Figure 4 - uploaded by Valerio Lucarini
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Geostrophic balanced flow; pressure gradient force (upper arrow) and Coriolis force (lower arrow) cancel out and the flow (horizontal arrow) is parallel to the isobars.
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Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated - and feature nonlinear interactions of several different components taking place on a vast range of time-space...
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Mars has inspired our imagination and scientific research. While space missions in the 1960 and 1970s set up a milestone in the study of Mars, discovery of meteorites apparently from the Red Planet led scientific research into a new dimension. Easily identified and linked by their nitrogen and noble gas isotopic signatures, martian meteorites have...
Citations
... Therefore, disregarding the Coriolis effects on the direction of the urban wind flow is deemed an acceptable assumption. This claim can be further argued by assessing the non-dimensional Rossby number (R o ), which quantifies the ratio of inertial to Coriolis forces [47]. Given the typical velocity and length scales in urban studies, R o is estimated to be in the order of 10 3 , which indicates a strong dominance of inertial forces [35]. ...
To improve the reliability of the computational fluid dynamics (CFD) models of wind-driven pollutant dispersion within urban settings, a re-calibration study is conducted to optimize the standard k−ε model. A modified optimization framework based on the genetic algorithm is adapted to alleviate the computational expenses and to further identify ranges for each empirical coefficient to achieve the most reliable and accurate predictions. A robust objective function is defined, incorporating both the flow parameters and pollutant concentration through several linear and logarithmic measures. The coefficients are trained using high-quality and full-scale tracer experiments in a mock urban arrangement simulating a building array. The proposed ranges are 0.14≤Cμ≤0.15, 1.30≤Cε1≤1.46, 1.68≤Cε2≤1.80, 1.12≤σε≤1.20, and 0.87≤σk≤1.00. A thorough evaluation of the predicted flow and concentration fields indicates the modified closure is effective. The fraction of predictions within the acceptable ranges from measurements has increased by 8% for pollutant concentration and 27% for turbulence kinetic energy. The generality of the calibrated model is further tested by modeling additional cases with different meteorological conditions, in which the calculated validation metrics attest to the noteworthy improvements in predictions.
... To further evaluate the validity of this assumption, the non-dimensionalized Rossby number (R o ) was estimated. R o is defined as the ratio of the inertial forces to the Coriolis forces and can be expressed as [46]: ...
Computational Fluid Dynamics (CFD) is used to accurately model and predict the dispersion of a passive scalar in the atmospheric wind flow field within an urban setting. The Mock Urban Setting Tests (MUST) experiment was recreated in this work to test and evaluate various modeling settings and to form a framework for reliable representation of dispersion flow in compact urban geometries. Four case studies with distinct source locations and configurations are modeled using Reynolds-Averaged Navier–Stokes (RANS) equations with ANSYS CFX. The performance of three widely suggested closure models of standard k−ε, RNG k−ε, and SST k−ω is assessed by calculating and interpreting the statistical performance metrics with a specific emphasis on the effects of the source locations. This work demonstrates that the overprediction of the turbulent kinetic energy by the standard k−ε counteracts the general underpredictions by RANS in geometries with building complexes. As a result, the superiority of the standard k−ε in predicting the scalar concentration field over the two other closures in all four cases is observed, with SST k−ω showing the most discrepancies with the field measurements. Additionally, a sensitivity study is also conducted to find the optimum turbulent Schmidt number (Sct) using two approaches of the constant and locally variable values.
... First, we motivate the use of stochastic dynamics for investigating the properties of geophysical flows by introducing the concept of filtering and the development of evolution equations based on dynamical balances and specialised for specific scales of motion [122,123,5]. The introduction of stochastic parametrizations [124,125,126,127,5] is motivated through the use of the Mori-Zwanzig formalism [128,129]. ...
... The partial differential equations that describe the evolution of the field variables are based on the budget of mass (including different chemical species), momentum and energy. Since the climate system features variability on a vast range of spatial and temporal scales, as mentioned above, a key procedure one needs to apply, both on theoretical grounds and for reasons of defining efficient numerical models, is to specialise the evolution equations to a desired range of spatial and temporal scales of interest by the use of suitable approximations based on the validity of approximate dynamical balances [122,123,5]. Additionally, when constructing an actual numerical model, the three-dimensional fields are discretized on a lattice, either in the physical space, or in the reciprocal space via spectral projection, or in a suitable combination of the two. ...
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of great urgency, especially given the ongoing climate change and the evolving climate crisis. In statistical physics, complex, many-particle systems are studied successfully using the mathematical framework of Large Deviation Theory (LDT). A great potential exists for applying LDT to problems relevant for geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the fundamental properties of persistent deviations of climatic fields from the long-term averages and for associating them to low-frequency, large scale patterns of climatic variability. Additionally, LDT can be used in conjunction with so-called rare events algorithms to explore rarely visited regions of the phase space and thus to study special dynamical configurations of the climate. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides powerful tools for evaluating the probability of noise-induced transitions between competing metastable states of the climate system or of its components. This in turn essential for improving our understanding of the global stability properties of the climate system and of its predictability of the second kind in the sense of Lorenz. The goal of this review is manifold. First, we want to provide an introduction to the derivation of large deviation laws in the context of stochastic processes. We then relate such results to the existing literature showing the current status of applications of LDT in climate science and geophysical fluid dynamics. Finally, we propose some possible lines of future investigations.
... We will present some basic results pertaining to stochastic and to deterministic chaotic dynamical systems, for the sake of completeness, and because the modelling of geophysical flows follows both dynamical paradigms. First, we motivate the use of stochastic dynamics for investigating the properties of geophysical flows by introducing the concept of filtering and the development of evolution equations based on dynamical balances and specialised for specific scales of motion [104,142,247]. The introduction of stochastic parametrizations [16,92,104,143,277] is motivated through the use of the Mori-Zwanzig formalism [188,288]. ...
... The partial differential equations that describe the evolution of the field variables are based on the budget of mass (including different chemical species), momentum and energy. Since the climate system features variability on a vast range of spatial and temporal scales, as mentioned above, a key procedure one needs to apply, both on theoretical grounds and for reasons of defining efficient numerical models, is to specialise the evolution equations to a desired range of spatial and temporal scales of interest by the use of suitable approximations based on the validity of approximate dynamical balances [104,142,247]. Additionally, when constructing an actual numerical model, the threedimensional fields are discretised on a lattice, either in the physical space, or in the reciprocal space via spectral projection, or in a suitable combination of the two. ...
The climate is a complex, chaotic system with many degrees of freedom. Attaining a deeper level of understanding of climate dynamics is an urgent scientific challenge, given the evolving climate crisis. In statistical physics, many-particle systems are studied using Large Deviation Theory (LDT). A great potential exists for applying LDT to problems in geophysical fluid dynamics and climate science. In particular, LDT allows for understanding the properties of persistent deviations of climatic fields from long-term averages and for associating them to low-frequency, large-scale patterns. Additionally, LDT can be used in conjunction with rare event algorithms to explore rarely visited regions of the phase space. These applications are of key importance to improve our understanding of high-impact weather and climate events. Furthermore, LDT provides tools for evaluating the probability of noise-induced transitions between metastable climate states. This is, in turn, essential for understanding the global stability properties of the system. The goal of this review is manifold. First, we provide an introduction to LDT. We then present the existing literature. Finally, we propose possible lines of future investigations. We hope that this paper will prepare the ground for studies applying LDT to solve problems encountered in climate science and geophysical fluid dynamics.
... The description of the macroscopic dynamics of the climate system is based on the systematic use of dominant balances derived on a phenomenological basis in order to specialize the dynamical equations. Such balances are suitable classes of approximate solutions of the evolution equations representing a reasonably good approximation to the actual observed fields when sufficiently large spatial or temporal averages are considered (Speranza and Lucarini 2005 Such an approach reflects the fundamentally heuristic/inductive nature of the scientific research in this field, where the traditional reductionist scientific method is not necessarily effective. Climate science is a quickly evolving subject resulting from the intersection of a growing number of disciplines, such as: -Meteorology, Oceanography, Remote Sensing, Radiative Transfer; -Statistical Physics, Thermodynamics, Fluid Dynamics; -Chaotic and Stochastic Dynamical Systems; -Statistics, Data Assimilation, Data reconstruction from Proxy indicators; -Numerical Methods, Modeling, Coding; -Biology, Ecology, Geochemistry. ...
... The description of the macroscopic dynamics of the climate system is based on the systematic use of dominant balances derived on a phenomenological basis in order to specialize the dynamical equations. Such balances are suitable classes of approximate solutions of the evolution equations representing a reasonably good approximation to the actual observed fields when sufficiently large spatial or temporal averages are considered (Speranza and Lucarini 2005). Actually, different balances have to be considered depending on the time and space scales we are focusing our interest on. ...
... The description of the macroscopic dynamics of the climate system is based on the systematic use of dominant balances derived on a phenomenological basis in order to specialize the dynamical equations. Such balances are suitable classes of approximate solutions of the evolution equations representing a reasonably good approximation to the actual observed fields when sufficiently large spatial or temporal averages are considered (Speranza and Lucarini 2005). Actually, different balances have to be considered depending on the time and space scales we are focusing our interest on. ...
We briefly review some of the scientific challenges and epistemological
issues related to climate science. We discuss the formulation and testing of
theories and numerical models, which, given the presence of unavoidable
uncertainties in observational data, the non-repeatability of
world-experiments, and the fact that relevant processes occur in a large
variety of spatial and temporal scales, require a rather different approach
than in other scientific contexts. A brief discussion of the intrinsic
limitations of geo-engineering solutions to global warming is presented, and a
framework of investigation based upon non-equilibrium thermodynamics is
proposed. We also critically discuss recently proposed perspectives of
development of climate science based purely upon massive use of supercomputer
and centralized planning of scientific priorities.
... The magnetic/fluorescent heterostructure nanoparticles synthesized here might be used as dualmode contrast agents for magnetic resonance and optical fluorescence imaging. For MRI, there are two important materials-dependent parameters, the longitudinal and transverse spin relaxation times, T 1 and T 2 [65,66]. These parameters were measured for the FePt@SiO 2 (Rubpy) and Fe 2 O 3 @SiO 2 (Rubpy) nanoparticles in water at room temperature. ...
... The possibility of an Fe-rich and Pt-rich region within the FePt core could result from the particle growth process, in which a Pt nanocrystal is first formed, followed by heterogeneous Fe deposition and subsequent Fe-Pt alloying during the particle growth process [25,50,78]. An Fe-rich shell surrounding a Pt-rich core could increase the local magnetic field gradient at the surface of the FePt@SiO 2 nanoparticles, increasing the proton dephasing rate and causing a higher r 2 [65,79]. Because the SQUID measurements correspond to the volume average of the nanoparticles, they are not sensitive to the local field gradients at the surface of the particle. ...
Multifunctional colloidal core-shell nanoparticles of magnetic nanocrystals (of iron oxide or FePt) or gold nanorods encapsulated in silica shells doped with the fluorescent dye, Tris(2,2'-bipyridyl)dichlororuthenium(II) hexahydrate (Rubpy) were synthesized. The as-prepared magnetic nanocrystals are initially hydrophobic and were coated with silica using a microemulsion approach, while the as-prepared gold nanorods are hydrophilic and were coated with silica using a Stöber-type of process. Each approach yielded monodisperse nanoparticles with uniform fluorescent dye-doped silica shells. These colloidal heterostructures have the potential to be used as dual-purpose tags-exhibiting a fluorescent signal that could be combined with either dark-field optical contrast (in the case of the gold nanorods), or enhanced contrast in magnetic resonance images (in the case of magnetic nanocrystal cores). The optical and magnetic properties of the fluorescent silica-coated gold nanorods and magnetic nanocrystals are reported.
... As an example, we may interpret (23) as the fact that the static response function-measuring climate sensitivity-can be related to the outof-phase response to same forcing at all frequencies, at least in first approximation. The concepts behind the Ruelle response theory also clarify the meaning of some common ensemble simulation practices, which are widely adopted by the climate modelling community with the goal of estimating the uncertainty on the statistical properties of the model outputs, when a specific set of observables is considered [45][46][47]. Three different strategies, which are nevertheless more and more hybridized, can be pointed out: ...
We consider the general response theory proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions allows for writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of observable susceptibilities obey Kramers-Kronig relations. Specific results are provided for arbitrary order harmonic response, which allows for a very comprehensive Kramers-Kronig analysis and the establishment of sum rules connecting the asymptotic behavior of the susceptibility to the short-time response of the system. These results generalize previous findings on optical Hamiltonian systems and simple mechanical models, and shed light on the general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks for any experimental and model generated dataset. In order to connect the response theory for equilibrium and non equilibrium systems, we rewrite the classical results by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. We briefly discuss how these results, taking into account the chaotic hypothesis, might be relevant for climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, Kramers-Kronig relations might be more robust tools for the definition of a self-consistent theory of climate change.
... When considering the dynamics of the atmosphere at mid-latitudes, on spatial and temporal scales comparable with or larger than those of the synoptic weather (about 1000 km and 1 day, respectively), the hydrostatic and geostrophic balances are phenomenologically well established. From the set of ab-initio dynamic and thermodynamic equations of the atmosphere it is possible to obtain a set of simplified prognostic equations for the synoptic weather atmospheric fields in a domain centered at mid-latitudes – the QG equations – by assuming that the fluid obeys the hydrostatic balance and undergoes small departures from the geostrophic balance [13,58,77]. A great number of physical phenomena are filtered out of the equations by the QG approximation: various types of waves associated with strong local divergence, turbulent motions, etc. Again, there is no doubt that these are small on the time–space scales of the motions we consider. ...
A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference TE. As TE increases, a transition takes place from a stationary regime–Hadley equilibrium–to a periodic regime, and eventually to a chaotic regime where evolution takes place on a strange attractor. The attractor dimension, metric entropy, and bounding box volume in phase space have a smooth dependence on TE, which results in power-law scaling properties. Power-law scalings with respect to TE are detected also for the statistical properties of global physical observables — the total energy of the system and the averaged zonal wind. The scaling laws, which constitute the main novel result of the present work, can be thought to result from the presence of a statistical process of baroclinic adjustment, which tends to decrease the equator-to-pole temperature difference and determines the properties of the attractor of the system. The self-similarity could be of great help in setting up a theory for the overall statistical properties of the general circulation of the atmosphere and in guiding–on a heuristic basis–both data analysis and realistic simulations, going beyond the unsatisfactory mean field theories and brute force approaches. A leading example for this would be the possibility of estimating the sensitivity of the output of the system with respect to changes in the parameters.
