Height Zm Research Articles

Assessment of RANS-based turbulence model for forced plume dynamics in a linearly stratified environment

We present a computational study on the dynamics of a forced plume released in a linearly stratified medium for a range of buoyancy frequencies N∞=0 - 0.7 s−1. Three dimensional unsteady Reynolds-Averaged Navier–Stokes (RANS) simulations are performed using the standard k−ε turbulence model. The mean flow parameters such as the maximum height Zm, mean centerline velocity 〈wc〉, mean axial velocity 〈w〉, and turbulence parameters such as shear production (P), buoyancy production (B), and dissipation rate (ε) are compared with the experimental results of Mirajkar et al. (2020) and a good agreement is found. The validated model is then used to study the forced plume characteristics and energetics at various values of N∞. The passive scalar contours reveal that the plume reaches a maximum height in a stratified medium where the momentum becomes zero, then falls back to the neutral buoyancy height before spreading in the lateral direction. We also found that the maximum height reached by the plume decreases with increasing value of N∞, consistent with the previous studies. Quantification of turbulence parameters reveal that the production flux, P, and viscous dissipation, ε, from the RANS computation are in reasonable agreement with the experimental values at N∞ = 0.4 s−1. Further, the residual, given by 〈〈P〉〉 + 〈〈B〉〉 - 〈〈ε〉〉, is found to be larger for higher N∞, indicating more non-homogeneity in the flow at higher stratification. Overall, the RANS modeling is found to accurately predict the mean flow quantities, such as mean centerline velocity and maximum height reached by the plume. The comparison of the modeled turbulence quantities with experimental data seems satisfactory, but indicates a need for some improvement at high values of N∞.

The Generation and Propagation of Atmospheric Internal Waves Caused by Volcanic Eruptions

Observations from the island of Montserrat in the Caribbean have shown that volcanic eruptions (particularly explosive ones) can generate internal waves in the atmosphere that can be observed by microbarographs at ground level. It is possible that observations of such waves may give early information about volcanic eruptions when other methods are unavailable (because of bad weather, nocturnal eruptions, and poor visibility or remoteness), if it is possible to interpret them. This paper describes a dynamical model of the forcing of internal waves in which the eruption is modelled as a turbulent plume, forced by a source of buoyancy at ground level that specifies the total height and relevant properties of the eruption. Specifically, the rising plume entrains environmental air from ground level to 70% of its maximum height zM, and above 0.7zM the rising fluid spreads radially. During the eruption, this flow forces horizontal motion in the surrounding fluid that generates internal waves, which may be computed by assuming that this is due to a linear dynamical process. Properties of the resulting waves are described for a variety of parameters that include the strength and height of the eruption, the effect of the tropopause, generation in the stratosphere for large eruptions, and the differing effects of the duration of the eruption. Implications for characterising eruptions from observations of these properties are discussed.

Negatively buoyant projectiles – from weak fountains to heavy vortices

An experimental investigation to establish the maximum rise height zm attained by a finite volume of fluid forced impulsively vertically upwards against its buoyancy into quiescent surroundings of uniform density is described. In the absence of a density contrast, the release propagates as a vortex ring and the vertical trajectory is limited by viscous effects. On increasing the source density of the release, gravitational effects limit the trajectory and a maximum rise height zm is reached. For these negatively buoyant releases, the dependence of zm on the length L of the column of ejected fluid, nozzle diameter D (= 2r0), dispensing time and source reduced gravity is determined by injecting saline solution into a fresh-water environment. For 3.4 ≲ L/D ≲ 9.0, zm/r0 is shown to scale on the source parameter η = Fr(L/D), a product of the source Froude number Fr and the aspect ratio L/D for the finite-volume release. Our results show that the morphology of the cap that develops above the source and the vortical motion induced within are sensitively dependent on the source conditions. Moreover, three rise-height regimes are identified: ‘weak-fountain-transition’, ‘vorticity-development’ and ‘forced-release’ regimes, each with a distinct morphology and dependence of dimensionless rise height on η.

Characterising line fountains

We present analytical solutions for the initial rise heightzmof two-dimensional turbulent fountains issuing from a horizontal linear source of width 2b0into a quiescent environment of uniform density. Using the initial rise height prediction as a measure we classify line fountains into three types depending on their source conditions. For source Froude numbersFr0≫ 1, the near-source flow of the ‘forced’ fountain is dominated by source momentum flux and behaves like a jet; the asymptotic solution to the fountain equations yields, in agreement with previous studies,zm/b0~Fr04/3. ForFr0=O(1) the fountain is ‘weak’ and fluid is projected vertically to a height that is consistent with an energy-conserving flow – the sensitivity of the rise height withFr0increases aszm/b0~Fr02. ForFr0≪ 1, the fountain is ‘very weak’ and we find thatzm/b0~Fr02/3. As the local value of the Froude number decreases with height, all three forms of fountain behaviour identified are expected above a highly forced source and we provide scalings for the three lengths that contribute to the total rise height. Comparisons between our predicted rise heights and the previous experimental results show good agreement across a wide range ofFr0. The collated data highlights that experiments have focused in the majority on fountains above sources with intermediateFr0. Notably there is a lack of measurements on very weak line fountains and of independent experimental confirmation of the initial rise heights across the range ofFr0.

Density Effect on Round Turbulent Hypersaline Fountain

An experiment was conducted to examine a round hypersaline fountain. When the discharge was turbulent, and for large densimetric Froude numbers, the results have indicated that the maximum height of the fountain Zm ∕ Lm , in a quiescent and homogeneous surrounding, was a function of relative density difference. The height Zm ∕ Lm decreased from 3.06 at Δρ∕ ρa =0.001 to 2.59 at Δρ∕ ρa =0.1 . The observed density effects on the height of the fountain have indicated that the Boussinesq’s approximation was valid when the relative density difference was typically less than 0.003.

Effects of the solar eclipse of March 29, 2006, in the ionosphere and atmosphere

The observations of the effects of the partial (about 77%) solar eclipse (SE) of March 29, 2006, in the ionospheric plasma are presented. The experimental data were obtained using the Kharkov incoherent scatter radar. At the moment of the maximum phase of SE, a decrease in the critical frequency of the ionospheric F2 layer by 18%, a depletion of the density in the F2 layer maximum by 33%, and an increase in the maximum height zm by 30 km were observed. The solar eclipse caused a decrease in the electron and ion temperatures by 150–300 and 100–200 K, respectively, within the height range 210–490 km. An increase in the relative density of the hydrogen ions during the maximum phase of SE by 20–25% within the height range 900–1200 km is detected. Calculations of the parameters of dynamical processes and thermal regime of the ionospheric plasma during SE are performed.

A numerical study of daily transitions in the convective boundary layer

We examine daily (morning–afternoon) transitions in the atmospheric boundary layer based on large-eddy simulations. Under consideration are the effects of the stratification at the top of the mixed layer and of the wind shear. The results describe the transitory behaviour of temperature and wind velocity, their second moments, the boundary-layer height Z m (defined by the maximum of the potential temperature gradient) and its standard deviation σ m , the mixed-layer height z i (defined by the minimum of the potential temperature flux), entrainment velocity W e, and the entrainment flux H i . The entrainment flux and the entrainment velocity are found to lag slightly in time with respect to the surface temperature flux. The simulations imply that the atmospheric values of velocity variances, measured at various instants during the daytime, and normalized in terms of the actual convective scale w*, are not expected to collapse to a single curve, but to produce a significant scatter of observational points. The measured values of the temperature variance, normalized in terms of the actual convective scale Θ*, are expected to form a single curve in the mixed layer, and to exhibit a considerable scatter in the interfacial layer.

Height and seasonal dependence of aerosol optical properties over southeast Italy

Systematic Raman lidar measurements performed from May 2000 to August 2002 in the framework of the European Aerosol Research Lidar Network are analyzed and discussed. Main results on height dependence and seasonal cycle of extinction α(z) and backscatter β(z) coefficients, aerosol optical depths AOD(z), and lidar ratios S(z) are presented. Yearly‐averaged vertical profiles of extinction and backscatter coefficients reveal that both α(z) and β(z) decrease more than 75% within the lowermost 2 km. Yearly‐averaged lidar ratios increase from about 42–48 sr in the lowermost 2 km to between 67–72 sr in the air masses above 2 km. The changes in lidar ratios are indicative of changes in the physical characteristics of the monitored aerosols and suggest that over the monitoring site, the lowermost air masses (z < 2 km) are on average characterized by a larger concentration of particles leading to S values typical of marine aerosols, while the elevated air masses (z > 2 km) are characterized by lidar ratios typical of continental aerosol type. The seasonal cycle analysis reveals that the average maximum height zM at which aerosols are detected by the lidar that is about 5 km in spring‐summer, and decreases up to about 3 km in autumn‐winter. Monthly AODs span the 0.16–0.26 range in autumn‐winter and the 0.26–0.4 range in spring‐summer. The scarce renovation of air masses, occurring in spring‐summer as a consequence of the weather stability, favours the accumulation of the atmospheric aerosol particles and may account for the larger AODs and zM values.

Stratospheric residence time and its relationship to mean age

Transport inaccuracies in stratospheric models are a major source of uncertainty in predicting the environmental impact of trace gases with stratospheric source, such as emissions from high‐flying aircraft. Because there are no observed tracers of stratospheric aircraft emissions, a direct evaluation of the models' transport of the emissions is not possible. Here we examine the relationship between the stratospheric residence time τR for tracers of midlatitude stratosphere source and the mean age Γ, a transport diagnostic for which observations are available and have been used to evaluate stratospheric models. Employing a representation of the stratosphere that includes the basic kinematic features of the global circulation, we find that τR and Γ are correlated over a range of plausible circulations, but that the correlation is imperfect. A major (but not sole) limitation on Γ as a proxy for τR is the midlatitude tropopause height ZM. Elevating ZM reduces τR significantly, while Γ is only weakly affected. The relationship between τR and Γ seen among the participants of a recent stratospheric model intercomparison is consistent with this analysis.

How Far is Far Enough?: The Fetch Requirements for Micrometeorological Measurement of Surface Fluxes

Abstract Recent model estimates of the flux footprint are used to examine the fetch requirements for accurate micro-meteorological measurement of surface fluxes of passive, conservative scalars within the surface flux layer. The required fetch is quantified by specifying an acceptable ratio of the measured flux to the local surface flux. When normalized by the measurement height zm, the fetch is found to be a strong function of atmospheric stability as quantified by zm/L, where L is the Obukhov length, and a weaker function of the normalized measurement height zm/zo, where zo is the roughness length. Stable conditions are found to require a much greater fetch than do unstable conditions, and the fetch required for even moderately stable conditions is for many situations considerably greater than 100 times the measurement height.

Footprint estimation for scalar flux measurements in the atmospheric surface layer

The flux footprint is the contribution, per unit emission, of each element of a surface area source to the vertical scalar flux measured at height z m ; it is equal to the vertical flux from a unit surface point source. The dependence of the flux footprint on crosswind location is shown to be identical to the crosswind concentration distribution for a unit surface point source; an analytic dispersion model is used to estimate the crosswind-integrated flux footprint. Based on the analytic dispersion model, a normalized crosswind-integrated footprint is proposed that principally depends on the single variable z/z m , where z is a measure of vertical dispersion from a surface source. The explicit dependence of the crosswind-integrated flux footprint on downwind distance, thermal stability and surface roughness is contained in the dependence of z on these variables. By also calculating the flux footprint with a Lagrangian stochastic dispersion model, it is shown that the normalized flux footprint is insensitive to the analytic model assumption of a self-similar vertical concentration profile.

Studies of Energy and Gas Exchange within Crop Canopies (9)

The canopy photosynthesis and the CO2 environment within a crop canopy are studied numerically by employing the model based on transfer equation of CO2 within the canopy. The transfer of CO2 can be expressed by-d/dz(KdC/dz)=-fL(z)p(z)+fL(z)rp, where p(z) is CO2 uptake intensity of leaves, rp respiration intensity of leaves, fL(z) leaf area density function, K transfer coefficient and C concentration of CO2 in the air. Numerical computations were made on an electric computer (Tosbac 3400) to give profiles of CO2 concentration and cumulative CO2 flux profiles. Iterative formulae (5) and (6) were used for numerical integration of the transfer equation of CO2. The following relations are assumedp=Dc, max⋅C(Q/a+Q), rp=const=αp∞, K=KH-δ(H-z), Q=QHk/1-τexp{-k∫HzfL(z′)dz′}, where Dc, max is the effective exchange velocity for CO2 exchange between ambient air and photosynthetic action center in leaves under sufficiently high light intensity, Q intensity of short-wave radiation on leaves, KH transfer coefficient at the canopy top (z=H), QH intensity of short-wave radiation at the canopy top, k extinction coefficient, τ, transmissibility of leaves for short-wave radiation and a, α and δ proportionality constants. The boundary conditions used in the computations are expressed by Eq. (4).1. CO2 profiles within a model canopy are presented in Fig. 1. The top half of Fig. 1 shows CO2 profiles within the canopy (LAI=Ft=4.0) as a function of radiation intensity and transfer coefficient. The CO2 profiles as influenced by the soil CO2 flux are shown in the bottom half of Fig. 1. In the case of low transfer coefficient and high intensity of short-wave radiation, CO2 concentration profiles are characterized by a minimum in the middle layer of the canopy. The minimum value droppes to 41⋅10-8g CO2/cm3 (i.e. down to 74 per cent of the normal concentration). A similar drop of CO2 concentration was also observed in a corn canopy on calm and sunny days. The height (zm) of the minimum concentration moves towards the canopy top with decreasing radiation intensity (see Fig. 2). The dependence of the height zm on radiation intensity was well approximated by an exponential formula.2. Fig. 3 shows that the daily range of CO2 concentration decreases rapidly with increasing wind velocity and approaches about 10ppm with wind velocity of about 6m/sec. A similar conclusion was reached in a slightly different approach to the problems (UCHIJIMA et al. 1967). The relation between the daily range of CO2 concentration at the canopy top and the leaf area index was well fitted to a rectangular hyperbolic equation (Eq. 4). Increase of the extinction coefficient and the transfer coefficient leads to decrease in the maximum daily range of CO2 concentration at the canopy top. The daily range of CO2 concentration within the canopy increased gradually with the canopy depth.3. Fig. 8 gives profiles of cumulative flux of CO2 in the canopy in relation to the canopy denseness, radiation intensity and extinction coefficient. The profiles presented hear are of the same general patterns as those determined experimentally in a corn canopy (INOUE et al. 1968).