The quasi-nondispersive regimes of long extratropical baroclinic rossby waves over (slowly varying) topography

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio tau, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with tau, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f/h(alpha c) = a constant (alpha(c) is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, "fast" and "slow" westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound ( in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and K se is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.

Perturbed Rankine vortices in surface quasi-geostrophic dynamics

An analytical dispersion relation is derived for linear perturbations to a Rankine vortex governed by surface quasi-geostrophic dynamics. Such a Rankine vortex is a circular region of uniform anomalous surface temperature evolving under quasi-geostrophic dynamics with uniform interior potential vorticity. The dispersion relation is analysed in detail and compared to the more familiar dispersion relation for a perturbed Rankine vortex governed by the Euler equations. The results are successfully verified against numerical simulations of the full equations. The dispersion relation is relevant to problems including wave propagation on surface temperature fronts and the stability of vortices in quasi-geostrophic turbulence.

Dynamic modelling of a wind catcher/tower turret for natural ventilation

This paper discusses experimental and theoretical investigations and Computational Fluid Dynamics (CFD) modelling considerations to evaluate the performance of a square section wind catcher system connected to the top of a test room for the purpose of natural ventilation. The magnitude and distribution of pressure coefficients (C-p) around a wind catcher and the air flow into the test room were analysed. The modelling results indicated that air was supplied into the test room through the wind catcher's quadrants with positive external pressure coefficients and extracted out of the test room through quadrants with negative pressure coefficients. The air flow achieved through the wind catcher depends on the speed and direction of the wind. The results obtained using the explicit and AIDA implicit calculation procedures and CFX code correlate relatively well with the experimental results at lower wind speeds and with wind incidents at an angle of 0 degrees. Variation in the C-p and air flow results were observed particularly with a wind direction of 45 degrees. The explicit and implicit calculation procedures were found to be quick and easy to use in obtaining results whereas the wind tunnel tests were more expensive in terms of effort, cost and time. CFD codes are developing rapidly and are widely available especially with the decreasing prices of computer hardware. However, results obtained using CFD codes must be considered with care, particularly in the absence of empirical data.

Investigation of air quality, comfort parameters and effectiveness for two floor-level air supply systems in classrooms

The method of distributing the outdoor air in classrooms has a major impact on indoor air quality and thermal comfort of pupils. In a previous study, ([11] Karimipanah T, Sandberg M, Awbi HB. A comparative study of different air distribution systems in a classroom. In: Proceedings of Roomvent 2000, vol. II, Reading, UK, 2000. p. 1013-18; [13] Karimipanah T, Sandberg M, Awbi HB, Blomqvist C. Effectiveness of confluent jets ventilation system for classrooms. In: Idoor Air 2005, Beijing, China, 2005 (to be presented).) presented results for four and two types of air distribution systems tested in a purpose built classroom with simulated occupancy as well as computational fluid dynamics (CFD) modelling. In this paper, the same experimental setup has been used to investigate the indoor environment in the classroom using confluent jet ventilation, see also ([12]Cho YJ, Awbi HB, Karimipanah T. The characteristics of wall confluent jets for ventilated enclosures. In: Proceedings of Roomvent 2004, Coimbra, Portugal, 2004.) Measurements of air speed, air temperature and tracer gas concentrations have been carried out for different thermal conditions. In addition, 56 cases of CFD simulations have been carried to provide additional information on the indoor air quality and comfort conditions throughout the classroom, such as ventilation effectiveness, air exchange effectiveness, effect of flow rate, effect of radiation, effect of supply temperature, etc., and these are compared with measured data.

Generation of inertia-gravity waves in the rotating thermal annulus by a localised boundary layer instability

Waves with periods shorter than the inertial period exist in the atmosphere (as inertia-gravity waves) and in the oceans (as Poincaré and internal gravity waves). Such waves owe their origin to various mechanisms, but of particular interest are those arising either from local secondary instabilities or spontaneous emission due to loss of balance. These phenomena have been studied in the laboratory, both in the mechanically-forced and the thermally-forced rotating annulus. Their generation mechanisms, especially in the latter system, have not yet been fully understood, however. Here we examine short period waves in a numerical model of the rotating thermal annulus, and show how the results are consistent with those from earlier laboratory experiments. We then show how these waves are consistent with being inertia-gravity waves generated by a localised instability within the thermal boundary layer, the location of which is determined by regions of strong shear and downwelling at certain points within a large-scale baroclinic wave flow. The resulting instability launches small-scale inertia-gravity waves into the geostrophic interior of the flow. Their behaviour is captured in fully nonlinear numerical simulations in a finite-difference, 3D Boussinesq Navier-Stokes model. Such a mechanism has many similarities with those responsible for launching small- and meso-scale inertia-gravity waves in the atmosphere from fronts and local convection.

The impact of urban wind environments on natural ventilation

The aim of this paper is to illustrate the impact of urban wind environments when assessing the availability of natural ventilation. A numerical study of urban airflow for a complex of five building blocks located at the University of Reading, UK is presented. The computational fluid dynamics software package ANSYS was used to simulate six typical cases of urban wind environments and the potential for natural ventilation assessed. The study highlights the impact of three typical architectural forms (street canyons, semi-enclosures and courtyards) on the local wind environment. Simulation results have also been compared with experimental data collected from six locations on the building complex. The study demonstrates that ventilation strategies formed using regional weather data, may have a propensity to over-estimate the potential for natural ventilation and cooling, due to the impact of urban form which creates a unique microclimate. Characteristics of urban wind flow patterns are presented as a guideline and can be used to assess the design and performance of natural or hybrid ventilation and the opportunity for passive cooling.

The Aqua-Planet Experiment (APE): CONTROL SST Simulation

Climate simulations by 16 atmospheric general circulation models (AGCMs) are compared on an aqua-planet, a water-covered Earth with prescribed sea surface temperature varying only in latitude. The idealised configuration is designed to expose differences in the circulation simulated by different models. Basic features of the aqua-planet climate are characterised by comparison with Earth. The models display a wide range of behaviour. The balanced component of the tropospheric mean flow, and mid-latitude eddy covariances subject to budget constraints, vary relatively little among the models. In contrast, differences in damping in the dynamical core strongly influence transient eddy amplitudes. Historical uncertainty in modelled lower stratospheric temperatures persists in APE. Aspects of the circulation generated more directly by interactions between the resolved fluid dynamics and parameterized moist processes vary greatly. The tropical Hadley circulation forms either a single or double inter-tropical convergence zone (ITCZ) at the equator, with large variations in mean precipitation. The equatorial wave spectrum shows a wide range of precipitation intensity and propagation characteristics. Kelvin mode-like eastward propagation with remarkably constant phase speed dominates in most models. Westward propagation, less dispersive than the equatorial Rossby modes, dominates in a few models or occurs within an eastward propagating envelope in others. The mean structure of the ITCZ is related to precipitation variability, consistent with previous studies. The aqua-planet global energy balance is unknown but the models produce a surprisingly large range of top of atmosphere global net flux, dominated by differences in shortwave reflection by clouds. A number of newly developed models, not optimised for Earth climate, contribute to this. Possible reasons for differences in the optimised models are discussed. The aqua-planet configuration is intended as one component of an experimental hierarchy used to evaluate AGCMs. This comparison does suggest that the range of model behaviour could be better understood and reduced in conjunction with Earth climate simulations. Controlled experimentation is required to explore individual model behaviour and investigate convergence of the aqua-planet climate with increasing resolution.

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.

On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

On Rossby waves modified by weak sinusoidal shear

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

Mean motions induced by baroclinic instability in a jet

A study is made of the zonal-mean motions induced by a growing baroclinic wave in several contexts, under the framework of three different analysis schemes: the conventional Eulerian mean (EM), the transformed Eulerian mean (TEM), and the generalized Lagrangian mean (GLM). The effect of meridional shear in the initial jet on these induced mean motions is considered by treating the instability problem in the context of the two-layer model. The conceptual simplicity of the TEM formulation is shown to be useful in diagnosing the dynamics of instability, much as it has been found helpful in many problems of wave, mean-flow interaction. In addition, it is found that the TEM vertical velocity is a very good indicator of the GLM vertical velocity. However, the GLM meridional velocity is always convergent towards the centre of instability activity, and is not at all well represented by the nondivergent TEM meridional velocity. In comparing the results with Uryu's (1979) calculation of the GLM circulation induced by a growing Eady wave, it is found that the inclusion of meridional jet shear in the present work leads to some strikingly different effects in the GLM zonal wind acceleration. In the case of pure baroclinic instability treated by Uryu, the Eulerian and Stokes accelerations nearly cancel each other in the centre of the channel, leaving a weak Lagrangian acceleration opposed to the Eulerian one. In the more general case of mixed baroclinic-barotropic instability, however, the Eulerian and Stokes accelerations can reinforce one another, leading to a very strong Lagrangian zonal wind

The non-conservation of potential vorticity by a dynamical core compared with the effects of parametrized physical processes

Numerical models of the atmosphere combine a dynamical core, which approximates solutions to the adiabatic, frictionless governing equations for fluid dynamics, with tendencies arising from the parametrization of other physical processes. Since potential vorticity (PV) is conserved following fluid flow in adiabatic, frictionless circumstances, it is possible to isolate the effects of non-conservative processes by accumulating PV changes in an air-mass relative framework. This “PV tracer technique” is used to accumulate separately the effects on PV of each of the different non-conservative processes represented in a numerical model of the atmosphere. Dynamical cores are not exactly conservative because they introduce, explicitly or implicitly, some level of dissipation and adjustment of prognostic model variables which acts to modify PV. Here, the PV tracers technique is extended to diagnose the cumulative effect of the non-conservation of PV by a dynamical core and its characteristics relative to the PV modification by parametrized physical processes. Quantification using the Met Office Unified Model reveals that the magnitude of the non-conservation of PV by the dynamical core is comparable to those from physical processes. Moreover, the residual of the PV budget, when tracing the effects of the dynamical core and physical processes, is at least an order of magnitude smaller than the PV tracers associated with the most active physical processes. The implication of this work is that the non-conservation of PV by a dynamical core can be assessed in case studies with a full suite of physics parametrizations and directly compared with the PV modification by parametrized physical processes. The nonconservation of PV by the dynamical core is shown to move the position of the extratropical tropopause while the parametrized physical processes have a lesser effect at the tropopause level.

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.