The MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument on the Envisat (Environmental satellite) satellite has provided vertical profiles of the atmospheric composition on a global scale for almost ten years. The MIPAS mission is divided in two phases: the full resolution phase, from 2002 to 2004, and the optimized resolution phase, from 2005 to 2012, which is characterized by a finer vertical and horizontal sampling attained through a reduction of the spectral resolution. While the description and characterization of the products of the ESA processor for the full resolution phase has been already described in previous papers, in this paper we focus on the performances of the latest version of the ESA (European Space Agency) processor, named ML2PP V6 (MIPAS Level 2 Prototype Processor), which has been used for reprocessing the entire mission. The ESA processor had to perform the operational near real time analysis of the observations and its products needed to be available for data assimilation. Therefore, it has been designed for fast, continuous and automated analysis of observations made in quite different atmospheric conditions and for a minimum use of external constraints in order to avoid biases in the products. The dense vertical sampling of the measurements adopted in the second phase of the MIPAS mission resulted in sampling intervals finer than the instantaneous field of view of the instrument. Together with the choice of a retrieval grid aligned with the vertical sampling of the measurements, this made ill-conditioned the retrieval problem of the MIPAS operational processor. This problem has been handled with minimal changes to the original retrieval approach but with significant improvements nonetheless. The Levenberg-Marquardt method, already present in the retrieval scheme for its capability to provide fast convergence for nonlinear problems, is now also exploited for the reduction of the ill-conditioning of the inversion. An expression specifically designed for the regularizing Levenberg-Marquardt method has been implemented for the computation of the covariance matrices and averaging kernels of the retrieved products. The regularization of the Levenberg-Marquardt method is controlled by the convergence criteria and is deliberately kept weak. The resulting oscillations of the retrieved profile are a posteriori damped by an innovative self-adapting Tikhonov regularization. The convergence criteria and the weakness of the self-adapting regularization ensure that minimum constraints are used and the best vertical resolution obtainable from the measurements is achieved in all atmospheric conditions. Random and systematic errors, as well as vertical and horizontal resolution are compared in the two phases of the mission for all products, namely: temperature, H2O, O-3, HNO3, CH4, N2O, NO2, CFC-11, CFC-12, N2O5 and ClONO2. The use in the two phases of the mission of different optimized sets of spectral intervals ensures that, despite the different spectral resolutions, comparable performances are obtained in the whole MIPAS mission in terms of random and systematic errors, while the vertical resolution and the horizontal resolution are significantly better in the case of the optimized resolution measurements.

A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based methods when the signal-to-noise ratio is low. The method depends on some hyperparameters which turn out to be essentially independent of the application. Therefore they can be fixed once and for all, giving rise to a black box method.

Universality properties of the distribution of the generalized eigenvalues of a pencil of random Hankel matrices, arising in the solution of the exponential interpolation problem of a complex discrete stationary process, are proved under the assumption that every finite set of random variables of the process have a multivariate spherical distribution. An integral representation of the condensed density of the generalized eigenvalues is also derived. The asymptotic behavior of this function turns out to depend only on stationarity and not on the specific distribution of the process.

An atomic random complex measure defined on the unit disk with normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving several moment problems are discussed.

Lattice Boltzmann models (LBM) and phase field models (PFM) are two of the most widespread approaches for the numerical study of multicomponent fluid systems. Both methods have been successfully employed by several authors but, despite their popularity, still remains unclear how to properly compare them and how they perform on the same problem. Here we present a unified framework for the direct (one-to-one) comparison of the multicomponent LBM against the PFM. We provide analytical guidelines on how to compare the Shan-Chen (SC) lattice Boltzmann model for non-ideal multicomponent fluids with a corresponding free energy (FE) lattice Boltzmann model. Then, in order to properly compare the LBM vs. the PFM, we propose a new formulation for the free energy of the Cahn-Hilliard/Navier-Stokes equations. Finally, the LBM model is numerically compared with the corresponding phase field model solved by means of a pseudo-spectral algorithm. This work constitute a first attempt to set the basis for a quantitative comparison between different algorithms for multicomponent fluids. We limit our scope to the few of the most common variants of the two most widespread methodologies, namely the lattice Boltzmann model (SC and FE variants) and the phase field model. (C) 2012 Elsevier Inc. All rights reserved.

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments. (C) 2013 Elsevier Inc. All rights reserved.

Reactions in turbulent flows, chemical reactions or combustion, are common. Typically reaction time scales are much shorter than turbulence timescales. In biological applications, as it is the case for bacterial and plankton populations living under the influence of currents in oceans and lakes, the typical lifetime can be long and thus can fall well within the inertial range of turbulence time scales. Under these conditions, turbulent transport interacts in a very complex way with the dynamics of growth and death of the individuals in the population. In the present paper, we quantitatively investigate the effect of the flow compressibility on the dynamics of populations. Small effective compressibility can be induced by several physical mechanisms, such as, e.g., by the density mismatch, by a small but finite size of microorganisms, and by gyrotaxis (an interaction between swimming and shear). We report, for the first time, how even a tiny effective compressibility can produce a dramatically large effect on global quantities like the carrying capacity of the ecosystem. We interpret our findings by means of a cumulative effect made possible by the long replication times of the organisms with respect to turbulence time scales. A statistical quantification of the fluctuations of population concentration is presented.

We study the static and dynamical behavior of the contact line between two fluids and a solid plate by means of the Lattice Boltzmann method (LBM). The different fluid phases and their contact with the plate are simulated by means of standard Shan-Chen models. We investigate different regimes and compare the multicomponent vs. the multiphase LBM models near the contact line. A static interface profile is attained with the multiphase model just by balancing the hydrostatic pressure (due to gravity) with a pressure jump at the bottom. In order to study the same problem with the multicomponent case we propose and validate an idea of a body force acting only on one of the two fluid components. In order to reproduce results matching an infinite bath, boundary conditions at the bath side play a key role. We quantitatively compare open and wall boundary conditions and study their influence on the shape of the meniscus against static and lubrication theory solution.

We report about a numerical algorithm based on the lattice Boltzmann method and its applications for simulations of turbulent convection in multi-phase flows. We discuss the issue of `latent heat' definition using a thermodynamically consistent pseudo-potential on the lattice. We present results of numerical simulations in 3D with and without boiling, showing the distribution of pressure, density and temperature fluctuations inside a convective cell.

An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow field needed for the computation of the Lagrangian trajectories. The accuracy of the interpolation method has direct consequences for the acceleration spectrum of the fluid particles and is therefore also important for the correct evaluation of the hydrodynamic forces for almost neutrally buoyant particles, common in many environmental applications. In order to systematically choose the optimal tradeoff between interpolation accuracy and computational cost we focus on comparing errors: the interpolation error is compared with the discretization error of the flow field. In this way one can prevent unnecessary computations and still retain the accuracy of the turbulent flow simulation. From the analysis a practical method is proposed that enables direct estimation of the interpolation and discretization error from the energy spectrum. The theory is validated by means of direct numerical simulations (DNS) of homogeneous, isotropic turbulence using a spectral code, where the trajectories of fluid tracers are computed using several interpolation methods. We show that B-spline interpolation has the best accuracy given the computational cost. Finally, the optimal interpolation order for the different methods is shown as a function of the resolution of the DNS simulation. DOI: 10.1103/PhysRevE.87.043307

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C-i(t) and of their instantaneous frequency omega(i) (t). On the basis of this decomposition we define the.-conditioned statistical moments of the C-i modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform-or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energy like quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)]. DOI: 10.1103/PhysRevE.87.041003

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al. [Phys. Rev. Lett. 108, 074506 (2012)]. (C) 2013 AIP Publishing LLC.

We study the dynamics of the interface between two immiscible fluids in contact with a chemically homogeneous moving solid plate. We consider the generic case of two fluids with any viscosity ratio and of a plate moving in either directions (pulled or pushed in the bath). The problem is studied by a combination of two models, namely, an extension to finite viscosity ratio of the lubrication theory and a Lattice Boltzmann method. Both methods allow to resolve, in different ways, the viscous singularity at the triple contact between the two fluids and the wall. We find a good agreement between the two models particularly for small capillary numbers. When the solid plate moves fast enough, the entrainment of one fluid into the other one can occur. The extension of the lubrication model to the case of a non-zero air viscosity, as developed here, allows us to study the dependence of the critical capillary number for air entrainment on the other parameters in the problem (contact angle and viscosity ratio). (C) 2013 AIP Publishing LLC.

We describe the implementation of a thermal compressible Lattice Boltzmann algorithm on an NVIDIA Tesla C2050 system based on the Fermi GP-GPU. We consider two different versions, including and not including reactive effects. We describe the overall organization of the algorithm and give details on its implementations. Efficiency ranges from 25% to 31% of the double precision peak performance of the GP-GPU. We compare our results with a different implementation of the same algorithm, developed and optimized for many-core Intel Westmere CPUs. (C) 2012 Elsevier Ltd. All rights reserved.

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed.

We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier-Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier-Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum E-back(k) similar to k(-5/3) and by a direct helicity cascade with a spectrum E-forw(k) similar to k(-7/3). Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier-Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.