Comparison of a grid-based CFD method and vortex dynamics predictions of low Reynolds number cylinder flow

Computational fluid dynamics models range from the finite difference type grid-based method to the Lagrangian style vortex cloud simulation technique for solving the Navier-Stokes equations. This paper undertakes a comparison of these two methods for the classical datum bluff body case of flow past a stationary circular cylinder at low Reynolds numbers in the range 10 to 220. Comparisons include time-history, time-mean and root-mean-square values of oscillating drag and lift coefficients, frequency of vortex shedding and related vortex street wake flow patterns. Particularly close agreement was obtained for Strouhal number versus Reynolds number, and good agreement for time-mean value of drag coefficients; comparison was also made with experimental results. Attempts are also made to calculate the skin friction and surface pressure components of the cylinder drag, revealing the significance of skin friction drag within this range and its relative insignificance above a Reynolds number of 220

A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis

In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes

Reduced-order models of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves

A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis

In Part I of this study Whitehouse et al. (2005) performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed

Lensed CMB power spectra from all-sky correlation functions

Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Non-perturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0.3-1% level. We describe a new, accurate and fast, full-sky correlation-function method for computing the lensing effect on CMB power spectra to better than 0.1% at l<2500 (within the approximation that the lensing potential is linear and Gaussian). We also discuss the effect of non-linear evolution of the gravitational potential on the lensed power spectra. Our fast numerical code is publicly available.Comment: 16 pages, 4 figures. Changes to match PRD version including new section on non-linear corrections. CAMB code available at http://camb.info

The 21cm angular-power spectrum from the dark ages

At redshifts z >~ 30 neutral hydrogen gas absorbs CMB radiation at the 21cm spin-flip frequency. In principle this is observable and a high-precision probe of cosmology. We calculate the linear-theory angular power spectrum of this signal and cross-correlation between redshifts on scales much larger than the line width. In addition to the well known redshift-distortion and density perturbation sources a full linear analysis gives additional contributions to the power spectrum. On small scales there is a percent-level linear effect due to perturbations in the 21cm optical depth, and perturbed recombination modifies the gas temperature perturbation evolution (and hence spin temperature and 21cm power spectrum). On large scales there are several post-Newtonian and velocity effects; although negligible on small scales, these additional terms can be significant at l <~ 100 and can be non-zero even when there is no background signal. We also discuss the linear effect of reionization re-scattering, which damps the entire spectrum and gives a very small polarization signal on large scales. On small scales we also model the significant non-linear effects of evolution and gravitational lensing. We include full results for numerical calculation and also various approximate analytic results for the power spectrum and evolution of small scale perturbations.Comment: 29 pages; significant extensions including: self-absorption terms (i.e. change to background radiation due to 21cm absorption); ionization fraction perturbations; estimates of non-linear effects; approximate analytic results; results for sharp redshift window functions. Code available at http://camb.info/sources

Electron-impact excitation of X 1Sigma_g⁺(v[double-prime]=0) to the a[double-prime] 1Sigma_g⁺, b 1Piu, c3 1Piu, o3 1Piu, b[prime] 1Sigma_u⁺, c₄^[prime] 1Sigma_u⁺, G 3Piu, and F 3Piu states of molecular nitrogen

Measurements of differential cross sections (DCSs) for electron-impact excitation of the a[double-prime] 1Sigmag+, b 1Piu, c3 1Piu, o3 1Piu, b[prime] 1Sigmau+, c4[prime] 1Sigmau+, G 3Piu, and F 3Piu states in N2 from the X 1Sigmag+(v[double-prime]=0) ground level are presented. The DCSs were obtained from energy-loss spectra in the region of 12 to 13.82 eV measured at incident energies of 17.5, 20, 30, 50, and 100 eV and for scattering angles ranging from 2° to 130°. The analysis of the spectra follows a different algorithm from that employed in a previous study of N2 for the valence states [Khakoo et al. Phys. Rev. A 71, 062703 (2005)], since the 1Piu and 1Sigmau+ states form strongly interacting Rydberg-valence series. The results are compared with existing data

Resummation Effects in Vector-Boson and Higgs Associated Production

Fixed-order QCD radiative corrections to the vector-boson and Higgs associated production channels, pp -> VH (V=W, Z), at hadron colliders are well understood. We combine higher order perturbative QCD calculations with soft-gluon resummation of both threshold logarithms and logarithms which are important at low transverse momentum of the VH pair. We study the effects of both types of logarithms on the scale dependence of the total cross section and on various kinematic distributions. The next-to-next-to-next-to-leading logarithmic (NNNLL) resummed total cross sections at the LHC are almost identical to the fixed-order perturbative next-to-next-to-leading order (NNLO) rates, indicating the excellent convergence of the perturbative QCD series. Resummation of the VH transverse momentum (p_T) spectrum provides reliable results for small values of p_T and suggests that implementing a jet-veto will significantly decrease the cross sections.Comment: 25 pages, references update