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.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

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.

A mixed-phase bulk orographic precipitation model with embedded convection

A novel analytical model for mixed-phase, unblocked and unseeded orographic precipitation with embedded convection is developed and evaluated. The model takes an idealised background flow and terrain geometry, and calculates the area-averaged precipitation rate and other microphysical quantities. The results provide insight into key physical processes, including cloud condensation, vapour deposition, evaporation, sublimation, as well as precipitation formation and sedimentation (fallout). To account for embedded convection in nominally stratiform clouds, diagnostics for purely convective and purely stratiform clouds are calculated independently and combined using weighting functions based on relevant dynamical and microphysical time scales. An in-depth description of the model is presented, as well as a quantitative assessment of its performance against idealised, convection-permitting numerical simulations with a sophisticated microphysics parameterisation. The model is found to accurately reproduce the simulation diagnostics over most of the parameter space considered.

Story telling in sustainable development projects

This paper constitutes an attempt to find a means to represent multiple stories in the strong narrative of conventional sustainable development (SD) projects. The authors' experience of such projects in various parts of the world indicates that they have a tendency to arise from and reflect a dominant mindset, placing the SD project in what can be a working environment that is inimical to the very ideals that SD is supposed to represent. Short-termism and value for money drive project formats and objectives, whilst counter-narratives and alternative stories arising from stakeholders in such projects are often ignored. Yet these alternative threads often contain strong SD messages of their own and could, if effectively utilized, enhance the SD project process. This paper sets out the case for a new field - 'project ethnography' - allied with the growing use of meta-analysis to compare project 'stories'. The analytical model applied to compare projects is based on the Kolb learning cycle and involves a (3 X 4)-fold questioning of project conceptual ization and roll-out. Copyright @ 2oo6 John Wiley & Sons, Ltd and ERP Environment.

The spacing of orographic rainbands triggered by small-scale topography

A combination of idealized numerical simulations and analytical theory is used to investigate the spacing between convective orographic rainbands over the Coastal Range of western Oregon. The simulations, which are idealized from an observed banded precipitation event over the Coastal Range, indicate that the atmospheric response to conditionally unstable flow over the mountain ridge depends strongly on the subridge-scale topographic forcing on the windward side of the ridge. When this small-scale terrain contains only a single scale (l) of terrain variability, the band spacing is identical to l, but when a spectrum of terrain scales are simultaneously present, the band spacing ranges between 5 and 10 km, a value that is consistent with observations. Based on the simulations, an inviscid linear model is developed to provide a physical basis for understanding the scale selection of the rainbands. This analytical model, which captures the transition from lee waves upstream of the orographic cloud to moist convection within it, reveals that the spacing of orographic rainbands depends on both the projection of lee-wave energy onto the unstable cap cloud and the growth rate of unstable perturbations within the cloud. The linear model is used in tandem with numerical simulations to determine the sensitivity of the band spacing to a number of environmental and terrain-related parameters.

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Modelling energy consumption of relay-enabled MAC protocols in ad hoc networks

To enhance the throughput of ad hoc networks, dual-hop relay-enabled transmission schemes have recently been proposed. Since in ad hoc networks throughput is normally related to their energy consumption, it is important to examine the impact of using relay-enabled transmissions on energy consumption. In this paper, we present an analytical energy consumption model for dual-hop relay-enabled medium access control (MAC) protocols. Based on the recently reported relay-enabled distributed coordination function (rDCF), we have shown the efficacy of the proposed analytical model. This is a generalized model and can be used to predict energy consumption in saturated relay-enabled ad hoc networks via energy decomposition. This is helpful in designing MAC protocols for cooperative communications and it is shown that using a relay results not only in a better throughput but also better energy efficiency.

Impact of interference on throughput in dense WLANs with multiple APs

The popularity of wireless local area networks (WLANs) has resulted in their dense deployments around the world. While this increases capacity and coverage, the problem of increased interference can severely degrade the performance of WLANs. However, the impact of interference on throughput in dense WLANs with multiple access points (APs) has had very limited prior research. This is believed to be due to 1) the inaccurate assumption that throughput is always a monotonically decreasing function of interference and 2) the prohibitively high complexity of an accurate analytical model. In this work, firstly we provide a useful classification of commonly found interference scenarios. Secondly, we investigate the impact of interference on throughput for each class based on an approach that determines the possibility of parallel transmissions. Extensive packet-level simulations using OPNET have been performed to support the observations made. Interestingly, results have shown that in some topologies, increased interference can lead to higher throughput and vice versa.

Modeling energy consumption of dual-hop relay based MAC protocols in ad hoc networks

Given that the next and current generation networks will coexist for a considerable period of time, it is important to improve the performance of existing networks. One such improvement recently proposed is to enhance the throughput of ad hoc networks by using dual-hop relay-based transmission schemes. Since in ad hoc networks throughput is normally related to their energy consumption, it is important to examine the impact of using relay-based transmissions on energy consumption. In this paper, we present an analytical energy consumption model for dual-hop relay-based medium access control (MAC) protocols. Based on the recently reported relay-enabled Distributed Coordination Function (rDCF), we have shown the efficacy of the proposed analytical model. This is a generalized model and can be used to predict energy consumption in saturated relay-based ad hoc networks. This model can predict energy consumption in ideal environment and with transmission errors. It is shown that using a relay results in not only better throughput but also better energy efficiency. Copyright (C) 2009 Rizwan Ahmad et al.

Multivariate analysis of the Fugl-Meyer outcome measures assessing the effectiveness of GENTLE/S robot-mediated stroke therapy

Background: Robot-mediated therapies offer entirely new approaches to neurorehabilitation. In this paper we present the results obtained from trialling the GENTLE/S neurorehabilitation system assessed using the upper limb section of the Fugl-Meyer ( FM) outcome measure. Methods: We demonstrate the design of our clinical trial and its results analysed using a novel statistical approach based on a multivariate analytical model. This paper provides the rational for using multivariate models in robot-mediated clinical trials and draws conclusions from the clinical data gathered during the GENTLE/S study. Results: The FM outcome measures recorded during the baseline ( 8 sessions), robot-mediated therapy ( 9 sessions) and sling-suspension ( 9 sessions) was analysed using a multiple regression model. The results indicate positive but modest recovery trends favouring both interventions used in GENTLE/S clinical trial. The modest recovery shown occurred at a time late after stroke when changes are not clinically anticipated. Conclusion: This study has applied a new method for analysing clinical data obtained from rehabilitation robotics studies. While the data obtained during the clinical trial is of multivariate nature, having multipoint and progressive nature, the multiple regression model used showed great potential for drawing conclusions from this study. An important conclusion to draw from this paper is that this study has shown that the intervention and control phase both caused changes over a period of 9 sessions in comparison to the baseline. This might indicate that use of new challenging and motivational therapies can influence the outcome of therapies at a point when clinical changes are not expected. Further work is required to investigate the effects arising from early intervention, longer exposure and intensity of the therapies. Finally, more function-oriented robot-mediated therapies or sling-suspension therapies are needed to clarify the effects resulting from each intervention for stroke recovery.

The temperature response to stratospheric water vapour changes

This study uses an analytical model, based on the cooling-to-space approximation, and a fixed dynamical heating model to investigate the structure of the stratospheric cooling that occurs in response to a uniform increase in stratospheric water vapour (SWV). At all latitudes, the largest cooling occurs in the lower stratosphere and decreases in magnitude with height. The cooling is strongly enhanced in the Extratropics compared to the Tropics. This is markedly different to the case of an increase in CO2, which causes maximum cooling near the stratopause and a small warming in the tropical lower stratosphere. The qualitative differences in the structure of the cooling can be explained by the smaller opacity of water vapour bands in the stratosphere compared to CO2. The small opacity means that the magnitude of the initial heating rate perturbation only decreases by a factor of four between the upper and lower stratosphere for a SWV perturbation. Therefore, to balance the heating rate perturbation, the largest temperature change is required in the lower stratosphere. Increasing the background concentration of SWV causes the water vapour bands to become more opaque. For a SWV perturbation applied to a background SWV concentration ≥30 ppmv, the heating rate perturbation and temperature change structurally resemble those from an increase in CO2. In the Extratropics, the lower height of the tropopause is found to cause the enhancement in the cooling at those latitudes. By controlling the depth of atmosphere which adjusts to the SWV perturbation, the tropopause height affects the net exchange of radiation between the layers in the stratosphere as they cool. The latitudinal gradient in upwelling infrared radiation at the tropopause and variations in the background temperature are found to have only a minor effect on the structure of the stratospheric temperature response to a change in SWV.

Ultra-distal tephra deposits from super-eruptions: examples from Toba, Indonesia and Taupo Volcanic Zone, New Zealand

Voluminous rhyolitic eruptions from Toba, Indonesia, and Taupo Volcanic Zone (TVZ), New Zealand, have dispersed volcanic ash over vast areas in the late Quaternary. The ~74 ka Youngest Toba Tuff (YTT) eruption deposited ash over the Bay of Bengal and the Indian subcontinent to the west. The ~340 ka Whakamaru eruption (TVZ) deposited the widespread Rangitawa Tephra, dominantly to the southeast (in addition to occurrences northwest of vent), extending across the landmass of New Zealand, and the South Pacific Ocean and Tasman Sea, with distal terrestrial exposures on the Chatham Islands. These super-eruptions involved ~2500 km^3 and ~1500 km3 of magma (dense-rock equivalent; DRE), respectively. Ultra-distal terrestrial exposures of YTT at two localities in India, Middle Son Valley, Madhya Pradesh, and Jurreru River Valley, Andhra Pradesh, at distances of >2000 km from the source caldera, show a basal ‘primary’ ashfall unit ~4 cm thick, although deposits containing reworked ash are up to ~3 m in total thickness. Exposures of Rangitawa Tephra on the Chatham Islands, >900 km from the source caldera, are ~15-30 cm thick. At more proximal localities (~200 km from source), Rangitawa Tephra is ~55-70 cm thick and characterized by a crystal-rich basal layer and normal grading. Both distal tephra deposits are characterized by very-fine ash (with high PM10 fractions) and are crystal-poor. Glass chemistry, stratigraphy and grain-size data for these distal tephra deposits are presented with comparisons of their correlation, dispersal and preservation. Using field observations, ash transport and deposition were modeled for both eruptions using a semi-analytical model (HAZMAP), with assumptions concerning average wind direction and strength during eruption, column shape and vent size. Model outputs provide new insights into eruption dynamics and better estimates of eruption volumes associ- ated with tephra fallout. Modeling based on observed YTT distal tephra thicknesses indicate a relatively low (<40 km high), very turbulent eruption column, consistent with deposition from a co-ignimbrite cloud extending over a broad region. Similarly, the Whakamaru eruption was modeled as producing a predominantly Plinian column (~45 km high), with dispersal to the southeast by strong prevailing winds. Significant ash fallout of the main dispersal direction, to the northwest of source, cannot be replicated in this modeling. The widespread dispersal of large volumes of fine ash from both eruptions may have had global environmental consequences, acutely affecting areas up to thousands of kilometers from vent.

The key role of the western boundary in linking the AMOC strength to the north-south pressure gradient

A key idea in the study of the Atlantic meridional overturning circulation (AMOC) is that its strength is proportional to the meridional density gradient, or more precisely, to the strength of the meridional pressure gradient. A physical basis that would tell us how to estimate the relevant meridional pressure gradient locally from the density distribution in numerical ocean models to test such an idea, has been lacking however. Recently, studies of ocean energetics have suggested that the AMOC is driven by the release of available potential energy (APE) into kinetic energy (KE), and that such a conversion takes place primarily in the deep western boundary currents. In this paper, we develop an analytical description linking the western boundary current circulation below the interface separating the North Atlantic Deep Water (NADW) and Antarctic Intermediate Water (AAIW) to the shape of this interface. The simple analytical model also shows how available potential energy is converted into kinetic energy at each location, and that the strength of the transport within the western boundary current is proportional to the local meridional pressure gradient at low latitudes. The present results suggest, therefore, that the conversion rate of potential energy may provide the necessary physical basis for linking the strength of the AMOC to the meridional pressure gradient, and that this could be achieved by a detailed study of the APE to KE conversion in the western boundary current.

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.