Discussion and Applications of Slab Models of the Convective Boundary Layer based on Turbulent Kinetic Energy Budget Parameterisations

Some of the most widely used slab model formulations for applications in the convective boundary layer are analysed and discussed. Three main classes are identified based on different approximations of the turbulent kinetic energy equation. The models appear to be quite insensitive to the initial values for boundary-layer height, and temperature discontinuity at the boundary-layer top. The slab models are applied to a case of sea-land transition from the literature, and a case of convective boundary layer time evolution over a homogeneous terrain at San Pietro Capofiume (Bologna, Italy). The different parameterisations turn out to be almost equivalent for the cases studied. The models generally underpredict the value for the height, while all give very good estimates for the mean mixed-layer temperature.     

Scaling Variances of Scalars in a Convective Boundary Layer Under Different Entrainment Regimes

For the presentation and analysis of atmospheric boundary-layer (ABL) data, scales are used to non-dimensionalise the observed quantities and independent variables. Usually, the ABL height, surface sensible heat flux and surface scalar flux are used. This works well, so long as the absolute values of the entrainment ratio for both the scalar and temperature are similar. The entrainment ratio for temperature naturally ranges from −0.4 to −0.1. However, the entrainment ratio for passive scalars can vary widely in magnitude and sign. Then the entrainment flux becomes relevant as well. The only customary scalar scale that takes into account both the surface flux and the entrainment flux is the bulk scalar scale, but this scale is not well-behaved for large negative entrainment ratios and for an entrainment ratio equal to −1. We derive a new scalar scale, using previously published large-eddy simulation results for the convective ABL. The scale is derived under the constraint that scaled scalar variance profiles are similar at those heights where the variance producing mechanisms are identical (i.e., either near the entrainment layer or near the surface). The new scale takes into account that scalar variance in the ABL is not only related to the surface flux of that scalar, but to the scalar entrainment flux as well. Furthermore, it takes into account that the production of variance by the entrainment flux is an order of magnitude larger than the production of variance by the surface flux (per unit flux). Other desirable features of the new scale are that it is always positive (which is relevant when scaling standard deviations) and that the scaled variances are always of order 1–10.     

Parameterization of Entrainment in a Sheared Convective Boundary Layer Using a First-order Jump Model

Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.The part of this work was done when the first author visited at NCAR.     

LIDAR DETERMINATION OF THE ENTRAINMENT ZONE THICKNESS AT THE TOP OF THE UNSTABLE MARINE ATMOSPHERIC BOUNDARY LAYER

The thickness of the entrainment zone at the top of the marine atmosphericboundary layer (MABL) has been documented by an airborne lidar on twoconsecutive days during a cold-air outbreak episode over the Mediterranean.In addition to the lidar observations, in situ turbulent flux measurementsat three levels in the MABL were made by a second aircraft. The flights' tracksare broken down in segments 25–30 km long and the data are filtered for theparametrization of turbulent entrainment in the MABL at scales smaller thana few kilometres. The structural parameters of the entrainment zone aredetermined by lidar from the distributions of the instantaneous MABL topheight. The average values Ph0 and Ph2 of the cumulativeprobability distributions are used to define the bottom and top heights of the entrainment zone h0 and h2, respectively. The parameters h0 andh2 are calculated by reference to a linear vertical buoyancy flux profilein the framework of a first-order jump model. The model is constrained by bothlidar and in situ data to determine Ph0 and Ph2 and so h0and h2. In unstable conditions theaverage fraction Ph0 is estimated to be 6.0 ± 1%. It is shown to beslightly sensitive to the presence of cloud at small cloud fractions.The mean value of the ratio of the inversion level buoyancy flux to the surfacebuoyancy flux ARv is found to range from 0.15 to 0.30 depending on the shearin the MABL. The average value is 0.22 ± 0.05. Our resultsare in good agreement with previous analysis at comparable spatial scales.In purely convective conditions, the value of ARv given by theparametrizations fitted to our results is about 0.10–0.12, a value smallerthan the commonly accepted value of 0.2. When compared to previousparametrization results, our proportionality constant for the mechanicalproduction of turbulent kinetic energy is also found to be scaled down, ingood agreement with large-eddy simulation results. It is suggestedthat mesoscale organized motions in the MABL is the source of thisdifference.     

On the analytical solution for two-dimensional convective plume and analytical modeling of the entrainment zone thickness

Analytical solution for two-dimensional thermal plume updraft velocity is obtained under the assumption of a uniform temperature excess inside the plume. In this way, the thermal plume motion is modeled in both mixed layer and entrainment zone. Also, a semi-analytical solution is obtained using an empirical model for the plume temperature excess in the mixed layer. In addition, an analytical model for entrainment zone thickness is obtained by computing the overshoot distance of the modeled plumes, and a semi-analytical model by using the empirical model for plume temperature. By using a nonlinear profile for the lapse rate in the surface layer based on the Monin–Obukhov similarity theory, our model predicts that the characteristics of the surface layer plays an important role in the structure of the entrainment zone. Finally, our solutions for plume velocity allow us to consider the effect of the lateral entrainment on the plume excess temperature and velocity in the convective boundary layer. It is shown that the lateral entrainment has an important role on the plume dynamics and the solutions in the zero entrainment limit offer large overestimated values for the plume velocity, which also result in overestimated values of the entrainment zone thickness.     

Erosion and morphology of a debris flow caused by a glacial lake outburst flood,Western Norway

This article documents a 240,000-m³ debris flow resulting from a glacial lake outburst flood in Fjærland, Western Norway, May 8, 2004. The event started when a glacial lake breached a moraine ridge. The ensuing debris flow was able to erode material along its path, increasing in volume from about 25,000 to 240,000 m³ before depositing about 3 km from its starting point. Field investigations, pre- and post-flow aerial photographs as well as airborne laser scanning (LIDAR) were used to describe and investigate the flow. The most striking and unusual feature of this case study is the very pronounced erosion and bulking. We have made a detailed study of this aspect. Erosion and entrainment is quantified and the final volume of the debris flow is determined. We also present geometrical and sedimentological features of the final deposit. Based on the Fjærland data, we suggest that a self-sustaining mechanism might partly explain the extreme growth of debris flows traversing soft terrain.     

Physical controls on mixing and transport within rising submarine hydrothermal plumes: A numerical simulation study

A computational fluid dynamics (CFD) model was developed to simulate the turbulent flow and species transport of deep-sea high temperature hydrothermal plumes. The model solves numerically the density weighted unsteady Reynolds-averaged Navier–Stokes equations and energy equation and the species transport equation. Turbulent entrainment and mixing is modeled by a k–ε turbulence closure model. The CFD model explicitly considers realistic vent chimney geometry, vent exit fluid temperature and velocity, and background stratification. The model uses field measurements as model inputs and has been validated by field data. These measurements and data, including vent temperature and plume physical structure, were made in the ABE hydrothermal field of the Eastern Lau Spreading Center. A parametric sensitivity study based on this CFD model was conducted to determine the relative importance of vent exit velocity, background stratification, and chimney height on the mixing of vent fluid and seawater. The CFD model was also used to derive several important scalings that are relevant to understanding plume impact on the ocean. These scalings include maximum plume rise height, neutrally buoyant plume height, maximum plume induced turbulent diffusivity, and total plume vertically transported water mass flux. These scaling relationships can be used for constructing simplified 1-dimensional models of geochemistry and microbial activity in hydrothermal plumes. Simulation results show that the classical entrainment assumptions, typically invoked to describe hydrothermal plume transport, only apply up to the vertical level of ~0.6 times the maximum plume rise height. Below that level, the entrainment coefficient remains relatively constant (~0.15). Above that level, the plume flow consists of a pronounced lateral spreading flow, two branches of inward flow immediately above and below the lateral spreading, and recirculation flanking the plume cap region. Both turbulent kinetic energy and turbulence dissipation rate reach their maximum near the vent; however, turbulent viscosity attains its maximum near the plume top, indicating strong turbulent mixing in that region. The parametric study shows that near vent physical conditions, including chimney height and fluid exit velocity, influence plume mixing from the vent orifice to a distance of ~10 times the vent orifice diameter. Thus, physical parameters place a strong kinetic constraint on the chemical reactions occurring in the initial particle-forming zone of hydrothermal plumes.     

Initiation conditions for debris flows generated by runoff at Chalk Cliffs, central Colorado

We have monitored initiation conditions for six debris flows between May 2004 and July 2006 in a 0.3 km² drainage basin at Chalk Cliffs; a band of hydrothermally-altered quartz monzonite in central Colorado. Debris flows were initiated by water runoff from colluvium and bedrock that entrained sediment from rills and channels with slopes ranging from about 14° to 45°. The availability of channel material is essentially unlimited because of thick channel fill and refilling following debris flows by rock fall and dry ravel processes. Rainfall exceeding I = 6.61(D)^− 0.77, where I is rainfall intensity (mm/h), and D is duration (h), was required for the initiation of debris flows in the drainage basin. The approximate minimum runoff discharge from the surface of bedrock required to initiate debris flows in the channels was 0.15 m³/s. Colluvium in the basin was unsaturated immediately prior to (antecedent) and during debris flows. Antecedent, volumetric moisture levels in colluvium at depths of 1 cm and 29 cm ranged from 4–9%, and 4–7%, respectively. During debris flows, peak moisture levels in colluvium at depths of 1 cm and 29 cm ranged from 10–20%, and 4–12%, respectively. Channel sediment at a depth of 45 cm was unsaturated before and during debris flows; antecedent moisture ranged from 20–22%, and peak moisture ranged from 24–38%. Although we have no measurements from shallow rill or channel sediment, we infer that it was unsaturated before debris flows, and saturated by surface-water runoff during debris flows.Our results allow us to make the following general statements with regard to debris flows generated by runoff in semi-arid to arid mountainous regions: 1) high antecedent moisture levels in hillslope and channel sediment are not required for the initiation of debris flows by runoff, 2) locations of entrainment of sediment by successive runoff events can vary within a basin as a function of variations in the thickness of existing channel fill and the rate of replenishment of channel fill by rock fall and dry ravel processes following debris flows, and 3) rainfall and simulated surface-water discharge thresholds can be useful in understanding and predicting debris flows generated by runoff and sediment entrainment.     

The entrainment factor in froth flotation: Model for particle size and other operating parameter effects

Accurately estimating entrainment is crucial when predicting flotation performance as it is essential for determining the concentrate grade achieved. It has been found previously that the amount of gangue entrained is proportional to the water recovery; this proportionality is referred to as the entrainment factor. Experimentally it has been found that entrainment is a strong function of particle size, as well as being dependent on other cell operating parameters such as froth depth and air rate.A simplified theoretical model for entrainment is developed which includes the effects of liquid motion and content, particle settling and particle dispersion. First, a detailed one-dimensional differential model for the entrainment factor is developed and solved numerically. Thereafter, a simplified analytical expression for the entrainment factor is produced which is a good approximation to the more detailed one-dimensional model. Both these models are shown to predict closely experimental trends for entrainment as a function of particle size and froth depth.     

Hydrodynamic behaviour of Taupo 1800a pumice: implications for the sedimentology of remobilized pyroclasts

Abstract Large‐scale explosive eruptions from silicic caldera volcanoes can generate huge volumes of pyroclastic material in terrestrial and marine environments. On land, erosion, remobilization and redeposition of this debris is predominantly carried out by running water in the form of precipitation run‐off. Conversely, in the submarine realm, both primary emplacement and subsequent remobilization are influenced by the presence of water as a transporting medium. Despite this, and the number of studies devoted to volcaniclastic sedimentation, relatively little attention has been paid to the hydrodynamic behaviour of the particles themselves, which ought to underpin any assessment of transport or depositional process. This is crucial, as many volcanic particles exhibit variable density: according to composition and as functions of differing degrees of vesiculation and the extent to which pore space is filled by water and/or gaseous phases during transport and deposition. Investigation of the physical and hydrodynamic properties of Taupo 1800a pumice, with reference to sedimentary facies developed during the eruption aftermath, shows that, although buoyant when dry, when sufficiently waterlogged, cool pumice clasts will sink and behave more like quartzo‐feldspathic material. Saturation is apparently achieved by a combination of rapid capillary flooding of large interconnected vesicles and slower diffusional air–water exchange in smaller pores. Low saturated pumice densities result in lower settling velocities and easier entrainment by tractional currents than those for equivalent‐sized quartzo‐feldspathic or crystal/lithic particles. Fine‐grained pumice is conversely harder to entrain because of the frictional interlocking of angular particles. These unusual properties of temporary buoyancy, variable saturation, low density and size‐dependent cohesion complicate interpretations of the depositional setting and energy of pumiceous sediments and give rise to several unique facies. These findings have implications not only for the analysis of remobilized pyroclastic facies in terrestrial and marine environments, but also for primary depositional processes during subaqueous explosive volcanism.