Effects of rotation and sloping terrain on fronts of density current fronts

The initial stage of the adjustment of a gravity current to the effects of rotation with angular velocity f/2 is analysed using a short time analysis where Coriolis forces are initiated in an inviscid von Kármán–Benjamin gravity current front at tF=0. It is shown how, on a time-scale of order 1/f, as a result of ageostrophic dynamics, the slope and front speed UF are much reduced from their initial values, while the transverse anticyclonic velocity parallel to the front increases from zero to O(NH0), where N=g′/H0−−−−−√ is the buoyancy frequency, and g′=gΔρ/ρ0 is the reduced acceleration due to gravity. Here ρ0 is the density and Δρ and H0 are the density difference and initial height of the current. Extending the steady-state theory to account for the effect of the slope σ on the bottom boundary shows that, without rotation, UF has a maximum value for σ=\upi/6, while with rotation, UF tends to zero on any slope. For the asymptotic stage when ftF≫1, the theory of unsteady waves on the current is reviewed using nonlinear shallow-water equations and the van der Pol averaging method. Their motions naturally split into a ‘balanced’ component satisfying the Margules geostrophic relation and an equally large ‘unbalanced’ component, in which there is horizontal divergence and ageostrophic vorticity. The latter is responsible for nonlinear oscillations in the current on a time scale f−1, which have been observed in the atmosphere and field experiments. Their magnitude is mainly determined by the initial potential energy in relation to that of the current and is proportional to the ratio \it Bu−−−−−√=LR/R0, where LR=NH0/f is the Rossby deformation radius and R0 is the initial radius. The effect of slope friction also prevents the formation of a steady front. From the analysis it is concluded that a weak mean radial flow must be driven by the ageostrophic oscillations, preventing the mean front speed UF from halting sharply at ftF∼1. Depending on the initial value of LR/R0, physical arguments show that UF decreases slowly in proportion to (ftF)−1/2, i.e. UF/UF0=F(ftF,\it Bu). Thus the front only tends to the geostrophic asymptotic state of zero radial velocity very slowly (i.e. as ftF→∞) for finite values of LR/R0. However, as LR/R0→0, it reaches this state when ftF∼1. This analysis of the overall nonlinear behaviour of the gravity current is consistent with two two-dimensional non-hydrostatic (Navier–Stokes) and axisymmetric hydrostatic (shallow-water) Eulerian numerical simulations of the varying form of the rotating gravity current. When the effect of surface friction is considered, it is found that the mean movement of the front is significantly slowed. Furthermore, the oscillations with angular frequency f and the slow growth of the radius, when ftF≥1, are consistent with recent experiments

The influence of the thermal diffusivity of the lower boundary on eddy motion in convection

The paper presents new concepts and results for the eddy structure of turbulent convection in a horizontal fluid layer of depth h which lies above a solid base with thickness hb. The fluid parameters are the kinematic viscosity ν, the thermal diffusivity κ, which is taken to be comparable with ν, the density ρ, the specific heat cp and the expansion parameter β. The thermal diffusivity of the solid is κb. The results are an extension of the more commonly studied cases, where a constant heat flux or constant temperature is applied at the interface between the fluid and the base. The buoyancy forces induce eddy motions with a typical velocity w∗∼(gβFθh)1/3 where ρcpFθ is the average heat flux and Fθ the covariance of the fluctuations of the temperature and of the vertical velocity. At moderate Reynolds numbers (Re=w∗h/ν), say less than about 103, an order-of-magnitude analysis shows that for the case of high diffusivity of the base (i.e. κb≫κ) elongated ‘plumes’ form at the surface and extend to the top of the fluid layer. When the base diffusivity is low (i.e. κb≤κ) the surface cools below the developing ‘plume’ and either the plume breaks up into elongated puffs or, if κb≪κ, horizontal pressure gradients form so that only small-scale puffs can form near the surface. At very high Reynolds numbers, approximately greater than 104, the surface boundary layer below each puff/plume is highly turbulent with a local logarithmic velocity and temperature profile. An approximate analysis indicates for this case that there is insufficient buoyancy flux from the base, irrespective of its diffusivity, to maintain plumes, because of the high turbulent heat transfer. So puffs dominate high-Reynolds-number thermal convection as numerical simulations and field experiments demonstrate. However, when the surface heat flux is uniform, for example as a result of radiant heat transfer or by forcing with a constant heat flux below a very thin conducting base, plumes are the dominant form of eddy motion, as is commonly observed. In the numerical solutions presented here, where Re∼3×102 and the slab thickness hb=h, it is shown that the spatial scales of eddy structures in the fluid layer close to the surface become significantly smaller as κb/κ is reduced from 100 to 0.1. At the same time in the core of the convective layer the change in the autocorrelation and spatial correlation function indicates that there is a transition from long-duration plumes into shorter-duration and smaller-length-scale elongated puffs. The simulations show that the largest temperature fluctuations near the surface occur when a constant heat flux is applied at the bottom of the fluid layer. The smallest temperature fluctuations are associated with the constant-temperature boundary condition. The finite base diffusivity cases lie in between these limits, with the largest fluctuations occurring when the thermal diffusivity of the base is small. The hypothesis introduced above has been tested qualitatively in a laboratory set-up when the effective diffusivity of the base was varied. The flow structure was observed as it changed from being characterized by nearly steady plumes, into unsteady plumes and finally into puffs when the thickness of the conducting base was first increased and then the diffusivity was decreased

Finding optimal geometries for noise barrier tops using scaled experiments

Scaled acoustic laboratory experiments are used to develop a methodology for obtaining the acoustic characteristics of different barrier top designs and for identifying geometries that may have advantages over the traditional thin vertical screen. The idea is to use a short impulsive spherical sound pulse possessing a broad frequency spectrum. If the duration of the pulse is sufficiently short, the entire primary signal, which travels by the shortest direct route diffracting at the top of the barrier, arrives at the receiver much earlier than any secondary signals reflected from the surroundings. Secondary signals may therefore be ignored and only the information from the primary signal can be analyzed. When the typical frequency band of the sound pulse is about an order of magnitude higher than typical traffic noise spectra, then scaled acoustic modeling using the same scaling factor for lengths and distances is possible. The results of such experiments are reported here for barriers with six different geometries. Using spectral analysis, insertion losses as functions of frequency were calculated for different source-receiver positions and barrier tops. The results were then rescaled for full-size traffic barriers and, using a typical traffic noise spectrum, single number ratings of barrier performance were obtained

Simulating meteorological profiles to study noise propagation from freeways

Forecasts of noise pollution from a highway line segment noise source are obtained from a sound propagation model utilizing effective sound speed profiles derived from a Numerical Weather Prediction (NWP) limited area forecast with 1 km horizontal resolution and near-ground vertical resolution finer than 20 m. Methods for temporal along with horizontal and vertical spatial nesting are demonstrated within the NWP model for maintaining forecast feasibility. It is shown that vertical nesting can improve the prediction of finer structures in near-ground temperature and velocity profiles, such as morning temperature inversions and low level jet-like features. Accurate representation of these features is shown to be important for modeling sound refraction phenomena and for enabling accurate noise assessment. Comparisons are made using the parabolic equation model for predictions with profiles derived from NWP simulations and from field experiment observations during mornings on November 7 and 8, 2006 in Phoenix, Arizona. The challenges faced in simulating accurate meteorological profiles at high resolution for sound propagation applications are highlighted and areas for possible improvement are discussed

A Simple Model for the Afternoon and Early-Evening Decay of Turbulence over Different Land Surfaces

Recent years have seen an increasing interest in the late-afternoon transition between the convective and stable regimes of the atmospheric boundary layer. There are several differences between the two regimes. On one hand, the convective boundary layer is characterized by an unstable stratification, turbulent mixing of mass, momentum and heat and buoyancy-driven eddies. On the other hand, the stable boundary layer is associated with a strong stable stratification that tends to suppress vertical motions generated by mechanical turbulence. One of the key processes of this complex transition period is the forcing time scale associated with the surface heat flux. Unfortunately, very few modeling studies have used realistic decaying time scales for the sensible heat flux. Therefore, in the first part of this study, we present a new function that better represents the afternoon and early-evening transitions and validate it with eddy covariance measurements over different land surfaces. The objectives are to capture the buoyancy forcing time scales observed in nature and the influence of surface properties. In the second part of the study, we show preliminary results of large-eddy simulation of atmospheric flow over heterogeneous cooling stripes. We focus our attention on the temperature advection between the different stripes as a result of their different cooling rates. Overall, this study is one of the first to model the convective decay of turbulence using realistic time scales over heterogeneous terrain

Hydrodynamic simulations of shell convection in stellar cores

Shell convection driven by nuclear burning in a stellar core is a common hydrodynamic event in the evolution of many types of stars. We encounter and simulate this convection (i) in the helium core of a low-mass red giant during core helium flash leading to a dredge-down of protons across an entropy barrier, (ii) in a carbon-oxygen core of an intermediate-mass star during core carbon flash, and (iii) in the oxygen and carbon burning shell above the silicon-sulfur rich core of a massive star prior to supernova explosion. Our results, which were obtained with the hydrodynamics code HERAKLES, suggest that both entropy gradients and entropy barriers are less important for stellar structure than commonly assumed. Our simulations further reveal a new dynamic mixing process operating below the base of shell convection zones.Comment: 8 pages, 3 figures .. submitted to a proceedings of conference about "Red Giants as Probes of the Structure and Evolution of the Milky Way" which has taken place between 15-17 November 2010 in Rom

Mixing to monsoons: Air-sea interactions in the bay of Bengal

More than 1 billion people depend on rainfall from the South Asian monsoon for their livelihoods. Summertime monsoonal precipitation is highly variable on intraseasonal time scales, with alternating "active" and "break" periods. These intraseasonal oscillations in large-scale atmospheric convection and winds are closely tied to 1°C-2°C variations of sea surface temperature in the Bay of Bengal