the source) of systematic recirculating motions within the canopy. (ii) The ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS% baaSqaaiabeI7aXjaab2gacaqGHbGaaeiEaaqabaGccaGGVaWaa0aa% aeaacqaH4oqCaaWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaa!41DF!\[\sigma _{\theta {\text{max}}} /\overline \theta _{{\text{max}}} \] (of maximum values on vertical profiles) decreased from 1 near the source to an asymptotic value of 0.4 far downstream, in good agreement with previous experimental and theoretical work for concentration fluctuations in the surface layer well above the canopy. (iii) The eddy diffusivity for heat from the line source (K HL ) increased, downstream of the source, to a nearly constant ‘far-field’ vertical profile. Within the canopy, the far-field K HL was an order of magnitude larger than K HP , the equivalent diffusivity for a plane source; well above the canopy, the two were equal. The time scale defined by (far-field K HL )/(vertical velocity variance) was independent of height within the canopy. (iv) Budgets for temperature variance, vertical heat flux and streamwise heat flux are remarkably similar to the equivalent budgets for an elevated line source in the surface layer well above the canopy, except in the lower part of the canopy in the far field, where vertical transport is much more important than in the surface layer. (v) A random flight simulation of the mean height and depth of the temperature plume was generally in good agreement with experiment. However, details of the temperature and streamwise turbulent heat flux profiles were not correct, suggesting that the model formulation needs to be improved.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio Τ S/Τ of the stress Τ s on the underlying ground surface to total stress Τ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation τS/τ= 1/(1+βλ), where λ= CRCS the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract We analyse single-point velocity statistics obtained in a wind tunnel within and above a model of a waving wheat crop, consisting of nylon stalks 47 mm high and 0.25 mm wide in a square array with frontal area index 0.47. The variability of turbulence measurements in the wind tunnel is illustrated by using a set of 71 vertical traverses made in different locations, all in the horizontally-homogeneous (above-canopy) part of the boundary layer. Ensemble-averaged profiles of the statistical moments up to the fourth order and profiles of Eulerian length scales are presented and discussed. They are consistent with other similar experiments and reveal the existence of large-scale turbulent coherent structures in the flow. The drag coefficient in this canopy as well as in other reported experiments is shown to exhibit a characteristic height-dependency, for which we propose an interpretation. The velocity spectra are analysed in detail; within and just above the canopy, a scaling based on fixed length and velocity scales (canopy height and mean horizontal wind speed at canopy top) is proposed. Examination of the turbulent kinetic energy and shear stress budgets confirms the role of turbulent transport in the region around the canopy top, and indicates that pressure transport may be significant in both cases. The results obtained here show that near the top of the canopy, the turbulence properties are more reminiscent of a plane mixing layer than a wall boundary layer.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z 0) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (Λ). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract Two-point, space-time correlations of streamwise and vertical velocity were obtained from a wind tunnel simulation of an atmospheric surface layer with an underlying model wheat canopy constructed of flexible nylon stalks. Velocity data extend from 1/6 canopy height to several canopy heights, with in excess of 2000 three-dimensional vector separations of the two x-wire probes. Isocorrelation contours over anx, z slice show the streamwise velocity autocorrelation to be roughly circular, such that vertical velocities at the same horizontal position but different heights are closely in phase. Cross-correlations between the two velocity components reflect this difference to some extent. Lateral displacements of the probes revealed side lobes with correlations of reversed sign but we cannot positively link this pattern to particular vorticular structures. Integral length scales obtained directly from the spatial correlations match similar scales deduced from single-point time series with Taylor's hypothesis at 2 to 3 times the canopy height but greatly exceed such scales at lower levels, particularly within the wheat. We conclude that the reversed sign lateral lobes are important components of the correlation field and that an integral length scale for the lateral direction must be defined such that they are included. Convective velocities obtained from the time lag to optimally restore correlation lost by physical separation of the probes change only slowly with height and greatly exceed the mean wind velocity within and immediately above the canopy. Thus, mean wind velocity is not a suitable proxy for convective velocity in the application of Taylor's hypothesis in this situation. The ratio of vertical to longitudinal convective velocity for the streawise velocity signal yields a downwind tilt angle of about 39° which is probably a better estimate of the slope of the dominant fluid motions than the tilt of the major axis of the isocorrellation contours mentioned previously.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract This paper describes wind-tunnel experiments on the flow around single and multiple porous windbreaks (height H), sheltering a model plant canopy (height H/3). The mean wind is normal to the windbreaks, which span the width of the wind tunnel. The incident turbulent flow simulates the adiabatic atmospheric surface layer. Five configurations are examined: single breaks of three solidities (low, medium, high; solidity = 1 - porosity), and medium-solidity multiple breaks of streamwise spacing 12H and 6H. The experimental emphases are on the interactions of the windbreak flow with the underlying plant canopy; the effects of solidity; the differences in shelter between single and multiple windbreaks; and the scaling properties of the flow. Principal results are: (1) the "quiet zones" behind each windbreak are smaller in multiple than single arrays, because of the higher turbulence level in the very rough-wall internal boundary layer which develops over the multiple arrays. Nevertheless, the overall shelter effectiveness is higher for multiple arrays than single windbreaks because of the "nonlocal shelter" induced by the array as a whole. (2) The flow approaching the windbreak decelerates above the canopy but accelerates within the canopy, particularly when the windbreak solidity is high. (3) A strong mixing layer forms just downwind of the top of each windbreak, showing some of the turbulence and scaling properties of the classical mixing layer formed between uniform, coflowing streams. (4) No dramatic increase in turbulence levels in the canopy is evident at the point where the deepening mixing layer contacts the canopy (around x/H = 3) but the characteristic inflection in the canopy wind profile is eliminated at this point.

Electronic Resource

1573-5052

Springer Online Journal Archives 1860-2000

Biology

Abstract This paper considers the modelling of available energy partition into sensible and latent heat at land surfaces, inter alia for GCM applications. In a preliminary discussion, processes at canopy scale are reviewed briefly by outlining two classes of model: comprehensive, multilayer Canopy-Atmosphere Models (CAMs) which attempt to include all physical and biological processes influencing the canopy microclimate and atmospheric exchanges, and single-layer Simplified Canopy-Atmosphere Models (SCAMs) which attempt a physically acceptable description of energy partition with the fewest possible parameters. Details of a four-parameter SCAM are outlined. It is suggested that CAMs are necessary for understanding the ‘downward” influence of climate on a canopy, but that SCAMs may be useful in modelling the ‘upward’ influence of vegetation on climate with GCMs. The main part of the paper considers the generalisation of land-surface models from homogeneous to flat, heterogeneous terrain in which local advection is prominent. The approach is to model the planetary boundary layer as well as the surface layer. A simple mixed-layer model is outlined for the daytime convective boundary layer (CBL). Boundary conditions for sensible and latent heat transfer at the ground are made separable by defining two new conserved scalar variables, a total energy content and a linearized saturation deficit. A new analytic solution of the energy partition problem is developed for the case of an encroaching CBL with the depth h proportional to the square root of time. The general model, with this analytic solution as a particular case, is then extended from homogeneous to heterogeneous surfaces by defining a CBL horizontal length scale X=hU/w * (where U is the horizontal velocity and w * the convective velocity scale). When individual terrain patches have scales much less than X, the inhomogeneity is microscale and is averaged out by the CBL itself; mesoscale inhomogeneity occurs when patches have scales much greater than X, leading to separate CBL development over each patch. The CBL equations yield a statement of the partition of surface sensible and latent heat fluxes among the surface patches in a heterogeneous landscape, and averaging operators for surface properties.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract Recent observations of flux-gradient anomalies in atmospheric flow close to forests, and similar rough surfaces, prompted a wind-tunnel investigation in which cross-wire anemometry was used to study the vertical development and horizontal variability of adiabatic flow over five regularly arrayed rough surfaces, encompassing a 32-fold range of roughness concentration λ. The roughness elements were cylinders, 6 mm in both height and diameter. Below a layer in which the velocity profile is semi-logarithmic, two surface influences upon the mean velocity field can be distinguished: wake diffusion and horizontal inhomogeneity. The wake diffusion effect causes non-dimensional vertical velocity gradients to be smaller than in the semi-logarithmic region; at least for elements with aspect ratios l/h ≲ 1, it is governed by the transverse dimension l of the roughness elements, and is observed when z 〉 h + 1.5l (where z is height above the underlying surface, and h is the height of the roughness elements). A simple diffusivity model successfully describes the horizontally averaged velocity profiles in the region of wake influence, despite conceptual disadvantages. The horizontal inhomogeneity of the flow is negligible when z 〉 h + D (D being the inter-element spacing), and does not entirely mask the wake diffusion effect except over very sparsely roughened surfaces (λ ≲ 0.02). A criterion for negligibility of both effects, and hence for applicability of conventional turbulent diffusivity theory for momentum, is z 〉 h + 1.5D. These results are compared with atmospheric data, and indicate that wake diffusion may well cause some underestimation of the zero-plane displacement d over typical vegetated surfaces.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract This paper describes a wind-tunnel experiment on the dispersion of trace heat from an effectively planar source within a model plant canopy, the source height being h s = 0.80 h c , where h c is the canopy height. A sensor assembly consisting of three coplanar hot wires and one cold wire was used to make simultaneous measurements of the temperature and the streamwise and vertical velocity components. It was found that: (i) The thermal layer consisted of two parts with different length scales, an inner sublayer (scaling with h s and h c ) which quickly reached streamwise equilibrium downstream of the leading edge of the source, and an outer sublayer which was self-preserving with a length scale proportional to the depth of the thermal layer. (ii) Below 2h c , the vertical eddy diffusivity for heat from the plane source (K HP ) was substantially less than the far-field limit of the corresponding diffusivity for heat from a lateral line source at the same height as the plane source. This shows that dispersion from plane or other distributed sources in canopies is influenced, near the canopy, by turbulence ‘memory’ and must be considered as a superposition of both near-field and far-field processes. Hence, one-dimensional models for scalar transport from distributed sources in canopies are wrong in principle, irrespective of the order of closure. (iii) In the budgets for temperature variance, and for the vertical and streamwise components of the turbulent heat flux, turbulent transport was a major loss between h s and h c and a principal gain mechanism below h s , as also observed in the budgets for turbulent energy and shear stress. (iv) Quadrant analysis of the vertical heat flux showed that sweeps and ejections contributed about equal amounts to the heat flux between h s and h c , though among the more intense events, sweeps were dominant. Below h s , almost all the heat was transported by sweeps.

Electronic Resource

1573-1472

Equilibrium evaporation ; Equilibrium energy partition ; Convective boundary layer ; Combination equation ; Penman–Monteith equation

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract A theory is developed for surface energy exchanges in well-mixed, partlyopen systems, embracing fully open and fully closed systems as limits.Conservation equations for entropy and water vapour are converted intoan exact rate equation for the potential saturation deficit D in a well-mixed, partly open region. The main contributions to changes in D arise from (1) the flux of D at the surface, dependent on a conductance gq that is a weighted sum of the bulk aerodynamic and surface conductances; and (2) the ‘exchange’ flux of D with the external environment by entrainment or advection, dependent on a conductance ge that is identifiable with the entrainment velocity when the partly open region is a growing convective boundary layer (CBL). The system is fully open when ge/gq → ∞, and fully closed when ge/gq → 0. The equations determine the steady state surface energy balance (SEB) in a partly open system, the associated steady-state deficit, and the settling time scale needed to reach the steady state. The general result for the steady-state SEB corresponds to the equations of conventional combination theory for the SEB of a vegetated surface, with the surface-layer deficit replaced by the external deficit and with gq replaced by the series sum (gq -1 + ge -1)-1. In the fully open limit D is entirely externally prescribed, while in the fully closed limit, D is internally determined and the SEB approaches thermodynamic equilibrium energy partition. In the case of the CBL, the conductances gq and ge are themselves functions of D through short-term feedbacks, induced by entrainment in the case of ge and by both physiological and aerodynamic (thermal stability) processes in the case of gq. The effects of these feedbacks are evaluated. It is found that a steady-state CBL is physically achievable only over surfaces with at least moderate moisture availability; that entrainment has a significant accelerating effect on equilibration; that the settling time scale is well approximated by h/(gq + ge), where h is the CBL depth; and that this scale is short enough to allow a steady state to evolve within a semi-diurnal time scale only when h is around 500 m or less.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract We present a wind-tunnel simulation of adiabatic atmospheric flow normal to a rough, two-dimensional ridge. The data are analyzed in physical streamline coordinates, which are described in some detail. The mean velocity speed-up on the hill top is adequately predicted by existing formulae while the behaviour of the wake flow fits into a pattern that emerges from other wind-tunnel experiments. The turbulent stresses evolve in response to the extra strain rates induced by the hill, streamline curvature and acceleration: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG1bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3456!\[u^{\bar 2}\]is coupled strongly to acceleration while % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqdaaqaaiaadw% hacaWG3baaaaaa!3462!\[\overline {uw}\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG3bWaaWbaaS% qabeaaceaIYaGbaebaaaaaaa!3458!\[w^{\bar 2}\]follow curvature. These differing responses lead to significant phase differences between the changes in the component stresses as the hill is traversed. An analogous response is seen in the components of turbulent stress divergence, which are computed as part of streamwise momentum budgets. Only very close to the surface is turbulent stress divergence comparable to the inertial and pressure terms in the momentum budget; over most of the flow regime, the mean flow response is approximately inviscid. Finally, we compare our results with data from other wind tunnel models and from real hills.

Electronic Resource

1573-1472

Springer Online Journal Archives 1860-2000

Geosciences

Physics

Abstract The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance Σ wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + δt) = aw(t) + bΣ wEζ + (1 − a)T L ∂(Σ wE 2)/∂z, where w(t) is the vertical velocity at time t, ζ a random number from a Gaussian distribution with zero mean and unit variance, T L the Lagrangian integral time scale for vertical velocity, a = exp(−δt/T L), and b = (1 − a 2)1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, Σ wE and T L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.

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