A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

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.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: III. Quasi-instantaneous convection responses in the Cowley-Lockwood paradigm

Using a numerical implementation of the Cowley and Lockwood (1992) model of flow excitation in the magnetosphere–ionosphere (MI) system, we show that both an expanding (on a _12-min timescale) and a quasiinstantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley–Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: II. Measuring expansions in the ionospheric flow response

A numerical model embodying the concepts of the Cowley-Lockwood (Cowley and Lockwood, 1992, 1997) paradigm has been used to produce a simple Cowley– Lockwood type expanding flow pattern and to calculate the resulting change in ion temperature. Cross-correlation, fixed threshold analysis and threshold relative to peak are used to determine the phase speed of the change in convection pattern, in response to a change in applied reconnection. Each of these methods fails to fully recover the expansion of the onset of the convection response that is inherent in the simulations. The results of this study indicate that any expansion of the convection pattern will be best observed in time-series data using a threshold which is a fixed fraction of the peak response. We show that these methods used to determine the expansion velocity can be used to discriminate between the two main models for the convection response to a change in reconnection.

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of lactating dairy cows

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant.

Label-free enrichment of avian Leucocytozoon using flow cytometric sorting

The group of haemosporidian parasites is of general interest to basic and applied science, since several species infect mammals, leading to malaria and associated disease symptoms. Although the great majority of haemosporidian parasites appear in bird hosts, as in the case of Leucocytozoon buteonis, there is little genomic information about genetic aspects of their co-evolution with hosts. Consequently, there is a high need for parasite-enrichment strategies enabling further analyses of the genomes, namely without exposure to DNA-intercalating dyes. Here, we used flow cytometry without an additional labelling step to enrich L. buteonis from infected buzzard blood. A specific, defined area of two-dimensional scattergramms was sorted and the fraction was further analysed. The successful enrichment of L. buteonis in the sorted fraction was demonstrated by Giemsa-staining and qPCR revealing a clear increase of parasite-specific genes, while host-specific genes were significantly decreased. This is the first report describing a labelling-free enrichment approach of L. buteonis from infected buzzard blood. The enrichment of parasites presented here is free of nucleic acid-intercalating dyes which may interfere with fluorescence-based methods or subsequent sequencing approaches.

Coupling an aerosol box model with one-dimensional flow: a tool for understanding observations of new particle formation events

Field observations of new particle formation and the subsequent particle growth are typically only possible at a fixed measurement location, and hence do not follow the temporal evolution of an air parcel in a Lagrangian sense. Standard analysis for determining formation and growth rates requires that the time-dependent formation rate and growth rate of the particles are spatially invariant; air parcel advection means that the observed temporal evolution of the particle size distribution at a fixed measurement location may not represent the true evolution if there are spatial variations in the formation and growth rates. Here we present a zero-dimensional aerosol box model coupled with one-dimensional atmospheric flow to describe the impact of advection on the evolution of simulated new particle formation events. Wind speed, particle formation rates and growth rates are input parameters that can vary as a function of time and location, using wind speed to connect location to time. The output simulates measurements at a fixed location; formation and growth rates of the particle mode can then be calculated from the simulated observations at a stationary point for different scenarios and be compared with the ‘true’ input parameters. Hence, we can investigate how spatial variations in the formation and growth rates of new particles would appear in observations of particle number size distributions at a fixed measurement site. We show that the particle size distribution and growth rate at a fixed location is dependent on the formation and growth parameters upwind, even if local conditions do not vary. We also show that different input parameters used may result in very similar simulated measurements. Erroneous interpretation of observations in terms of particle formation and growth rates, and the time span and areal extent of new particle formation, is possible if the spatial effects are not accounted for.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Under flow impedimetric measurements using magnetic particles for label-free detection affinity target

The necessity to adapt sensors based on electrochemical techniques for high throughput analysis control increases the interest to develop new analytical systems able to perform measurements under buffer now. In this report we explored the possibility of employing a new system to make impedimetric measurements to detect the interaction between proteins and small molecules. The well-known biotin-streptavidin interaction was adopted to evaluate the proposed assembly. This system allows us to perform experiments under flow. Magnetic beads functionalized with streptavidin were used and first characterized using AFM and FTIR. Non-faradic impedance spectroscopy allowed the detection of the biotin-streptavidin interaction. Using our new system and under a flow of PBS buffer, 5 10-5 M of biotin was detected with a stable signal. (c) 2007 Elsevier B.V. All rights reserved.

Temperature Dynamics Investigation At Small And Shallow Lakes Using Hydrodynamic Model

A three-dimensional time-dependent hydrodynamic and heat transport model of Lake Binaba, a shallow and small dam reservoir in Ghana, emphasizing the simulation of dynamics and thermal structure has been developed. Most numerical studies of temperature dynamics in reservoirs are based on one- or two-dimensional models. These models are not applicable for reservoirs characterized with complex flow pattern and unsteady heat exchange between the atmosphere and water surface. Continuity, momentum and temperature transport equations have been solved. Proper assignment of boundary conditions, especially surface heat fluxes, has been found crucial in simulating the lake’s hydrothermal dynamics. This model is based on the Reynolds Average Navier-Stokes equations, using a Boussinesq approach, with a standard k − ε turbulence closure to solve the flow field. The thermal model includes a heat source term, which takes into account the short wave radiation and also heat convection at the free surface, which is function of air temperatures, wind velocity and stability conditions of atmospheric boundary layer over the water surface. The governing equations of the model have been solved by OpenFOAM; an open source, freely available CFD toolbox. As its core, OpenFOAM has a set of efficient C++ modules that are used to build solvers. It uses collocated, polyhedral numerics that can be applied on unstructured meshes and can be easily extended to run in parallel. A new solver has been developed to solve the hydrothermal model of lake. The simulated temperature was compared against a 15 days field data set. Simulated and measured temperature profiles in the probe locations show reasonable agreement. The model might be able to compute total heat storage of water bodies to estimate evaporation from water surface.