Kolmogorov scaling from random force fields

We show that the classical Kolmogorov and Richardson scaling laws in fully developed turbulence are consistent with a random Gaussian force field. Numerical simulations of a shell model approximation to the Navier-Stokes equations suggest that the fluctuations in the force (acceleration) field are scale independent throughout the inertial regime. We conjecture that Lagrangian statistics of the relative velocity in a turbulent flow is determined by the typical force field, whereas the multiscaling is associated to extreme events in the force field fluctuations.Comment: 4 pages, 4 figure

Statistical properties of stochastic 2D Navier-Stokes equations from linear models

A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. In this paper, we investigate this conjecture for the 2D Navier-Stokes equations driven by an additive noise. In order to check this conjecture, we analyze the coupled system Navier-Stokes/linear advection system in the unknowns $(u,w)$. We introduce a parameter $\lambda$ which gives a system $(u^\lambda,w^\lambda)$; this system is studied for any $\lambda$ proving its well posedness and the uniqueness of its invariant measure $\mu^\lambda$. The key point is that for any $\lambda \neq 0$ the fields $u^\lambda$ and $w^\lambda$ have the same scaling exponents, by assuming universality of the scaling exponents to the force. In order to prove the same for the original fields $u$ and $w$, we investigate the limit as $\lambda \to 0$, proving that $\mu^\lambda$ weakly converges to $\mu^0$, where $\mu^0$ is the only invariant measure for the joint system for $(u,w)$ when $\lambda=0$.Comment: 23 pages; improved versio

Stochastic attractors for shell phenomenological models of turbulence

Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a "homotopy-like" coefficient $\lambda$ which bridges continuously between the two systems. That is, for $\lambda=1$ one obtains the full nonlinear model, and the corresponding linear advection model is achieved for $\lambda=0$. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter $\lambda$. Moreover, we show the existence of a finite-dimensional random attractor for each value of $\lambda$ and establish the upper semicontinuity property of this random attractors, with respect to the parameter $\lambda$. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models

Stress-driven phase transformation and the roughening of solid-solid interfaces

The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials with different porosities under normal compression stresses. This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of finger-like structures aligned with the principal direction of compaction. The model is proposed as an explanation for the roughening of stylolites - irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal direction of compaction.Comment: (4 pages, 4 figures

Changes in biodiversity and trade-offs among ecosystem services, stakeholders, and components of well-being: the contribution of the International Long-Term Ecological Research network (ILTER) to Programme on Ecosystem Change and Society (PECS)

The International Long-Term Ecological Research (ILTER) network comprises > 600 scientific groups conducting site-based research within 40 countries. Its mission includes improving the understanding of global ecosystems and informs solutions to current and future environmental problems at the global scales. The ILTER network covers a wide range of social-ecological conditions and is aligned with the Programme on Ecosystem Change and Society (PECS) goals and approach. Our aim is to examine and develop the conceptual basis for proposed collaboration between ILTER and PECS. We describe how a coordinated effort of several contrasting LTER site-based research groups contributes to the understanding of how policies and technologies drive either toward or away from the sustainable delivery of ecosystem services. This effort is based on three tenets: transdisciplinary research; cross-scale interactions and subsequent dynamics; and an ecological stewardship orientation. The overarching goal is to design management practices taking into account trade-offs between using and conserving ecosystems toward more sustainable solutions. To that end, we propose a conceptual approach linking ecosystem integrity, ecosystem services, and stakeholder well-being, and as a way to analyze trade-offs among ecosystem services inherent in diverse management options. We also outline our methodological approach that includes: (i) monitoring and synthesis activities following spatial and temporal trends and changes on each site and by documenting cross-scale interactions; (ii) developing analytical tools for integration; (iii) promoting trans-site comparison; and (iv) developing conceptual tools to design adequate policies and management interventions to deal with trade-offs. Finally, we highlight the heterogeneity in the social-ecological setting encountered in a subset of 15 ILTER sites. These study cases are diverse enough to provide a broad cross-section of contrasting ecosystems with different policy and management drivers of ecosystem conversion; distinct trends of biodiversity change; different stakeholders’ preferences for ecosystem services; and diverse components of well-being issues

Integrated assessment and valuation of ecosystem services - Guidelines and experiences

EU FP7 OpenNESS project deliverable D33 & D4

Thermodynamics of stressed solids:Slow deformation and roughening of material interfaces

At every turn in nature we are confronted with complex patterns. Patterns often formed in multiphase systems by an intricate dynamics of mass transport, e.g. diffusion and/or advection, and mass exchange between individual phases. Here we consider instabilities of phase boundaries in idealized stressed multiphase systems. Specifically, we study the growth of small perturbations of surfaces by considering mass transport from regions, where the stress and chemical potential is high, to surrounding regions where the stress and chemical potential is low. We present a linear stability analysis for various stress configurations and their corresponding stability diagrams