scholarly journals A New Mathematical Framework for Atmospheric Blocking Events

2021 ◽  
Author(s):  
Valerio Lucarini
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Zonal Flow ◽  
Atmospheric Model ◽  
Dynamical Analysis ◽  
Mathematical Framework ◽  
Specific Class ◽  
Unstable Periodic Orbits ◽  
Atmospheric Blocking ◽  
Mature Phase

<p>We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events, which are associated with low frequency, large scale waves in the atmosphere. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with conditions of anomalously high instability of the atmosphere. Additionally, the lifetime of a blocking is positively correlated with the intensity of such an anomaly, against intuition. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking, while a relative increase of predictability is found in the mature phase, while the opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. We associate blockings to a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor of the system. The UPOs differ substantially in terms of instability, which explains the diversity of the atmosphere in terms predictability. The UPOs associated to blockings are indeed anomalously unstable, which leads to them being rarely visited. The onset of a blocking takes place when the trajectory of the system hops into the neighbourhood of one of these special UPOs. The decay takes place when the trajectory hops back to the neighbourhood of usual, less unstable UPOs associated with zonal flow. This justifies the classical Markov chains-based analysis of transitions between weather regimes. The existence of UPOs differing in the dimensionality of their unstable manifold indicates a very strong violation of hyperbolicity in the model, which leads to a lack of structural stability. We propose that this is could be a generic feature of atmospheric models and might be a fundamental cause behind difficulties in representing blockings for the current climate and uncertainties in predicting how their statistics will change as a result of climate change.<br><br>References:<br>V. Lucarini, A. Gritsun, A. A new mathematical framework for atmospheric blocking events. Climate Dynamics 54, 575–598 (2020). https://doi.org/10.1007/s00382-019-05018-2<br>M. Ghil, V. Lucarini, The Physics of Climate Variability and Climate, Rev. Modern Physics, 92, 035002 (2020). https://link.aps.org/doi/10.1103/RevModPhys.92.035002  <br>S. Schubert, V. Lucarini, Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors. Q. J. R. Meteorol. Soc. 142, 2143-2158 (2016). https://doi.org/10.1002/qj.2808</p>

scholarly journals A new mathematical framework for atmospheric blocking events

2019 ◽  
Vol 54 (1-2) ◽  
pp. 575-598 ◽  
Author(s):  
Valerio Lucarini ◽  
Andrey Gritsun
Keyword(s):  
Numerical Models ◽  
Zonal Flow ◽  
Atmospheric Model ◽  
Relative Increase ◽  
Mathematical Framework ◽  
Specific Class ◽  
Unstable Periodic Orbits ◽  
Modes Of Variability ◽  
Finite Time Lyapunov Exponents ◽  
Mature Phase

Abstract We use a simple yet Earth-like hemispheric atmospheric model to propose a new framework for the mathematical properties of blocking events. Using finite-time Lyapunov exponents, we show that the occurrence of blockings is associated with conditions featuring anomalously high instability. Longer-lived blockings are very rare and have typically higher instability. In the case of Atlantic blockings, predictability is especially reduced at the onset and decay of the blocking event, while a relative increase of predictability is found in the mature phase. The opposite holds for Pacific blockings, for which predictability is lowest in the mature phase. Blockings are realised when the trajectory of the system is in the neighbourhood of a specific class of unstable periodic orbits (UPOs), natural modes of variability that cover the attractor the system. UPOs corresponding to blockings have, indeed, a higher degree of instability compared to UPOs associated with zonal flow. Our results provide a rigorous justification for the classical Markov chains-based analysis of transitions between weather regimes. The analysis of UPOs elucidates that the model features a very severe violation of hyperbolicity, due to the presence of a substantial variability in the number of unstable dimensions, which explains why atmospheric states can differ a lot in term of their predictability. Additionally, such a variability explains the need for performing data assimilation in a state space that includes not only the unstable and neutral subspaces, but also some stable modes. The lack of robustness associated with the violation of hyperbolicity might be a basic cause contributing to the difficulty in representing blockings in numerical models and in predicting how their statistics will change as a result of climate change. This corresponds to fundamental issues limiting our ability to construct very accurate numerical models of the atmosphere, in term of predictability of the both the first and of the second kind in the sense of Lorenz.

Generation of zonal flow and magnetic field in the ionospheric E-layer

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
L. Z. Kahlon ◽  
T. D. Kaladze
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Low Frequency ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Triple Interaction ◽  
Inverse Energy Cascade ◽  
Nonlinear Mechanism ◽  
Scale Perturbation ◽  
Low Frequency Waves

We review the generation of zonal flow and magnetic field by coupled electromagnetic ultra-low-frequency waves in the Earth’s ionospheric E-layer. It is shown that, under typical ionospheric E-layer conditions, different planetary low-frequency waves can couple with each other. Propagation of coupled internal-gravity–Alfvén, coupled Rossby–Khantadze and coupled Rossby–Alfvén–Khantadze waves is revealed and studied. A set of appropriate equations describing the nonlinear interaction of such waves with sheared zonal flow is derived. The conclusion on the instability of short-wavelength turbulence of such coupled waves with respect to the excitation of low-frequency and large-scale perturbation of the sheared zonal flow and sheared magnetic field is deduced. The nonlinear mechanism of the instability is based on the parametric triple interaction of finite-amplitude coupled waves leading to the inverse energy cascade towards longer wavelength. The possibility of generation of an intense mean magnetic field is shown. Obtained growth rates are discussed for each case of the considered coupled waves.

Influence of non-monochromaticity on zonal-flow generation by magnetized Rossby waves in the ionospheric E-layer

2009 ◽  
Vol 75 (3) ◽  
pp. 345-357 ◽  
Author(s):  
T. D. KALADZE ◽  
H. A. SHAH ◽  
G. MURTAZA ◽  
L. V. TSAMALASHVILI ◽  
M. SHAD ◽  
...  
Keyword(s):  
Large Scale ◽  
Laboratory Experiments ◽  
Low Frequency ◽  
Zonal Flow ◽  
Present Theory ◽  
Resonant Interaction ◽  
Finite Amplitude ◽  
Small Scale ◽  
Zonal Flows ◽  
Flow Generation

AbstractThe influence of non-monochromaticity on low-frequency, large-scale zonal-flow nonlinear generation by small-scale magnetized Rossby (MR) waves in the Earth's ionospheric E-layer is considered. The modified parametric approach is used with an arbitrary spectrum of primary modes. It is shown that the broadening of the wave packet spectrum of pump MR waves leads to a resonant interaction with a growth rate of the order of the monochromatic case. In the case when zonal-flow generation by MR modes is prohibited by the Lighthill stability criterion, the so-called two-stream-like mechanism for the generation of sheared zonal flows by finite-amplitude MR waves in the ionospheric E-layer is possible. The growth rates of zonal-flow instabilities and the conditions for driving them are determined. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere and in laboratory experiments.

scholarly journals Lyapunov, Floquet, and singular vectors for baroclinic waves

2001 ◽  
Vol 8 (6) ◽  
pp. 439-448 ◽  
Author(s):  
R. M. Samelson
Keyword(s):  
Differential Equation ◽  
Large Scale ◽  
Zonal Flow ◽  
Tangent Plane ◽  
Decay Rates ◽  
Asymptotic Model ◽  
Transient Growth ◽  
Unstable Periodic Orbits ◽  
Singular Vectors ◽  
Lyapunov Vector

Abstract. The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector f1 of the lowest-order unstable periodic orbit over most of the attractor. Departures of the Lyapunov vector from this orientation are primarily rotations of the vector in an approximate tangent plane to the large-scale attractor structure. Exponential growth and decay rates of the Lyapunov vector during individual Poincaré section returns are an order of magnitude larger than the Lyapunov exponent l ≈ 0.016. Relatively large deviations of the Lyapunov vector from parallel to f1 are generally associated with relatively large transient decays. The transient growth and decay of the Lyapunov vector is well described by the transient growth and decay of the leading Floquet vectors of the set of unstable periodic orbits associated with the attractor. Each of these vectors is also nearly parallel to f1. The dynamical splitting of the complete sets of Floquet vectors for the higher-order cycles follows the previous results on the lowest-order cycle, with the vectors divided into wave-dynamical and decaying zonal flow modes. Singular vectors and singular values also generally follow this split. The primary difference between the leading Lyapunov and singular vectors is the contribution of decaying, inviscidly-damped wave-dynamical structures to the singular vectors.

scholarly journals Wave–Mean Flow Interactions and the Maintenance of Superrotation in a Terrestrial Atmosphere

2016 ◽  
Vol 73 (8) ◽  
pp. 3181-3196 ◽  
Author(s):  
João Rafael Dias Pinto ◽  
Jonathan Lloyd Mitchell
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Zonal Flow ◽  
Equatorial Region ◽  
Rossby Number ◽  
Kelvin Wave ◽  
Mean Flow ◽  
Flow Process ◽  
Dynamical Interaction ◽  
The Mean

Abstract The interplay between mean meridional circulation and transient eddies through wave–mean flow interaction processes defines the general behavior of any planetary atmospheric circulation. Under a higher-Rossby-number regime, equatorward momentum transports provided by large-scale disturbances generate a strong zonal flow at the equatorial region. At intermediate Rossby numbers, equatorial Kelvin waves play a leading role in maintaining a superrotating jet over the equator. However, at high Rossby numbers, the Kelvin wave only provides equatorward momentum fluxes during spinup, and the wave–mean flow process that maintains this strongly superrotating state has yet to be identified. This study presents a comprehensive analysis of the tridimensional structure and life cycle of atmospheric waves and their interaction with the mean flow, which maintains the strong, long-lived superrotating state in a higher-Rossby-number-regime atmosphere. The results show that the mean zonal superrotating circulation is maintained by the dynamical interaction between mixed baroclinic–barotropic Rossby wave modes via low-frequency variations of the zonal-mean state in short and sporadic periods of stronger instability. The modulation of amplitude of the equatorial and extratropical Rossby waves suggests a nonlinear mechanism of eddy–eddy interaction between these modes.

The Nontraditional Coriolis Terms and Tropical Convective Clouds

2020 ◽  
Vol 77 (12) ◽  
pp. 3985-3998
Author(s):  
Matthew R. Igel ◽  
Joseph A. Biello
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Zonal Flow ◽  
Mathematical Framework ◽  
Freezing Level ◽  
Almost Everywhere ◽  
Mesoscale Convective ◽  
Simple Scaling ◽  
Upper Level ◽  
Scale Limit

AbstractThe full, three-dimensional Coriolis force includes the familiar sine-of-latitude terms as well as frequently dropped cosine-of-latitude terms [nontraditional Coriolis terms (NCT)]. The latter are often ignored because they couple the zonal and vertical momentum equations that in the large-scale limit of weak vertical velocity are considered insignificant almost everywhere. Here, we ask whether equatorial mesoscale clouds that fall outside the large-scale limit are affected by the NCT. A simple scaling indicates that a Lagrangian parcel convecting at 10 m s−1 through the depth of the troposphere should be deflected over 2 km to the west. To understand the real impact of NCT, we develop a mathematical framework that describes an azimuthally symmetric convective circulation with an analytical expression for an incompressible poloidal flow. Because the model incorporates the full three-dimensional flow associated with convection, it uniquely predicts not only the westward tilt of clouds but also a meridional diffluence of western cloud outflow. To test these predictions, we perform a set of cloud-resolving simulations whose results show preferential lifting of surface parcels with positive zonal momentum and zonal asymmetry in convective strength. RCE simulations show changes to the organization of coherent precipitation regions and a decrease in mean convective intensity of approximately 2 m s−1 above the freezing level. An additional pair of dry cloud-resolving simulations designed to mimic the steady-state flow of the model show maximum perturbations to the upper-level zonal flow of 8 m s−1. Together, the numerical and analytic results suggest the NCT consequentially alter equatorial mesoscale convective circulations and should be considered in conceptual models.

scholarly journals Controllable and decomposable multidirectional synchronizations

2021 ◽  
Author(s):  
Gábor Bergmann
Keyword(s):  
Systems Engineering ◽  
Large Scale ◽  
Mathematical Framework ◽  
Collaborative Systems ◽  
Consistency Constraints ◽  
Restoration Mechanism ◽  
Common Goals ◽  
Access Privileges ◽  
Novel Concept ◽  
Engineering Projects

AbstractStudying large-scale collaborative systems engineering projects across teams with differing intellectual property clearances, or healthcare solutions where sensitive patient data needs to be partially shared, or similar multi-user information systems over databases, all boils down to a common mathematical framework. Updateable views (lenses) and more generally bidirectional transformations are abstractions to study the challenge of exchanging information between participants with different read access privileges. The view provided to each participant must be different due to access control or other limitations, yet also consistent in a certain sense, to enable collaboration towards common goals. A collaboration system must apply bidirectional synchronization to ensure that after a participant modifies their view, the views of other participants are updated so that they are consistent again. While bidirectional transformations (synchronizations) have been extensively studied, there are new challenges that are unique to the multidirectional case. If complex consistency constraints have to be maintained, synchronizations that work fine in isolation may not compose well. We demonstrate and characterize a failure mode of the emergent behaviour, where a consistency restoration mechanism undoes the work of other participants. On the other end of the spectrum, we study the case where synchronizations work especially well together: we characterize very well-behaved multidirectional transformations, a non-trivial generalization from the bidirectional case. For the former challenge, we introduce a novel concept of controllability, while for the latter one, we propose a novel formal notion of faithful decomposition. Additionally, the paper proposes several novel properties of multidirectional transformations.

scholarly journals Experiment Investigation of Bistable Vibration Energy Harvesting with Random Wave Environment

2021 ◽  
Vol 11 (9) ◽  
pp. 3868
Author(s):  
Qiong Wu ◽  
Hairui Zhang ◽  
Jie Lian ◽  
Wei Zhao ◽  
Shijie Zhou ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Energy Harvesting ◽  
Cantilever Beam ◽  
Large Scale ◽  
Low Frequency ◽  
Vibration Energy ◽  
Random Wave ◽  
Periodic Signal ◽  
Vibration Energy Harvesting ◽  
Motion Activity

The energy harvested from the renewable energy has been attracting a great potential as a source of electricity for many years; however, several challenges still exist limiting output performance, such as the package and low frequency of the wave. Here, this paper proposed a bistable vibration system for harvesting low-frequency renewable energy, the bistable vibration model consisting of an inverted cantilever beam with a mass block at the tip in a random wave environment and also develop a vibration energy harvesting system with a piezoelectric element attached to the surface of a cantilever beam. The experiment was carried out by simulating the random wave environment using the experimental equipment. The experiment result showed a mass block’s response vibration was indeed changed from a single stable vibration to a bistable oscillation when a random wave signal and a periodic signal were co-excited. It was shown that stochastic resonance phenomena can be activated reliably using the proposed bistable motion system, and, correspondingly, large-scale bistable responses can be generated to realize effective amplitude enlargement after input signals are received. Furthermore, as an important design factor, the influence of periodic excitation signals on the large-scale bistable motion activity was carefully discussed, and a solid foundation was laid for further practical energy harvesting applications.

scholarly journals Kelvin/Rossby Wave Partition of Madden-Julian Oscillation Circulations

Climate ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Patrick Haertel
Keyword(s):  
Rossby Wave ◽  
Large Scale ◽  
Atmospheric Model ◽  
Circulation System ◽  
System Of Equations ◽  
Wave Component ◽  
Madden Julian Oscillation ◽  
Kelvin Wave ◽  
Realistic View ◽  
State Of Rest

The Madden Julian Oscillation (MJO) is a large-scale convective and circulation system that propagates slowly eastward over the equatorial Indian and Western Pacific Oceans. Multiple, conflicting theories describe its growth and propagation, most involving equatorial Kelvin and/or Rossby waves. This study partitions MJO circulations into Kelvin and Rossby wave components for three sets of data: (1) a modeled linear response to an MJO-like heating; (2) a composite MJO based on atmospheric sounding data; and (3) a composite MJO based on data from a Lagrangian atmospheric model. The first dataset has a simple dynamical interpretation, the second provides a realistic view of MJO circulations, and the third occurs in a laboratory supporting controlled experiments. In all three of the datasets, the propagation of Kelvin waves is similar, suggesting that the dynamics of Kelvin wave circulations in the MJO can be captured by a system of equations linearized about a basic state of rest. In contrast, the Rossby wave component of the observed MJO’s circulation differs substantially from that in our linear model, with Rossby gyres moving eastward along with the heating and migrating poleward relative to their linear counterparts. These results support the use of a system of equations linearized about a basic state of rest for the Kelvin wave component of MJO circulation, but they question its use for the Rossby wave component.

scholarly journals On the structural connectivity of large-scale models of brain networks at cellular level

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Giuseppe Giacopelli ◽  
Domenico Tegolo ◽  
Emiliano Spera ◽  
Michele Migliore
Keyword(s):  
Large Scale ◽  
Brain Networks ◽  
Structural Connectivity ◽  
Network Models ◽  
Brain Regions ◽  
Cellular Level ◽  
Scale Model ◽  
Mathematical Framework ◽  
Underlying Mechanisms ◽  
Experimental Findings

AbstractThe brain’s structural connectivity plays a fundamental role in determining how neuron networks generate, process, and transfer information within and between brain regions. The underlying mechanisms are extremely difficult to study experimentally and, in many cases, large-scale model networks are of great help. However, the implementation of these models relies on experimental findings that are often sparse and limited. Their predicting power ultimately depends on how closely a model’s connectivity represents the real system. Here we argue that the data-driven probabilistic rules, widely used to build neuronal network models, may not be appropriate to represent the dynamics of the corresponding biological system. To solve this problem, we propose to use a new mathematical framework able to use sparse and limited experimental data to quantitatively reproduce the structural connectivity of biological brain networks at cellular level.

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