A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. <br><br> Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing &nabla; &times; &nabla;, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. <br><br> In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly

A conservative Fourier-finite-element method for solving partial differential equations on the whole sphere

ABSTRACT: Solving transport equations on the whole sphere using an explicit time stepping and an Eulerian formulation on a latitude-longitude grid is relatively straightforward but suffers from the pole problem: due to the increased zonal resolution near the pole, numerical stability requires unacceptably small time steps. Commonly used workarounds such as near-pole zonal filters affect the qualitative properties of the numerical method. Rigorous solutions based on spherical harmonics have a high computational cost. The numerical method we propose to avoid this problem is based on a Galerkin formulation in a subspace of a Fourierfinite-element spatial discretization. The functional space we construct provides quasi-uniform resolution and high-order accuracy, while the Galerkin formalism guarantees the conservation of linear and quadratic invariants. For N 2 degrees of freedom, the computational cost is O(N 2 log N), dominated by the zonal Fourier transforms. This is more than with a finite-difference or finite-volume method, which costs O(N 2 ), and less than with a spherical harmonics method, which costs O(N 3 ). Differential operators with latitude-dependent coefficients are inverted at a cost of O(N 2 ). We present experimental results and standard benchmarks demonstrating the accuracy, stability and efficiency of the method applied to the advection of a scalar field by a prescribed velocity field and to the incompressible rotating Navier-Stokes equations. The steps required to extend the method towards compressible flows and the Saint-Venant equations are described

Coherent low-energy charge transport in a diffusive S-N-S junction

We have studied the current voltage characteristics of diffusive mesoscopic Nb-Cu-Nb Josephson junctions with highly-transparent Nb-Cu interfaces. We consider the low-voltage and high-temperature regime eV<\epsilon_{c}<k_{B}T where epsilon_{c} is the Thouless energy. The observed excess current as well as the observed sub-harmonic Shapiro steps under microwave irradiation suggest the occurrence of low-energy coherent Multiple Andreev Reflection (MAR).Comment: 4 pages, 4 figures, final versio

Stability of parallel wake flows in quasigeostrophic and frontal regimes

International audienceRecent laboratory experiments [G. Perret, A. Stegner, M. Farge, and T. Pichon, Phys. Fluids 18, 036603 (2006)] have shown that the vortex-street formed in the wake of a towed cylinder in a rotating shallow-water layer could present a strong cyclone-anticyclone asymmetry. In extreme cases, only large-scale anticyclones were observed in the far wake. This asymmetry occurs in the so-called frontal regime when the Rossby number is small and the surface deviation is large. This asymmetry may have various origins and in particular may be attributed to the asymmetry of the flow around the cylinder, to the linear stability property of the wake, or to its nonlinear evolution. To discriminate between these mechanisms, we study the stability of two idealized parallel flows in the quasigeostrophic and in the frontal regimes. These parallel flows correspond to two velocity profiles measured just behind the cylinder in a region where the perturbations are negligible. According to our linear stability analysis, the most unstable mode, in the frontal regime, is localized in the anticyclonic shear region whether the base flow profile is symmetric or not. On a linear basis, it is thus more the instability that imposes the asymmetry than the base flow. Direct numerical simulations of the synthetic parallel wake flows show that nonlinearity exacerbates the dominance of the anticyclonic mode linearly selected. By numerically studying the spatio-temporal evolution of a small perturbation localized in space, we show that, unlike incompressible two-dimensional wake flows and the symmetric wake in the quasigeostrophic regime, the parallel asymmetric wake is strongly convectively unstable in the frontal regime, and not absolutely unstable. When the surface deformation becomes large, the wake instability changes from the absolute instability in the quasi-geostrophic regime to the strongly convective instability of the frontal regime. This explains well the changes. © 2006 American Institute of Physics

Acoustic characterization of Hofstadter butterfly with resonant scatterers

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly

Erratum

Evolution des teneurs en polyamines dans les boutons floraux, les fleurs et les jeunes baies de Vitis villifera L. (cv. Cabernet Sauvignon) atteints d'eutypioseVitis 43 (3), 139-144 (2004