A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows

A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so – the terms can be included through a consistent derivation from the viscous primitive equations – and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the four cases, and the results provide some information as to the importance of dispersion and horizontal vorticity.     

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.     

Wake characterization downstream of a fog collector

The problem of wake geometry characterization downstream of a collector for getting water out of advection fog is investigated combining the results coming from wind tunnel trials and an experimental campaign in Peru (Lomas de Mejia), where a fog collection project was running. Results from a physical model of the fog collector at a 1:100 scale tested in a wind tunnel through anemometer velocity measurements and flow visualization techniques showed, at different heights from the ground, the general direction of the flow in the vicinity of the obstacle and the extension of the downstream-disturbed area. Wind speed data collection in Peru showed the reduction in wind speed depending on its intensity. The preliminary results show the utility of such an approach in order to improve the understanding of the flow motion downstream of permeable surfaces. The possibility of spatially characterizing the wake presence has a practical utilization whenever the knowledge of the geometry of the wake downstream of an obstacle is required.     

Aircraft Observations of the Development of Thermal Internal Boundary Layers and Scaling of the Convective Boundary Layer Over Non-Homogeneous Land Surfaces

This study investigates the convective boundary layer (CBL) that develops over anon-homogeneous surface under different thermal and dynamic conditions. Analysesare based on data obtained from a Russian research aircraft equipped with turbulentsensors during the GAME-Siberia experiment over Yakutsk in Siberia, from April to June 2000.Mesoscale thermal internal boundary layers (MTIBLs) that radically modified CBLdevelopment were observed under unstable atmospheric conditions. It was found thatMTIBLs strongly influenced the vertical and horizontal structures of virtual potentialtemperature, specific humidity and, most notably, the vertical sensible and latent heatfluxes. MTIBLs in the vicinity of the Lena River lowlands were confirmed by clouddistributions in satellite pictures.MTIBLs spread through the entire CBL and radically modify its structure if the CBL isunstable, and strong thermal features on the underlying surface have horizontal scalesexceeding 10 km. MTIBL detection is facilitated through the use of special parameterslinking shear stress and convective motion.The turbulent structure of the CBL with and without MTIBLs was scaled usingthe mosaic or flux aggregate approach. A non-dimensional parameterL_Rau/L_hetero (where L_Rau is Raupach's length and L_hetero is the horizontal scale of the surface heterogeneity)estimates the application limit of similarity and local similarity scaling models forthe mosaic parts over the surface. Normalized vertical profiles of wind speed, airtemperature, turbulent sensible and latent heat fluxes for the mosaic parts withL_RauL_hetero < 1 could be estimated by typical scalingcurves for the homogeneous CBL. Traditional similarity scaling models for the CBLcould not be applied for the mosaic parts with L_Rau/L_hetero > 1.For some horizontally non-homogeneous CBLs, horizontal sensible heat fluxes werecomparable with the vertical fluxes. The largest horizontal sensible heat fluxes occurred at the top of the surface layer and below the top of the CBL.Formerly affiliated to the Frontier Observational Research System for Global ChangeFormerly affiliated to the Frontier Observational Research System for Global Change     

Turbulent Statistics of Neutrally Stratified Flow Within and Above a Sparse Forest from Large-Eddy Simulation and Field Observations

Turbulent statistics of neutrally stratified shear-driven flow within and above a sparse forest canopy are presented from a large-eddy simulation (LES) and compared with those from observations within and above a deciduous forest with similar height and foliage density. First- and second-order moments from the LES agree with observations quite well. Third-order moments from the LES have the same sign and similar vertical patterns as those from the observations, but the LES yields smaller magnitudes of such higher-order moments. Turbulent spectra and cospectra from the LES agree well with observations above the forest. However, at the highest frequencies, the LES spectra have steeper slopes than observations. Quadrant and conditional analyses of the LES resolved-scale flow fields also agree with observations. For example, both LES and observation find that sweeps are more important than ejections for the transport of momentum within the forest, while inward and outward interaction contributions are both small, except near the forest floor. The intermittency of the transport of momentum and scalar increases with depth into the forest. Finally, ramp structures in the time series of a passive scalar at multiple levels within and above the forest show similar features to those measured from field towers. Two-dimensional (height-time cross-section) contours of the passive scalar and wind vectors show sweeps and ejections, and the characteristics of the static pressure perturbation near the ground resemble those deduced from field tower-based measurements. In spite of the limited grid resolution (2 m × 2 m × 2 m) and domain size (192 m × 192 m × 60 m) used in this LES, we demonstrate that the LES is capable of resolving the most important characteristics of the turbulent flow within and above a forest canopy.     

Parameterization and Micrometeorological Measurement of Air–Sea Gas Transfer

Because of the combination of smallconcentrations and/or small fluxes, the determinationof air–sea gas fluxes presents unusual measurementdifficulties. Direct measurements (i.e., eddycorrelation) of the fluxes are rarely attempted. Inthe last decade, there has been an intense scientificeffort to improve measurement techniques and to placebulk parameterizations of gas transfer on firmertheoretical grounds. Oceanic tracer experiments,near-surface mean concentration profiles, eddyaccumulation, and direct eddy covariance methods haveall been used. Theoretical efforts have focusedprimarily in the realm of characterizing the transferproperties of the oceanic molecular sublayer. Recentmajor field efforts organized by the U.S.A. (GASEX-98) andthe European Union (ASGAMAGE) have yielded atmospheric-derivedresults much closer to those from oceanographicmethods. In this paper, we review the physical basisof a bulk-to-bulk gas transfer parameterization thatis generalized for solubility and Schmidt number. Wealso discuss various aspects of recent sensor andtechnique developments used for direct measurementsand demonstrate experimental progress with resultsfrom ASGAMAGE and GASEX-98. It is clear that sensornoise, sensitivity, and cross talk with other speciesand even ship motion corrections still need improvement foraccurate measurements of trace gas exchange over theocean. Significant work remains to resolve issuesassociated with the effects of waves, bubbles, andsurface films.     

地球磁层顶湍动重联的数值模拟

用二维磁流体力学数值模拟研究了磁层顶的磁场湍动重联．提出了一个新的磁场湍动重联模型．数值模拟表明,如果磁层顶是一个开放系统并同时存在磁场剪切和流场剪切,当雷诺数和磁雷诺数超过某临界数值时,磁场重联具有很强的湍动特性,可产生许多不同尺度的磁岛和涡旋结构．随着雷诺数和磁雷诺数的增大和减小,大尺度结构能破碎成中小尺度结构,小尺度结构也能合并成大中尺度结构．湍动重联是涡旋诱发重联在一定条件下的过渡．依据本文的模拟结果,我们预言：磁层预可发生准定常重联、瞬时局地重联和湍动重联等多种重联过程;大中小不同尺度的结构都可以存在于磁层顶;湍动重联及其所产生的中小尺度结构在太阳风－磁层的能量、动量和质量耦合过程中可起重要作用．     

The formation of high-grade ignimbrites, I: Experiments on high- and low-concentration transport systems containing sticky particles

 High-grade ignimbrites are thought to be deposited by pyroclastic flows at temperatures exceeding minimum welding temperature or even solidus temperature. Corresponding pyroclastic-flow particles range from plastic to partially liquid and are able to aggregate or coalesce. This contrasts with particles in pyroclastic flows producing unwelded ignimbrite, which are capable of elastic grain interactions. The low aspect ratio and great areal extent of high-grade ignimbrites requires transport in a particulate state either by (a) high-concentration mass flow facilitated by fluidizing gas reducing internal friction, or by (b) expanded turbulent flow of low but downward increasing concentration. This paper presents experiments designed to investigate the effects of plastic to liquid particles on these two contrasting transport mechanisms. Gas fluidization experiments using polyethyleneglycole (PEG) powders heated above minimum sintering (T_ms) and melting (T_m) temperatures cover a wide range of fluidization velocities (U_mf>U_a>0.6·U_t) but are always in the bubbly fluidization regime similar to fluidized ignimbrite ash, where particle volume concentration outside the bubbles is high (≈10^–1). When the powders reach a critical temperature T_m≥T≥T_ms, defluidization by catastrophic particle aggregation immediately commences in both stationary and laterally moving fluidized beds as well as in experiments using mixtures of high- and low-T_m (≥30 wt.%) PEG powders, when T≥T_ms of the lower-T_m powder. This indicates that extended particulate transport at T≥T_ms is not possible at such high particle concentrations. In the turbulent flow experiments, liquid sprays of molten PEG or water, vertically injected into a high-Re (>10⁴) horizontal air flow, form a low-concentration (10^–5 to 10^–4) turbulent suspension current. Proximal formation of partially coalesced aggregates, which settle faster than individual particles, causes the measured downstream decay of sedimentation rate to be steeper than predicted by theory of single solid-particle sedimentation from turbulent suspensions. As particles become finer downstream and coalescence efficiency decreases in response to cooling, more distally formed aggregates become too small and rare to modify sedimentation-rate decay from that of suspension flows containing solid particles. The key difference between the two transport systems is particle concentration, C. Since particle collision rate R_coll∝C², collision rates in fluidized beds are so high that all particles immediately aggregate when coalescence efficiency (1≥E_coal≥0) is larger than 10^-3. Low-concentration suspensions, on the other hand, require much higher values of E_coal for significant aggregation to occur. Dilute pyroclastic flows will have higher particle volume fractions (≈10^–3) than the experimental currents, but then viscous pyroclasts should have lower coalescence efficiencies than PEG droplets. Experimental results thus support an expanded turbulent transport mechanism of pyroclastic flows generating extensive high-grade ignimbrite sheets. Received: 28 August 1996 / Accepted: 3 December 1997     

The Footprint for Estimation of Atmosphere-Surface Exchange Fluxes by Profile Techniques

The flux footprint, that is the contribution per unit emission from each element of the upwind surface area to measurement of the vertical flux of a passive scalar, is calculated for fluxes estimated by micrometeorological profile techniques. It is found that the upwind extent of the footprint for concentration-profile flux estimates is similar to that of the footprint for eddy-covariance flux measurements, when the eddy-covariance measurement is made at a height equal to the arithmetic mean of the highest and lowest profile measurement heights for stable stratification or the geometric mean for unstable stratification. The concentration-profile flux footprint depends on the ratio of the highest to the lowest measurement height, but is insensitive to the number of measurement levels. The concentration-profile flux footprint extends closer to the measurement location than does the 'equivalent eddy-covariance flux footprint, and the difference becomes more pronounced as the ratio of the profile measurement heights increases. The flux footprint for the Bowen-ratio technique is identical to that for a two-level profile measurement only for very limited circumstances. In the more general case, a flux footprint cannot be defined for the Bowen-ratio technique and the uniform upwind fetch required for representative flux measurements depends on the specific spatial distribution of surface fluxes.     

Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method

The application of autoregressive running mean filtering (RMF) and linear detrending (LDT) in the estimation of turbulent fluxes by the eddy covariance method is analysed. The systematic, as well as the random, errors of the fluxes arising from filtering and/or limited observation time effects are described. To observe negligible systematic errors in fluxes, the RMF has to be applied with moderately long time constants. However, the obtained flux values are subject to increased random errors during periods of non-stationarity and the method leads to systematic overestimation of variances. These shortcomings are not inherent in the LDT approach, which is recommended for use. But the systematic errors of fluxes due to LDT are not negligible under certain experimental conditions and have to be accounted for. The corrections are important because the relatively small errors in short-period fluxes can translate to significant errors in long-period averages. The corrections depend on the turbulence time scales, which should be preferably estimated as ensemble mean variables for a particular site.