The methane hydrate formation and the resource estimate resulting from free gas migration in seeping seafloor hydrate stability zone

It is a typical multiphase flow process for hydrate formation in seeping seafloor sediments. Free gas can not only be present but also take part in formation of hydrate. The volume fraction of free gas in local pore of hydrate stable zone (HSZ) influences the formation of hydrate in seeping seafloor area, and methane flux determines the abundance and resource of hydrate-bearing reservoirs. In this paper, a multiphase flow model including water (dissolved methane and salt)-free gas hydrate has been established to describe this kind of flow-transfer-reaction process where there exists a large scale of free gas migration and transform in seafloor pore. In the order of three different scenarios, the conversions among permeability, capillary pressure, phase saturations and salinity along with the formation of hydrate have been deducted. Furthermore, the influence of four sorts of free gas saturations and three classes of methane fluxes on hydrate formation and the resource has also been analyzed and compared. Based on the rules drawn from the simulation, and combined information gotten from drills in field, the methane hydrate(MH) formation in Shenhu area of South China Sea has been forecasted. It has been speculated that there may breed a moderate methane flux below this seafloor HSZ. If the flux is about 0.5 kg m-2 a-1, then it will go on to evolve about 2700 ka until the hydrate saturation in pore will arrive its peak (about 75%). Approximately 1.47 109 m3 MH has been reckoned in this marine basin finally, is about 13 times over preliminary estimate.

Effects and numerical analysis of argon gas flow on the oxygen concentration in Czochralski silicon single crystal growth

Argon gas, as a protective environment and carrier of latent heat, has an important effect on the temperature distribution in crystals and melts. Numeric simulation is a potent tool for solving engineering problems. In this paper, the relationship between argon gas flow and oxygen concentration in silicon crystals was studied systematically. A flowing stream of argon gas is described by numeric simulation for the first time. Therefore, the results of experiments can be explained, and the optimum argon flow with the lowest oxygen concentration can be achieved. (C) 2002 Elsevier Science B.V. All rights reserved.

Pool Boiling on Wire in Microgravity - What Have We Learned

In the past years, steady pool boiling of degassed R113 on thin platinum wires has been studied systematically in our lab, including experiments in long-term microgravity aboard RS-22, in short-term microgravity in the Drop Tower Beijing / NMLC, and in normal gravity on the ground. Slight enhancement of nucleate boiling heat transfer is observed in microgravity, while dramatic changes of bubble behaviors are much evident. The value of CHF in microgravity is lower than that in normal gravity, but it can be predicted well by the Lienhard-Dhir correlation, although the dimensionless radius in the present case is far beyond its initial application range. The scaling of CHF with gravity is thus much different from the traditional viewpoint. Considering the influence of the Marangoni effects, the different characteristics of bubble behaviors in microgravity have been explained. A new bubble departure model has also been proposed, which can predict the whole observation both in microgravity and in normal gravity.

THERMAL AND MECHANICAL-PROPERTIES OF PHENOLPHTHALEIN POLYETHERSULFONE POLY(PHENYLENE SULFIDE) BLENDS

The thermal and mechanical properties of phenolphthalein polyethersulfone/poly(phenylene sulfide) (PES-C/PPS) blends were studied using a differential scanning calorimeter, a dynamic mechanical analyzer, and mechanical characterization. The morphologies of fracture surfaces were observed by scanning electron microscopy. The blends are multiphase systems with strong interaction between the two phases. It is of interest that, although the strength and ductility of PPS are lower than those of PES-C, the addition of PPS can improve markedly the impact strength of PES-C without changing its higher strength. The PPS can also act as a flow aid for PES-C. (C) 1995 John Wiley and Sons, Inc.

二氧化碳在孔隙咸水层中多相流动数值模拟研究

There has been a growing concern about the use of fossil fuels and its adverse effects on the atmospheric greenhouse and ecological environment. A reduction in the release rate of CO2 into the atmosphere poses a major challenge to the land ecology of China. The most promising way of achieving CO2 reduction is to dispose of CO2 in deep saline aquifers. Deep aquifers have a large potential for CO2 sequestration in geological medium in terms of volume and duration. Through the numerical simulation of multiphase flow in a porous media, the transformation and motion of CO2 in saline aquifers has been implemented under various temperature and hydrostatic pressure conditions, which plays an important role to the assessment of the reliability and safety of CO2 geological storage. As expected, the calculated results can provide meaningful and scientific information for management purposes. The key problem to the numerical simulation of multiphase flow in a porous media is to accurately capture the mass interface and to deal with the geological heterogeneity. In this study, the updated CE/SE (Space and time conservation element and solution element) method has been proposed, and the Hybrid Particle Level Set method (HPLS) has extended for multiphase flows in porous medium, which can accurately trace the transformation of the mass interface. The benchmark problems have been applied to evaluate and validate the proposed method. In this study, the reliability of CO2 storage in saline aquifers in Daqingzi oil field in Sunlong basin has been discussed. The simulation code developed in this study takes into account the state for CO2 covering the triple point temperature and pressure to the supercritical region. The geological heterogeneity has been implemented, using the well known geostatistical model (GSLIB) on the base of the hard data. The 2D and 3D model have been set up to simulate the CO2 multiphase flow in the porous saline aquifer, applying the CE/SE method and the HPLS method .The main contents and results are summarized as followings. (1) The 2D CE/SE method with first and second –order accuracy has been extended to simulate the multiphase flow in porous medium, which takes into account the contribution of source and sink in the momentum equation. The 3D CE/SE method with the first accuracy has been deduced. The accuracy and efficiency of the proposed CE/SE method have been investigated, using the benchmark problems. (2) The hybrid particle level set method has been made appropriate and extended for capturing the mass interface of multiphase flows in porous media, and the numerical method for level set function calculated has been formulated. (3) The closed equations for multiphase flow in porous medium has been developed, adept to both the Darcy flow and non-Darcy flow, getting over the limitation of Reynolds number to the calculation. It is found that Darcy number has a decisive influence on pressure as well as velocity given the Darcy number. (4) The new Euler scheme for numerical simulations of multiphase flows in porous medium has been proposed, which is efficient and can accurately capture the mass interface. The artificial compressibility method has been used to couple the velocities and pressure. It is found that the Darcy number has determinant effects on the numerical convergence and stability. In terms of the different Darcy numbers, the coefficient of artificial compressibility and the time step have been obtained. (5) The time scale of the critical instability for critical CO2 in the saline aquifer has been found, which is comparable with that of completely CO2 dissolved saline aquifer. (6) The concept model for CO2 multiphase flows in the saline aquifer has been configured, based on the temperature, pressure, porosity as well as permeability of the field site .Numerical simulation of CO2 hydrodynamic trapping in saline aquifers has been performed, applying the proposed CE/SE method. The state for CO2 has been employed to take into account realistic reservoir conditions for CO2 geological sequestration. The geological heterogeneity has been sufficiently treated , using the geostatistical model. (7) It is found that the Rayleigh-Taylor instability phenomenon, which is associated with the penetration of saline fluid into CO2 fluid in the direction of gravity, has been observed in CO2 multiphase flows in the saline aquifer. Development of a mushroom-type spike is a strong indication of the formation of Kelvin-Helmholtz instability due to the developed short wavelength perturbations present along the interface and parallel to the bulk flow. Additional key findings: the geological heterogeneity can distort the flow convection. The ascending of CO2 can induce the persistent flow cycling effects. The results show that boundary conditions of the field site have determinant effects on the transformation and motion of CO2 in saline aquifers. It is confirmed that the proposed method and numerical model has the reliability to simulate the process of the hydrodynamic trapping, which is the controlling mechanism for the initial period of CO2 storage at time scale of 100 years.

Parametrical modeling and design optimization of blood plasma separation device with microchannel mechanism

This paper presents an analysis of biofluid behavior in a T-shaped microchannel device and a design optimization for improved biofluid performance in terms of particle liquid separation. The biofluid is modeled with single phase shear rate non-Newtonian flow with blood property. The separation of red blood cell from plasma is evident based on biofluid distribution in the microchannels against various relevant effects and findings, including Zweifach-Fung bifurcation law, Fahraeus effect, Fahraeus-Lindqvist effect and cell free phenomenon. The modeling with the initial device shows that this T-microchannel device can separate red blood cell from plasma but the separation efficiency among different bifurcations varies largely. In accordance with the imbalanced performance, a design optimization is conducted. This includes implementing a series of simulations to investigate the effect of the lengths of the main and branch channels to biofluid behavior and searching an improved design with optimal separation performance. It is found that changing relative lengths of branch channels is effective to both uniformity of flow rate ratio among bifurcations and reduction of difference of the flow velocities between the branch channels, whereas extending the length of the main channel from bifurcation region is only effective for uniformity of flow rate ratio.

Examination of the flow rheological and textural properties of polymer gels composed of poly(methylvinylether-co-maleic anhydride) and poly(vinylpyrrolidone): rheological and mathematical interpretation of textural parameters.

The purpose of this study was to mathematically characterize the effects of defined experimental parameters (probe speed and the ratio of the probe diameter to the diameter of sample container) on the textural/mechanical properties of model gel systems. In addition, this study examined the applicability of dimensional analysis for the rheological interpretation of textural data in terms of shear stress and rate of shear. Aqueous gels (pH 7) were prepared containing 15% w/w poly(methylvinylether-co-maleic anhydride) and poly(vinylpyrrolidone) (PVP) (0, 3, 6, or 9% w/w). Texture profile analysis (TPA) was performed using a Stable Micro Systems texture analyzer (model TA-XT 2; Surrey, UK) in which an analytical probe was twice compressed into each formulation to a defined depth (15 mm) and at defined rates (1, 3, 5, 8, and 10 mm s-1), allowing a delay period (15 s) between the end of the first and beginning of the second compressions. Flow rheograms were performed using a Carri-Med CSL2-100 rheometer (TA Instruments, Surrey, UK) with parallel plate geometry under controlled shearing stresses at 20.0°?±?0.1°C. All formulations exhibited pseudoplastic flow with no thixotropy. Increasing concentrations of PVP significantly increased formulation hardness, compressibility, adhesiveness, and consistency. Increased hardness, compressibility, and consistency were ascribed to enhanced polymeric entanglements, thereby increasing the resistance to deformation. Increasing probe speed increased formulation hardness in a linear manner, because of the effects of probe speed on probe displacement and surface area. The relationship between formulation hardness and probe displacement was linear and was dependent on probe speed. Furthermore, the proportionality constant (gel strength) increased as a function of PVP concentration. The relationship between formulation hardness and diameter ratio was biphasic and was statistically defined by two linear relationships relating to diameter ratios from 0 to 0.4 and from 0.4 to 0.563. The dramatically increased hardness, associated with diameter ratios in excess of 0.4, was accredited to boundary effects, that is, the effect of the container wall on product flow. Using dimensional analysis, the hardness and probe displacement in TPA were mathematically transformed into corresponding rheological parameters, namely shearing stress and rate of shear, thereby allowing the application of the power law (??=?k?n) to textural data. Importantly, the consistencies (k) of the formulations, calculated using transformed textural data, were statistically similar to those obtained using flow rheometry. In conclusion, this study has, firstly, characterized the relationships between textural data and two key instrumental parameters in TPA and, secondly, described a method by which rheological information may be derived using this technique. This will enable a greater application of TPA for the rheological characterization of pharmaceutical gels and, in addition, will enable efficient interpretation of textural data under different experimental parameters.

High-frequency oscillations in a solar active region observed with the RAPID DUAL IMAGER

High-cadence, synchronized, multiwavelength optical observations of a solar active region (NOAA 10794) are presented. The data were obtained with the Dunn Solar Telescope at the National Solar Observatory/Sacramento Peak using a newly developed camera system: the rapid dual imager. Wavelet analysis is undertaken to search for intensity related oscillatory signatures, and periodicities ranging from 20 to 370 s are found with significance levels exceeding 95%. Observations in the H-α blue wing show more penumbral oscillatory phenomena when compared to simultaneous G-band observations. The H-α oscillations are interpreted as the signatures of plasma motions with a mean velocity of 20 km s-1. The strong oscillatory power over H-α blue-wing and G-band penumbral bright grains is an indication of the Evershed flow with frequencies higher than previously reported.

Avaliação do débito máximo da tosse (peak cough flow) na doença pulmonar obstrutiva crónica

Resumo Objectivos: Avaliação da Tosse em doentes com Doença Pulmonar Obstrutiva Crónica (DPOC). Identificar e determinar a relação dos factores preditivos que contribuem para a deterioração da capacidade de tosse nestes indivíduos. Tipo de estudo: Estudo observacional descritivo de natureza transversal. Definição dos casos: Os critérios de diagnóstico da DPOC são o quadro clínico e o Gold standard para diagnóstico da DPOC – a espirometria. População-alvo: Todos os utentes com patologia primária de DPOC diagnosticada que se desloquem ao serviço de função respiratória do Hospital de Viseu, para realizar provas. Método de Amostragem: Foi utilizada uma amostra aleatória constituída por todos os indivíduos, que cumpriram os critérios de inclusão, conscientes e colaborantes, que aceitaram participar neste estudo. Dimensão da amostra: Uma amostra de 55 indivíduos que se deslocaram ao serviço de função respiratória, entre Janeiro e Junho de 2009, para realizar provas de função respiratória. Condução do estudo: Os utentes que aceitaram participar neste estudo foram sujeitos a um questionário de dados clínicos e realizaram 5 testes: índice de massa corporal (IMC), estudo funcional respiratório e gasometria arterial, avaliação da força dos músculos respiratórios (PImax e PEmax) e avaliação do débito máximo da tosse (Peak Cough Flow). Análise estatística: Foram obtidos dados caracterizadores da amostra em estudo, sendo posteriormente correlacionado o valor de débito máximo da tosse (Peak Cough Flow) com os resultados obtidos para as avaliações do IMC, estudo funcional respiratório, PImax e PEmax, gasometria, avaliação da capacidade de Tosse e número de internamentos no último ano por agudização da DPOC. Tendo sido encontrados os valores de correlação entre o Peak Cough Flow e os restantes parâmetros. Resultados: Após análise dos resultados, foram obtidos os valores de Peak Cough Flow para a população com DPOC e verificou-se valores diminuídos em comparação com os valores normais da população, tendo-se verificado maiores valores de PCF em indivíduos do sexo masculino, em comparação aos valores do sexo feminino. Foi analisada a relação entre o PCF e a idade, peso, altura e IMC, não tendo sido encontrada relação, dado que a tosse não apresenta uma variação segundo os valores antropométricos, tal como a relação com os valores espirométricos. Quanto aos parâmetros funcionais respiratórios foram analisadas as relações com o PCF. Verificou-se relações significativas entre o PCF e o FEV1, a FVC, o PEF, apresentando uma relação positiva, onde maiores valores destes parâmetros estão correlacionados com maiores picos de tosse. Quanto a RAW e RV, o PCF apresenta uma relação negativa, onde uma maior resistência da via aérea ou doentes mais hiperinsuflados leva a menores valores de PCF. Por outro lado não foi encontrada relação entre o PCF e a FRC e o TLC. Quanto à força dos músculos respiratórios, verificou-se relação significativa com o PImax e a PEmax em que a fraqueza ao nível dos músculos respiratórios contribuem para um menor valor de PCF. Relativamente aos valores da gasometria arterial, verificou-se relação entre o PCF e a PaO2 de forma positiva, em que doentes hipoxémicos apresentam menores valores de tosse, e a PaCO2, de forma negativa, em que os doentes hipercápnicos apresentam menores valores de PCF tendo sido verificada relação entre o PCF e o pH e sO2. Quanto à relação entre o número de internamentos por agudização da DPOC no último ano e o PCF verificou-se uma relação significativa, onde um menor valor de PCF contribui para uma maior taxa de internamento por agudização da DPOC. Conclusão: Este conjunto de conclusões corrobora a hipótese inicialmente formulada, de que o Peak Cough Flow se encontra diminuído nos indivíduos com Doença Pulmonar Obstrutiva Crónica onde a variação do PCF se encontra directamente relacionada com os parâmetros funcionais respiratórios, com a força dos músculos respiratórios e com os valores de gasometria arterial. ABSTRACT: Aims: Cough evaluation in Chronic Obstructive Pulmonary Disease (COPD) patients. Identify and determine the relation of the predictive factors that contribute to the cough capacity degradation in this type of patients. Type of study: Descriptive observational study of transversal nature. Case definition: The COPD diagnosis criteria are the clinical presentation and the gold standard to the COPD diagnosis- the Spirometry. Target Population: Every patients, with primary pathology of COPD diagnosed, who went to the respiratory function service of Viseu hospital to perform tests. Sampling Method: It was used a random sample constituted by all the, conscious and cooperating individuals, who complied with the inclusion criteria and who accepted to make part of this study. Sample size: A sample of 55 individuals that went to the respiratory function service between January and June 2009 to perform respiratory function tests. Study: The patients who accepted to make part of this study were submitted to a clinical data questionary and performed 5 tests: body mass index (BMI), respiratory functional study, arterial blood gas level, evaluation of respiratory muscles strength (maximal inspiratory pressure (MIP) and maximum expiratory pressure (MEP)), and Peak Cough Flow evaluation. Statistic Analysis: Were obtained characterizing data of the sample in study, and later correlated the value of the Peak Cough Flow with the results from the evaluation of the body mass index (BMI), the respiratory functional study the MIP and MEP, the arterial blood gas level and also with the ability to cough evaluation and the number of hospitalizations in the last year for COPD exacerbations. The values of correlation between the Peak Cough Flow and the other parameters were found. Results: After analyzing the results, were obtained the values of Peak Cough Flow for the population with COPD. There were decreased values compared with the population normal values, having been found higher values of PCF in males compared to female values. It was analyzed the relation between the PCF and the age, weight, height and BMI but no relation was found on account of the fact that the cough does not show a variation according to anthropometric parameters, such as the relation with spirometric values. As for the respiratory functional parameters were analyzed relations with the PCF. There were significant relations between the PCF and FEV1, the FVC, the PEF, presenting a positive relation, where higher values of these parameters are correlated with higher incidence of cough. Concerning the RAW and RV, the PCF has a negative relation, in which a higher airway resistance or in more hyperinflated patients, leads to lower values of PCF. On the other hand no correlation was found between the PCF and the FRC and TLC. Regarding the respiratory muscle strength, there was a significant relation with the MIP and MEP, in which the weakness at the level of respiratory muscles contribute to a lower value of PCF. For values of arterial blood gas level, there was no relation between the PCF and PaO2, in a positive way, in which patients with hypoxemia present lower values of cough, and PaCO2, in a negative way in which hypercapnic patients had lower values of PCF, having being founded a relation between the PCF and the pH and sO2. As for the relation between the number of hospitalizations for COPD exacerbation in the last year and the PCF was found a significant relation, in which a smaller value of PCF contributes to a higher rate of hospitalization for COPD exacerbation. Conclusion: This set of findings supports the hypothesis first formulated that Peak Cough Flow is decreased in individuals with Chronic Obstructive Pulmonary Disease, in which the variation of the PCF is directly related to the respiratory function parameters, the strength of respiratory muscles and the values of arterial blood gases.

La danse comme outil d'intervention sociale : exploration pratique et théorique de l'intervention sociale auprès de préadolescents et adolescents

Plusieurs hypothèses planant autour de la danse, des cultures juvéniles et de l’intervention permettent de repérer l’existence d’une multiplicité de regards, mais sans rapport apparent entre eux. Les tenants du courant humaniste s'intéressent à la forme et à la structure de la danse en tant qu'art dans les pays de culture occidentale. Les tenants de l’approche anthropologique y voient un instrument de socialisation qui permet de créer, refléter ou renforcer des liens entre les participants, tout en transmettant les valeurs de la culture héritée (Blacking: 1963, Spencer: 1985, Ward: 1993, Bourdieu: 2002). D’un point de vue somatique, la danse permet la prédominance du corps sur l’esprit, car l’apprentissage se fait généralement par imitation (Guilcher: 1963, Faure: 2004). Dans ce cas, les participants sont appelés à « s’ouvrir à autrui » en montrant et en apprenant des autres, créant une circularité dans leurs échanges sur un rythme qui « unit » les participants (Schott-Billman: 2001, Hampartzoumian : 2004). Ce projet se pose comme une réflexion sur le ou les sens de la danse comme outil d’intervention sociale auprès de jeunes amateurs amenés à vivre des inégalités sociales. En privilégiant un contexte d’atelier, où certains ajustements sont tolérés par l’enseignant, un espace de créativité s’organise de manière informelle face à un objectif donné : une représentation publique dansée. Cet angle d’approche s’inspire de « la métaphore du bricolage » au sujet des cultures populaires par M. De Certeau (1980), où la créativité populaire est repérable dans « les manières de faire avec » les produits imposés par la culture dominante, la politique, l’économie et les enjeux sociaux dominants. Ainsi, le participant qui « perturbe » les règles d’usage d’une intervention prescrite n’est pas un sujet en marge de la société. C’est par des actions pareilles qu’il prend sa place comme acteur social. Cet événement permet « d’in-corps-porer » le double discours existant entre les danses de représentation et les danses populaires chez les participants.

Tropical cyclones in a T159 Resolution Global Climate Model: comparison with observations and re-analyses

Tropical cyclones have been investigated in a T159 version of the MPI ECHAM5 climate model using a novel technique to diagnose the evolution of the 3-dimensional vorticity structure of tropical cyclones, including their full life cycle from weak initial vortex to their possible extra-tropical transition. Results have been compared with reanalyses (ERA40 and JRA25) and observed tropical storms during the period 1978-1999 for the Northern Hemisphere. There is no indication of any trend in the number or intensity of tropical storms during this period in ECHAM5 or in re-analyses but there are distinct inter-annual variations. The storms simulated by ECHAM5 are realistic both in space and time, but the model and even more so the re-analyses, underestimate the intensities of the most intense storms (in terms of their maximum wind speeds). There is an indication of a response to ENSO with a smaller number of Atlantic storms during El Niño in agreement with previous studies. The global divergence circulation responds to El Niño by setting up a large-scale convergence flow, with the center over the central Pacific with enhanced subsidence over the tropical Atlantic. At the same time there is an increase in the vertical wind shear in the region of the tropical Atlantic where tropical storms normally develop. There is a good correspondence between the model and ERA40 except that the divergence circulation is somewhat stronger in the model. The model underestimates storms in the Atlantic but tends to overestimate them in the Western Pacific and in the North Indian Ocean. It is suggested that the overestimation of storms in the Pacific by the model is related to an overly strong response to the tropical Pacific SST anomalies. The overestimation in 2 the North Indian Ocean is likely to be due to an over prediction in the intensity of monsoon depressions, which are then classified as intense tropical storms. Nevertheless, overall results are encouraging and will further contribute to increased confidence in simulating intense tropical storms with high-resolution climate models.

A SAXS study of flow alignment of thermotropic liquid crystal mixtures

We report on the capillary flow behaviour of thermotropic liquid crystal mixtures containing 4-n-octyl-4'-cyanobiphenyl (8CB) and 4-n-pentyl-4'-cyanobiphenyl (5CB). The liquid crystal mixtures are studied in the Nematic (N) and Smectic (SA) phases at room temperature. Polarised optical microscopy (POM), rheology and simultaneous X-ray diffraction (XRD)/capillary flow experiments are performed to characterise the system. Polarised optical microscopy reveals a dramatic change in optical texture when the 5CB content is increased from 20 to 30% in the mixtures. X-ray diffraction results show that the system goes through a SA-N phase transition, such that the mixtures are smectic for 10-20% 5CB and nematic for 30-90% 5CB. Smectic mixtures flow with the layers aligned along the flow direction (mesogens perpendicular to flow) while nematic mixtures flow with the mesogens aligned in the flow direction. Simultaneous XRD/shear flow experiments show that the SA-N transition is independent of the flow rate in the range 1-6 ml min-1. The correlation length of the liquid crystal order decreases with increasing 5CB content. Rheology is used to prove that the correlation length behaviour is related to a reduction in the viscosity of the mixture.

On the momentum fluxes associated with mountain waves in directionally sheared flows

The direct impact of mountain waves on the atmospheric circulation is due to the deposition of wave momentum at critical levels, or levels where the waves break. The first process is treated analytically in this study within the framework of linear theory. The variation of the momentum flux with height is investigated for relatively large shears, extending the authors’ previous calculations of the surface gravity wave drag to the whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation is used to treat inviscid, steady, nonrotating, hydrostatic flow with directional shear over a circular mesoscale mountain, for generic wind profiles. This approximation must be extended to third order to obtain momentum flux expressions that are accurate to second order. Since the momentum flux only varies because of wave filtering by critical levels, the application of contour integration techniques enables it to be expressed in terms of simple 1D integrals. On the other hand, the momentum flux divergence (which corresponds to the force on the atmosphere that must be represented in gravity wave drag parameterizations) is given in closed analytical form. The momentum flux expressions are tested for idealized wind profiles, where they become a function of the Richardson number (Ri). These expressions tend, for high Ri, to results by previous authors, where wind profile effects on the surface drag were neglected and critical levels acted as perfect absorbers. The linear results are compared with linear and nonlinear numerical simulations, showing a considerable improvement upon corresponding results derived for higher Ri.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.