Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

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].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Combined use of satellite estimates and rain gauge observations to generate high-quality historical rainfall time series over Ethiopia

Climate data are used in a number of applications including climate risk management and adaptation to climate change. However, the availability of climate data, particularly throughout rural Africa, is very limited. Available weather stations are unevenly distributed and mainly located along main roads in cities and towns. This imposes severe limitations to the availability of climate information and services for the rural community where, arguably, these services are needed most. Weather station data also suffer from gaps in the time series. Satellite proxies, particularly satellite rainfall estimate, have been used as alternatives because of their availability even over remote parts of the world. However, satellite rainfall estimates also suffer from a number of critical shortcomings that include heterogeneous time series, short time period of observation, and poor accuracy particularly at higher temporal and spatial resolutions. An attempt is made here to alleviate these problems by combining station measurements with the complete spatial coverage of satellite rainfall estimates. Rain gauge observations are merged with a locally calibrated version of the TAMSAT satellite rainfall estimates to produce over 30-years (1983-todate) of rainfall estimates over Ethiopia at a spatial resolution of 10 km and a ten-daily time scale. This involves quality control of rain gauge data, generating locally calibrated version of the TAMSAT rainfall estimates, and combining these with rain gauge observations from national station network. The infrared-only satellite rainfall estimates produced using a relatively simple TAMSAT algorithm performed as good as or even better than other satellite rainfall products that use passive microwave inputs and more sophisticated algorithms. There is no substantial difference between the gridded-gauge and combined gauge-satellite products over the test area in Ethiopia having a dense station network; however, the combined product exhibits better quality over parts of the country where stations are sparsely distributed.

Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

On L2 Clustering and Resetting the Null Subject Parameter in L2 Spanish: Implications and Observations.

In this article, along with others, we take the position that the Null-Subject Parameter (NSP) (Chomsky 1981; Rizzi 1982) cluster of properties is narrower in scope than some originally contended. We test for the resetting of the NSP by English L2 learners of Spanish at the intermediate level, including poverty-of-the stimulus knowledge of the Overt Pronoun Constraint (Montalbetti 1984). Our participants are tested before and after five months' residency in Spain in an effort to see if increased amounts of native exposure are particularly beneficial for parameter resetting. Although we demonstrate NSP resetting for some of the L2 learners, our data essentially demonstrate that even with the advent of time/exposure to native input, there is no immediate gainful effect for NSP resetting.

Investigating mechanisms underpinning the detrimental impact of a high-fat diet in the developing and adult hypermuscular myostatin null mouse

Background: Obese adults are prone to develop metabolic and cardiovascular diseases. Furthermore, over-weight expectant mothers give birth to large babies who also have increased likelihood of developing metabolic and cardiovascular diseases. Fundamental advancements to better understand the pathophysiology of obesity are critical in the development of anti-obesity therapies not only for this but also future generations. Skeletal muscle plays a major role in fat metabolism and much work has focused in promoting this activity in order to control the development of obesity. Research has evaluated myostatin inhibition as a strategy to prevent the development of obesity and concluded in some cases that it offers a protective mechanism against a high-fat diet. Results: We hypothesised that myostatin inhibition should protect not only the mother but also its developing foetus from the detrimental effects of a high-fat diet. Unexpectedly, we found muscle development was attenuated in the foetus of myostatin null mice raised on a high-fat diet. We therefore re-examined the effect of the high-fat diet on adults and found myostatin null mice were more susceptible to diet-induced obesity through a mechanism involving impairment of inter-organ fat utilization. Conclusions: Loss of myostatin alters fatty acid uptake and oxidation in skeletal muscle and liver. We show that abnormally high metabolic activity of fat in myostatin null mice is decreased by a high-fat diet resulting in excessive adipose deposition and lipotoxicity. Collectively, our genetic loss-of-function studies offer an explanation of the lean phenotype displayed by a host of animals lacking myostatin signalling. Keywords: Muscle, Obesity, High-fat diet, Metabolism, Myostatin

Toward multifactorial null models of range contraction in terrestrial vertebrates

The contraction of a species’ distribution range, which results from the extirpation of local populations, generally precedes its extinction. Therefore, understanding drivers of range contraction is important for conservation and management. Although there are many processes that can potentially lead to local extirpation and range contraction, three main null models have been proposed: demographic, contagion, and refuge. The first two models postulate that the probability of local extirpation for a given area depends on its relative position within the range; but these models generate distinct spatial predictions because they assume either a ubiquitous (demographic) or a clinal (contagion) distribution of threats. The third model (refuge) postulates that extirpations are determined by the intensity of human impacts, leading to heterogeneous spatial predictions potentially compatible with those made by the other two null models. A few previous studies have explored the generality of some of these null models, but we present here the first comprehensive evaluation of all three models. Using descriptive indices and regression analyses we contrast the predictions made by each of the null models using empirical spatial data describing range contraction in 386 terrestrial vertebrates (mammals, birds, amphibians, and reptiles) distributed across the World. Observed contraction patterns do not consistently conform to the predictions of any of the three models, suggesting that these may not be adequate null models to evaluate range contraction dynamics among terrestrial vertebrates. Instead, our results support alternative null models that account for both relative position and intensity of human impacts. These new models provide a better multifactorial baseline to describe range contraction patterns in vertebrates. This general baseline can be used to explore how additional factors influence contraction, and ultimately extinction for particular areas or species as well as to predict future changes in light of current and new threats.