Estimation of the friction velocity in stably stratified boundary-layer flows over hills

A method is suggested for the calculation of the friction velocity for stable turbulent boundary-layer flow over hills. The method is tested using a continuous upstream mean velocity profile compatible with the propagation of gravity waves, and is incorporated into the linear model of Hunt, Leibovich and Richards with the modification proposed by Hunt, Richards and Brighton to include the effects of stability, and the reformulated solution of Weng for the near-surface region. Those theoretical results are compared with results from simulations using a non-hydrostatic microscale-mesoscale two-dimensional numerical model, and with field observations for different values of stability. These comparisons show a considerable improvement in the behaviour of the theoretical model when the friction velocity is calculated using the method proposed here, leading to a consistent variation of the boundary-layer structure with stability, and better agreement with observational and numerical data.

Internal wave drag in stratified flow over mountains on a beta plane

The impact of the variation of the Coriolis parameter f on the drag exerted by internal Rossby-gravity waves on elliptical mountains is evaluated using linear theory, assuming constant wind and static stability and a beta-plane approximation. Previous calculations of inertia-gravity wave drag are thus extended in an attempt to establish a connection with existing studies on planetary wave drag, developed primarily for fluids topped by a rigid lid. It is found that the internal wave drag for zonal westerly flow strongly increases relative to that given by the calculation where f is assumed to be a constant, particularly at high latitudes and for mountains aligned meridionally. Drag increases with mountain width for sufficiently wide mountains, reaching values much larger than those valid in the non-rotating limit. This occurs because the drag receives contributions from a low wavenumber range, controlled by the beta effect, which accounts for the drag amplification found here. This drag amplification is shown to be considerable for idealized analogues of real mountain ranges, such as the Himalayas and the Rocky mountains, and comparable to the barotropic Rossby wave drag addressed in previous studies.

Linear criteria for gravity-wave breaking in resonant stratified flow over a ridge

Using linear theory, it is shown that, in resonant flow over a 2D mountain ridge, such as exists when a layer of uniform wind is topped by an environmental critical level, the conditions for internal gravity-wave breaking are different from those determined in previous studies for non-resonant flows. For Richardson numbers in the shear layer not exceeding 2.25, two zones of flow overturning exist, respectively below and downstream and above and upstream of the expected locations. Flow overturning occurs for values of the dimensionless height of the ridge smaller than those required for a uniform wind profile. These results may have implications for the physical understanding of high-drag states.

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z_1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z_1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z_1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region z < z_1, while drag minima correspond to destructive interference. The reflection coefficient at the interface z = z_1 increases as Ri decreases. The critical level, z_c, plays no role in the drag amplification. A preliminary numerical treatment of nonlinear effects is presented, where z_c appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood.

Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

Terahertz pulse imaging of stratified architectural materials for cultural heritage studies

Terahertz pulse imaging (TPI) is a novel noncontact, nondestructive technique for the examination of cultural heritage artifacts. It has the advantage of broadband spectral range, time-of-flight depth resolution, and penetration through optically opaque materials. Fiber-coupled, portable, time-domain terahertz systems have enabled this technique to move out of the laboratory and into the field. Much like the rings of a tree, stratified architectural materials give the chronology of their environmental and aesthetic history. This work concentrates on laboratory models of stratified mosaics and fresco paintings, specimens extracted from a neolithic excavation site in Catalhoyuk, Turkey, and specimens measured at the medieval Eglise de Saint Jean-Baptiste in Vif, France. Preparatory spectroscopic studies of various composite materials, including lime, gypsum and clay plasters are presented to enhance the interpretation of results and with the intent to aid future computer simulations of the TPI of stratified architectural material. The breadth of the sample range is a demonstration of the cultural demand and public interest in the life history of buildings. The results are an illustration of the potential role of TPI in providing both a chronological history of buildings and in the visualization of obscured wall paintings and mosaics.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Lightning-induced extensive charge sheets provide long range electrostatic thunderstorm detection

By combining electrostatic measurements of lightning-induced electrostatic field changes with radio frequency lightning location, some field changes from exceptionally distant lightning events are apparent which are inconsistent with the usual inverse cube of distance. Furthermore, by using two measurement sites, a transition zone can be identified beyond which the electric field response reverses polarity. For these severe lightning events, we infer a horizontally extensive charge sheet above a thunderstorm, consistent with a mesospheric halo of several hundred kilometers’ extent.

Electronic charge transfer between ceria surfaces and gold adatoms: a GGA+U investigation

We use density functional theory calculations with Hubbard corrections (DFT+U) to investigate electronic aspects of the interaction between ceria surfaces and gold atoms. Our results show that Au adatoms at the (111) surface of ceria can adopt Au0, Au+ or Au� electronic configurations depending on the adsorption site. The strongest adsorption sites are on top of the surface oxygen and in a bridge position between two surface oxygen atoms, and in both cases charge transfer from the gold atom to one of the Ce cations at the surface is involved. Adsorption at other sites, including the hollow sites of the surface, and an O–Ce bridging site, is weaker and does not involve charge transfer. Adsorption at an oxygen vacancy site is very strong and involves the formation of an Au� anion. We argue that the ability of gold atoms to stabilise oxygen vacancies at the ceria surface by moving into the vacancy site and attracting the excess electrons of the defect could be responsible for the enhanced reducibility of ceria surfaces in the presence of gold. Finally, we rationalise the differences in charge transfer behaviour from site to site in terms of the electrostatic potential at the surface and the coordination of the species.

A self-calibrating electrometer for atmospheric charge measurements from a balloon platform

Charged aerosol particles and water droplets are abundant throughout the lower atmosphere, and may influence interactions between small cloud droplets. This note describes a small, disposable sensor for the measurement of charge in non-thunderstorm cloud, which is an improvement of an earlier sensor [K. A. Nicoll and R. G. Harrison, Rev. Sci. Instrum. 80, 014501 (2009)]. The sensor utilizes a self-calibrating current measurement method. It is designed for use on a free balloon platform alongside a standard meteorological radiosonde, measuring currents from 2 fA to 15 pA and is stable to within 5 fA over a temperature range of 5 °C to −60 °C. During a balloon flight with the charge sensor through a stratocumulus cloud, charge layers up to 40 pC m−3 were detected on the cloud edges.

Irreversible compressible work and APE dissipation in turbulent stratified fluid

Although it plays a key role in the theory of stratified turbulence, the concept of available potential energy (APE) dissipation has remained until now a rather mysterious quantity, owing to the lack of rigorous result about its irreversible character or energy conversion type. Here, we show by using rigorous energetics considerations rooted in the analysis of the Navier-Stokes for a fully compressible fluid with a nonlinear equation of state that the APE dissipation is an irreversible energy conversion that dissipates kinetic energy into internal energy, exactly as viscous dissipation. These results are established by showing that APE dissipation contributes to the irreversible production of entropy, and by showing that it is a part of the work of expansion/contraction. Our results provide a new interpretation of the entropy budget, that leads to a new exact definition of turbulent effective diffusivity, which generalizes the Osborn-Cox model, as well as a rigorous decomposition of the work of expansion/contraction into reversible and irreversible components. In the context of turbulent mixing associated with parallel shear flow instability, our results suggests that there is no irreversible transfer of horizontal momentum into vertical momentum, as seems to be required when compressible effects are neglected, with potential consequences for the parameterisations of momentum dissipation in the coarse-grained Navier-Stokes equations.

RuII(α-diimine) or RuIII(α-diimine·–)? Structural, spectroscopic, and theoretical evidence for the stabilization of a prominent metal-to-Ligand charge- transfer excited-state configuration in the ground state

The new compounds [Ru(R-DAB)(acac)2] (R-DAB = 1,4-diorganyl- 1,4-diazabuta-1,3-diene; R = tert-butyl, 4-methoxyphenyl, 2,6-dimethylphenyl; acac– = 2,4-pentanedionate) exhibit intrachelate ring bond lengths 1.297charge-transfer absorption band in the visible region and by DFT calculations. Oxidation of the compounds occurs mainly at the R-DAB·– radical ligand to produce UV/Vis/NIR and electron paramagnetic resonance (EPR) spectroelectrochemically detectable RuIII species, whereas the reduction proceeds less reversibly and yields predominantly (R-DAB)-ligand-based spin for the 4-methoxyphenyl derivative, measured at low temperature. The results are discussed with respect to metal-to-ligand chargetransfer (MLCT) excited states of conventional (α-diimine)- ruthenium(II) complexes and in view of other (α-diimine)- metal complexes with ambiguous oxidation-state assignments.

On the validity of single-parcel energetics to assess the importance of internal energy and compressibility effects in stratified fluids

It is often assumed on the basis of single-parcel energetics that compressible effects and conversions with internal energy are negligible whenever typical displacements of fluid parcels are small relative to the scale height of the fluid (defined as the ratio of the squared speed of sound over gravitational acceleration). This paper shows that the above approach is flawed, however, and that a correct assessment of compressible effects and internal energy conversions requires considering the energetics of at least two parcels, or more generally, of mass conserving parcel re-arrangements. As a consequence, it is shown that it is the adiabatic lapse rate and its derivative with respect to pressure, rather than the scale height, which controls the relative importance of compressible effects and internal energy conversions when considering the global energy budget of a stratied fluid. Only when mass conservation is properly accounted for is it possible to explain why available internal energy can account for up to 40 percent of the total available potential energy in the oceans. This is considerably larger than the prediction of single-parcel energetics, according to which this number should be no more than about 2 percent.

Terahertz analysis of stratified wall plaster at buildings of cultural importance across Europe

Terahertz (THz) radiation is being developed as a tool for the analysis of cultural heritage, and due to recent advances in technology is now available commercially in systems which can be deployed for field analysis. The radiation is capable of penetrating up to one centimetre of wall plaster and is delivered in ultrafast pulses which are reflected from layers within this region. The technique is non-contact, non-invasive and non-destructive. While sub-surface radar is able to penetrate over a metre of wall plaster, producing details of internal structures, infrared and ultraviolet techniques produce information about the surface layers of wall plaster. THz radiation is able to provide information about the interim region of up to approximately one centimetre into the wall surface. Data from Chartres Cathedral, France, Riga Dome Cathedral, Latvia, and Chartreuse du Val de Bénédiction, France is presented each with different research questions. The presence of sub-surface paint layers was expected from documentary evidence, dating to the 13th Century, at Chartres Cathedral. In contrast, at the Riga Dome Cathedral surface painting had been obscured as recently as 1941 during the Russian occupation of Latvia using white lead-based paint. In the 13th Century, wall paintings at the Chapel of the Frescos, Chartreuse du Val de Benediction in Villeneuve les Avignon were constructed using sinopia under-painting on plaster covering uneven stonework.. This paper compares and contrasts the ability of THz radiation to provide information about sub-surface features in churches and Cathedrals across Europe by analysing depth based profiles gained from the reflected signal. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).