Selective decay by Casimir dissipation in fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in 3D flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in \cite{SaBa1981,SaBa1985}. Several examples are given and a general theory of selective decay is developed that uses the Lie-Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parameterizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic, two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlov et al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary djnlx.tex fil

Global modelling of the early Martian climate under a denser CO2 atmosphere: Water cycle and ice evolution

We discuss 3D global simulations of the early Martian climate that we have performed assuming a faint young Sun and denser CO2 atmosphere. We include a self-consistent representation of the water cycle, with atmosphere-surface interactions, atmospheric transport, and the radiative effects of CO2 and H2O gas and clouds taken into account. We find that for atmospheric pressures greater than a fraction of a bar, the adiabatic cooling effect causes temperatures in the southern highland valley network regions to fall significantly below the global average. Long-term climate evolution simulations indicate that in these circumstances, water ice is transported to the highlands from low-lying regions for a wide range of orbital obliquities, regardless of the extent of the Tharsis bulge. In addition, an extended water ice cap forms on the southern pole, approximately corresponding to the location of the Noachian/Hesperian era Dorsa Argentea Formation. Even for a multiple-bar CO2 atmosphere, conditions are too cold to allow long-term surface liquid water. Limited melting occurs on warm summer days in some locations, but only for surface albedo and thermal inertia conditions that may be unrealistic for water ice. Nonetheless, meteorite impacts and volcanism could potentially cause intense episodic melting under such conditions. Because ice migration to higher altitudes is a robust mechanism for recharging highland water sources after such events, we suggest that this globally sub-zero, `icy highlands' scenario for the late Noachian climate may be sufficient to explain most of the fluvial geology without the need to invoke additional long-term warming mechanisms or an early warm, wet Mars.Comment: Minor revisions to text, one new table, figs. 1,3 11 and 18 redon

Indian Ocean Experiment: An integrated analysis of the climate forcing and effects of the great Indo-Asian haze

Every year, from December to April, anthropogenic haze spreads over most of the North Indian Ocean, and South and Southeast Asia. The Indian Ocean Experiment (INDOEX) documented this Indo-Asian haze at scales ranging from individual particles to its contribution to the regional climate forcing. This study integrates the multiplatform observations (satellites, aircraft, ships, surface stations, and balloons) with one- and four-dimensional models to derive the regional aerosol forcing resulting from the direct, the semidirect and the two indirect effects. The haze particles consisted of several inorganic and carbonaceous species, including absorbing black carbon clusters, fly ash, and mineral dust. The most striking result was the large loading of aerosols over most of the South Asian region and the North Indian Ocean. The January to March 1999 visible optical depths were about 0.5 over most of the continent and reached values as large as 0.2 over the equatorial Indian ocean due to long-range transport. The aerosol layer extended as high as 3 km. Black carbon contributed about 14% to the fine particle mass and 11% to the visible optical depth. The single-scattering albedo estimated by several independent methods was consistently around 0.9 both inland and over the open ocean. Anthropogenic sources contributed as much as 80% (±10%) to the aerosol loading and the optical depth. The in situ data, which clearly support the existence of the first indirect effect (increased aerosol concentration producing more cloud drops with smaller effective radii) are used to develop a composite indirect effect scheme. The Indo-Asian aerosols impact the radiative forcing through a complex set of heating (positive forcing) and cooling (negative forcing) processes. Clouds and black carbon emerge as the major players. The dominant factor, however, is the large negative forcing (–20 ± 4 W M–2) at the surface and the comparably large atmospheric heating. Regionally, the absorbing haze decreased the surface solar radiation by an amount comparable to 50% of the total ocean heat flux and nearly doubled the lower tropospheric solar heating. We demonstrate with a general circulation model how this additional heating significantly perturbs the tropical rainfall patterns and the hydrological cycle with implications to global climate

A Comparison of Error Subspace Kalman Filters

Three advanced filter algorithms based on the Kalman filter arereviewed and presented in a unified notation. They are the wellknown Ensemble Kalman filter (EnKF), the Singular EvolutiveExtended Kalman (SEEK) filter, and the less common SingularEvolutive Interpolated Kalman (SEIK) filter.For comparison, the mathematical formulations of the filters arereviewed in relation to the extended Kalman filter as errorsubspace Kalman filters. The algorithms are presented in theiroriginal form and possible variations are discussed. The comparisonof the algorithms shows their theoretical capabilities forefficient data assimilation with large-scale nonlinear systems. Inparticular, problems of the analysis equations are apparent in theoriginal EnKF algorithm due to the Monte Carlo sampling ofensembles. Theoretically, the SEIK filter appears to be anumerically very efficient algorithm with high potential for usewith nonlinear models.The superiority of the SEIK filter is demonstrated on the basis ofidentical twin experiments using a shallow water model with nonlinearevolution. Identical initial conditions for all three filters allowfor a consistent comparison of the data assimilation results. Theseshow how choices of particular state ensembles and assimilationschemes lead to significant variations of the filterperformance. This is related to different qualities of thepredicted error subspaces as is demonstrated in a examination ofthe predicted state covariance matrices