24 research outputs found
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 . We introduce a parameter which gives a
system ; this system is studied for any
proving its well posedness and the uniqueness of its invariant measure
.
The key point is that for any the fields and
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 and , we investigate the limit as , proving that
weakly converges to , where is the only invariant
measure for the joint system for when .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
which bridges continuously between the two systems. That is, for
one obtains the full nonlinear model, and the corresponding linear
advection model is achieved for . 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 . Moreover, we show the
existence of a finite-dimensional random attractor for each value of
and establish the upper semicontinuity property of this random attractors, with
respect to the parameter . 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