On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.

Functional model for catecholase-like activity: A mechanistic approach with manganese(III) complexes of salen type Schiff base ligands

Three new Mn(III) complexes [MnL1(OOCH)(OH2)] (1), [MnL2(OH2)(2)][Mn2L22(NO2)(3)] (2) and [Mn2L21(NO2)(2)] (3) (where H2L1 = H(2)Me(2)Salen = 2,7-bis(2-hydroxyphenyl)-2,6-diazaocta-2,6-diene and H2L2 = H(2)Salpn = 1,7-bis(2-hydroxyphenyl)-2,6-diazahepta-1,6-diene) have been synthesized. X-ray crystal structure analysis reveals that 1 is a mononuclear species whereas 2 contains a mononuclear cationic and a dinuclear nitrite bridged (mu-1 kappa O:2 kappa O') anionic unit. Complex 3 is a phenoxido bridged dimer containing terminally coordinated nitrite. Complexes 1-3 show excellent catecholase-like activity with 3,5-di-tert-butylcatechol (3,5-DTBC) as the substrate. Kinetic measurements suggest that the rate of catechol oxidation follows saturation kinetics with respect to the substrate and first order kinetics with respect to the catalyst. Formation of bis(mu-oxo)dimanganese(III,III) as an intermediate during the course of reaction is identified from ESI-MS spectra. The characteristic six line EPR spectra of complex 2 in the presence of 3,5-DTBC supports the formation of manganese(II)-semiquinonate as an intermediate species during the catalytic oxidation of 3,5-DTBC.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Physically consistent responses of the global atmospheric hydrological cycle in models and observations

Robust and physically understandable responses of the global atmospheric water cycle to a warming climate are presented. By considering interannual responses to changes in surface temperature (T), observations and AMIP5 simulations agree on an increase in column integrated water vapor at the rate 7 %/K (in line with the Clausius­Clapeyron equation) and of precipitation at the rate 2-­3 %/K (in line with energetic constraints). Using simple and complex climate models, we demonstrate that radiative forcing by greenhouse gases is currently suppressing global precipitation (P) at ~ -0.15 %/decade. Along with natural variability, this can explain why observed trends in global P over the period 1988-2008 are close to zero. Regional responses in the global water cycle are strongly constrained by changes in moisture fluxes. Model simulations show an increased moisture flux into the tropical wet region at 900 hPa and an enhanced outflow (of smaller magnitude) at around 600 hPa with warming. Moisture transport explains an increase in P in the wet tropical regions and small or negative changes in the dry regions of the subtropics in CMIP5 simulations of a warming climate. For AMIP5 simulations and satellite observations, the heaviest 5-day rainfall totals increase in intensity at ~15 %/K over the ocean with reductions at all percentiles over land. The climate change response in CMIP5 simulations shows consistent increases in P over ocean and land for the highest intensities, close to the Clausius-Clapeyron scaling of 7 %/K, while P declines for the lowest percentiles, indicating that interannual variability over land may not be a good proxy for climate change. The local changes in precipitation and its extremes are highly dependent upon small shifts in the large-scale atmospheric circulation and regional feedbacks.

An evaluation of the spatiotemporal structure of large-scale European drought within the HiGEM climate model

We compare the characteristics of synthetic European droughts generated by the HiGEM1 coupled climate model run with present day atmospheric composition with observed drought events extracted from the CRU TS3 data set. The results demonstrate consistency in both the rate of drought occurrence and the spatiotemporal structure of the events. Estimates of the probability density functions for event area, duration and severity are shown to be similar with confidence > 90%. Encouragingly, HiGEM is shown to replicate the extreme tails of the observed distributions and thus the most damaging European drought events. The soil moisture state is shown to play an important role in drought development. Once a large-scale drought has been initiated it is found to be 50% more likely to continue if the local soil moisture is below the 40th percentile. In response to increased concentrations of atmospheric CO2, the modelled droughts are found to increase in duration, area and severity. The drought response can be largely attributed to temperature driven changes in relative humidity. 1 HiGEM is based on the latest climate configuration of the Met Office Hadley Centre Unified Model (HadGEM1) with the horizontal resolution increased to 1.25 x 0.83 degrees in longitude and latitude in the atmosphere and 1/3 x 1/3 degrees in the ocean.

Understanding advances in the simulation of intraseasonal variability in the ECMWF model. Part II: the application of process-based diagnostics

In Part I of this study it was shown that moving from a moisture-convergent- to a relative-humidity-dependent organized entrainment rate in the formulation for deep convection was responsible for significant advances in the simulation of the Madden – Julian Oscillation (MJO) in the ECMWF model. However, the application of traditional MJO diagnostics were not adequate to understand why changing the control on convection had such a pronounced impact on the representation of the MJO. In this study a set of process-based diagnostics are applied to the hindcast experiments described in Part I to identify the physical mechanisms responsible for the advances in MJO simulation. Increasing the sensitivity of the deep convection scheme to environmental moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid troposphere. Due to the modified precipitation – moisture relationship more moisture is able to build up, which effectively preconditions the tropical atmosphere for the t ransition t o d eep convection. R esults from this study suggest that a tropospheric moisture control on convection is key to simulating the interaction between the convective heating and the large-scale wave forcing associated with the MJO.

Chemistry–climate model simulations of twenty-first century stratospheric climate and circulation changes

The response of stratospheric climate and circulation to increasing amounts of greenhouse gases (GHGs) and ozone recovery in the twenty-first century is analyzed in simulations of 11 chemistry–climate models using near-identical forcings and experimental setup. In addition to an overall global cooling of the stratosphere in the simulations (0.59 6 0.07 K decade21 at 10 hPa), ozone recovery causes a warming of the Southern Hemisphere polar lower stratosphere in summer with enhanced cooling above. The rate of warming correlates with the rate of ozone recovery projected by the models and, on average, changes from 0.8 to 0.48 Kdecade21 at 100 hPa as the rate of recovery declines from the first to the second half of the century. In the winter northern polar lower stratosphere the increased radiative cooling from the growing abundance of GHGs is, in most models, balanced by adiabatic warming from stronger polar downwelling. In the Antarctic lower stratosphere the models simulate an increase in low temperature extremes required for polar stratospheric cloud (PSC) formation, but the positive trend is decreasing over the twenty-first century in all models. In the Arctic, none of the models simulates a statistically significant increase in Arctic PSCs throughout the twenty-first century. The subtropical jets accelerate in response to climate change and the ozone recovery produces awestward acceleration of the lower-stratosphericwind over theAntarctic during summer, though this response is sensitive to the rate of recovery projected by the models. There is a strengthening of the Brewer–Dobson circulation throughout the depth of the stratosphere, which reduces the mean age of air nearly everywhere at a rate of about 0.05 yr decade21 in those models with this diagnostic. On average, the annual mean tropical upwelling in the lower stratosphere (;70 hPa) increases by almost 2% decade21, with 59% of this trend forced by the parameterized orographic gravity wave drag in the models. This is a consequence of the eastward acceleration of the subtropical jets, which increases the upward flux of (parameterized) momentum reaching the lower stratosphere in these latitudes.

Model-measurement comparison of mesospheric temperature inversions, and a simple theory for their occurrence

Mesospheric temperature inversions are well established observed phenomena, yet their properties remain the subject of ongoing research. Comparisons between Rayleigh-scatter lidar temperature measurements obtained by the University of Western Ontario's Purple Crow Lidar (42.9°N, 81.4°W) and the Canadian Middle Atmosphere Model are used to quantify the statistics of inversions. In both model and measurements, inversions occur most frequently in the winter and exhibit an average amplitude of ∼10 K. The model exhibits virtually no inversions in the summer, while the measurements show a strongly reduced frequency of occurrence with an amplitude about half that in the winter. A simple theory of mesospheric inversions based on wave saturation is developed, with no adjustable parameters. It predicts that the environmental lapse rate must be less than half the adiabatic lapse rate for an inversion to form, and it predicts the ratio of the inversion amplitude and thickness as a function of environmental lapse rate. Comparison of this prediction to the actual amplitude/thickness ratio using the lidar measurements shows good agreement between theory and measurements.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

Heat and moisture budgets from airborne measurements and high-resolution model simulations

High-resolution simulations with a mesoscale model are performed to estimate heat and moisture budgets of a well-mixed boundary layer. The model budgets are validated against energy budgets obtained from airborne measurements over heterogeneous terrain in Western Germany. Time rate of change, vertical divergence, and horizontal advection for an atmospheric column of air are estimated. Results show that the time trend of specific humidity exhibits some deficiencies, while the potential temperature trend is matched accurately. Furthermore, the simulated turbulent surface fluxes of sensible and latent heat are comparable to the measured fluxes, leading to similar values of the vertical divergence. The analysis of different horizontal model resolutions exhibits improved surface fluxes with increased resolution, a fact attributed to a reduced aggregation effect. Scale-interaction effects could be identified: while time trends and advection are strongly influenced by mesoscale forcing, the turbulent surface fluxes are mainly controlled by microscale processes.

Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation

The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number kE corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime (k →0) is theoretically derived to be E(k) ∼k5, using a quasinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads (k,p,q) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux Π(k) for k< kE can be entirely expressed by Π(-)(k), which is the total net input of energy to wave numbers k. Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log (k/kE)<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four. ©2001 The Physical Society of Japan

A time-invariant visco-elastic windkessel model relating blood flow and blood volume

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure–volume relationship of blood vessels is treated as a state variable dependent on the rate of change of CBV, producing hysteresis in the pressure–volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems.