Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

Bed sediment entrainment by streamflow: State of the science

In fluvial sedimentology, bed sediment entrainment by streamflow has a decisive role in controlling several fluvial processes. Owing to its huge practical importance, the subject has been painstakingly explored for over a century. However, a detailed understanding of the mechanism of the bed sediment entrainment phenomenon achieved hitherto is far from complete. The central theme of bed sediment entrainment is occupied by the sediment entrainment threshold, which varies enormously in its qualitative definition, identification and quantification encompassing a broad range of spatiotemporal scales. This article presents the state of the science of the entrainment of non‐cohesive bed sediments under a steady‐unidirectional streamflow. It begins with the diverse definitions and representations of the entrainment threshold criterion from both qualitative and quantitative perspectives, scrutinising its suitability and ambit of applicability. Then, the effects of energetic factors that drive the entrainment threshold criterion are critically appraised. The indispensable mechanisms of bed sediment entrainment, including the theoretical background and modelling strategies, the role of turbulent bursting phenomenon and the phenomenological perspective into the origin of the scaling laws of sediment entrainment, are explained. Throughout the article, special emphasis is given to the strengths and weaknesses of the current state of the science. In addition, a deliberate attempt is made to invoke the thought‐provoking ideas on the multifarious features of bed sediment entrainment. Finally, the innovative perspectives on the bed sediment entrainment are provided and the concluding remarks are made, elucidating the major challenges and suggesting the prospective ways to resolve them as a future scope of research.     

Laboratory and Numerical Studies of the Convective Boundary Layer Capped by a Strong Inversion

The convective boundary layer (CBL) with a wide range of stability is simulated experimentally using a thermally stratified wind tunnel, and numerically by direct numerical simulation (DNS). The turbulence structures and flow characteristics of various CBL flows, capped by a strong temperature inversion and affected by surface shear, are investigated. The various vertical profiles of turbulence statistics similar to those from the observed CBL in the field are successfully simulated in both the wind-tunnel experiment and in DNS. The comparison of the wind-tunnel data and DNS results with those of atmospheric observations and water-tank studies shows the crucial dependence of the turbulence statistics in the upper part of the layer on the strength of the inversion layer, as well as the modification of the CBL turbulence regime by the surface shear.     

Parameterization of Sheared Convective Entrainment in the First-Order Jump Model: Evaluation Through Large-Eddy Simulation

In this note, two different approaches are used to estimate the entrainment-flux to surface-flux ratio for a sheared convective boundary layer (CBL); both are derived under the framework of the first-order jump model (FOM). That suggested by Sun and Wang (SW approach) has the advantage that there is no empirical constant included, though the dynamics are described in an implicit manner. The second, which was proposed by Kim et al. and Pino et al. (KP approach), explicitly characterizes the dynamics of the sheared entrainment, but uncertainties are induced through the empirical constants. Their performances in parameterizing the CBL growth rate are compared and discussed, and a new value of the parameter A ₃ in the KP approach is suggested. Large-eddy simulation (LES) data are employed to test both approaches: simulations are conducted for the CBL growing under varying conditions of surface roughness, free-atmospheric stratification, and wind shear, and data used when the turbulence is in steady state. The predicted entrainment rates in each case are tested against the LES data. The results show that the SW approach describes the evolution of the sheared CBL quite well, and the KP approach also reproduces the growth of the CBL reasonably, so long as the value of A ₃ is modified to 0.6.     

Countergradient Fluxes of Conserved Variables in the Clear convective and Stratocumulus-topped Boundary Layer: The role of the Entrainment Flux

Large-eddy simulations of a clear convective boundary layer (CBL)and a stratocumulus-topped boundary layer are studied. Bottom-upand a top-down scalars were included in the simulations, and theprinciple of linear superposition of variables was applied toreconstruct the fields of any arbitrary conserved variable.This approach allows a systematic analysis of countergradient fluxesas a function of the flux ratio, which is defined as the ratio betweenthe entrainment flux and the surface flux of the conserved quantity.In general, the turbulent flux of an arbitrary conserved quantityis counter to the mean vertical gradient if the heights where thevertical flux and the mean vertical gradient change sign do notcoincide. The regime where the flux is countergradient is thereforebounded by the so-called zero-flux and zero-gradient heights. Becausethe vertical flux changes sign only if the entrainment flux has anopposite sign to the surface flux, countergradient fluxes arepredominantly found for negative flux ratios. In the CBL the fluxratio for the virtual potential temperature is, to a good approximation,constant, and equal to -0.2. Only if the moisture contribution to thevirtual potential temperature is negligibly small will the flux ratio forthe potential temperature be equal to this value. Otherwise, theflux ratio for the potential temperature can have any arbitrary(negative) value, and, as a consequence, the fluxes for thepotential temperature and the virtual potential temperature willbe countergradient at different heights. As a practical application ofthe results, vertical profiles of the countergradient correction termfor different entrainment-to-surface-flux ratios are discussed.     

流动环境中倾斜浮力射流的积分方法

给出了基于积分方法的一种倾斜浮力射流的数学模型,且流速、密度和浓度差剖面假定为高斯分布,并导出了用来封闭该数学模型的较为完全的掺入率公式.用计算精度较高的有限分析法计算这类定解问题,计算结果与试验资料基本吻合.     

An alternative depth-integrated formulation for granular avalanches over temporally varying topography with small curvature

An alternative formulation is proposed for deriving depth-integrated equations for gravity-driven granular avalanches over a non-trivial topography with small curvature. The coordinate system of Bouchut and Westdickenberg (2004 Bouchut, F and Westdickenberg, M. 2004. Gravity driven shallow water models for arbitrary topography. Commun. Math. Sci., 2: 359–389. [Crossref] , [Google Scholar]) is combined with the unified coordinate (UC) method, so that it can evolve in accordance with the entrainment–deposition processes at the basal surface. The resultant mass and momentum equations are formulated as a conservation system of the Cartesian components of the conservative physical variables. The motion of the flows is driven by the basal topography-induced pressure, pressure gradient, and resisted by the basal friction. The best benefit of this formulation is that it greatly simplifies the computation of the varying coordinate orientations. The features and advantages of this formulation are illustrated by the sliding-mass examples where we simulate the motion of a finite mass of granular material sliding down an inclined chute, running through a transition zone, and being deposited onto a horizontal plane.     

Entrainment of circumpolar water in the Indian Ocean region of the Antarctic

The net influx of the circumpolar water on the western (approximately along 10°E) and eastern (approximately 115°E) boundaries of the Indian Ocean, adopting the method of Montgomery and Stroup is computed on bivariate distribution of potential thermosteric anomaly and salinity to identify the characteristics of the flux. The zonal flux at both the boundaries indicates an alternate strong easterly and westerly flow between 36°S and 45°S, south of which the flow is mainly easterly but weak up to 56°S. At the western boundary the easterly flow is 146 Sv and westerly is 98.07 Sv, while at the eastern boundary (115°E) the corresponding fluxes are 123.46 Sv and 27.20 Sv respectively, indicating a net outflux of 48.33 Sv. This water should have been accounted by the melting of ice and influx of the Equatorial Pacific Ocean Water.     

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.     

Seismic reflection along the path of the Mediterranean Undercurrent

Seismic reflection profiling is applied to the study of large scale physical oceanographic processes in the Gulf of Cádiz and western Iberian coast, coinciding with the path of the Mediterranean Undercurrent. The multi-channel seismic reflection method provides clear images of thermohaline fine structure with a horizontal resolution approximately two orders of magnitude higher than CTD casting. The seismic data are compared with co-located historical oceanographic data. Three seismic reflectivity zones are identified: North Atlantic Central Water, Mediterranean Water and North Atlantic Deep Water. Seismic evidence for the path of the Mediterranean Undercurrent is found in the near-slope reflectivity patterns, with rising reflectors between about 500 and 1500 m. However, the core of the undercurrent is largely transparent. Seismic images show that central and, particularly, intermediate Mediterranean Waters have fine structure coherent over horizontal distances of several tens of kilometers. However, the intensity of the reflectors, and their horizontal coherence, decreases downstream. This change in seismic reflectivity is probably the result of diminished vertical thermohaline contrasts between adjacent water masses, so that double-diffusion processes become unable to sustain temperature and salinity staircases. Comparison of root-mean-square seismic amplitudes with temperature and salinity differences between the Mediterranean Undercurrent and the overlying central waters suggests a causal relationship between observed thermohaline fine structure and true seismic amplitudes. We estimate that, within this intermediate water stratum, impedance contrasts are mainly controlled by sound speed contrasts (a factor between 3.5 and 10 times larger than density contrasts), which are mainly controlled by temperature contrasts (a factor between 1.5 and 5 times larger than salinity contrasts).