Seasonality of surface stirring by geostrophic flows in the Bay of Bengal

2020 ◽  
Author(s):  
Nihar Paul ◽  
Jai Sukhatme
Keyword(s):  
Lyapunov Exponent ◽  
Power Law ◽  
Bay Of Bengal ◽  
Numerical Models ◽  
Finite Size ◽  
Power Spectra ◽  
Relative Dispersion ◽  
Eddy Diffusivities ◽  
Finite Time Lyapunov Exponent ◽  
Passive Tracers

<p>Stirring of passive tracers in the Bay of Bengal driven by altimetry derived daily geostrophic surface currents, is studied on subseasonal timescales. To begin with, Hovmöller plots, wavenumber-frequency diagrams and power spectra confirm the multiscale nature of the flow. Advection of latitudinal and longitudinal bands highlights the chaotic nature of stirring in the Bay via repeated straining and filamentation of the tracer field. An immediate finding is that stirring is local, i.e. of the scale of the eddies, and does not span the entire basin. Further, stirring rates are enhanced along the coast of the Bay and are relatively higher in the pre- and post-monsoonal seasons. Indeed, Finite Time Lyapunov Exponent (FTLE) and Finite Size Lyapunov Exponent (FSLE) maps in all the seasons are patchy with minima scattered through the interior of the Bay. Further, these maps bring out a seasonal cycle wherein rapid stirring progressively moves from the northern to southern Bay during pre- and post-monsoonal periods, respectively. The non-uniform stirring of the Bay is reflected in long tailed probability density functions of FTLEs, that become more stretched for longer time intervals. Quantitatively, advection for a week shows the mean FTLE lies between 0.13±0.07 day<sup>-1</sup>, while extremes reach almost 0.6 day<sup>-1</sup> . Averaged over the Bay, Relative dispersion initially grows exponentially, followed by a power-law at scales between approximately 100 and 250 km, which finally transitions to an eddy-diffusive regime. Quantitatively, below 250 km, a scale dependent diffusion coefficient is extracted that behaves as a power-law with cluster size, while above 250 km, eddy-diffusivities range from 6 × 10<sup>3</sup> - 1.6 × 10<sup>4  </sup> m<sup>2</sup>s<sup>-1</sup> in different regions of the Bay. These estimates provide a useful guide for resolution dependent diffusivities in numerical models that hope to properly represent surface stirring in the Bay.</p>

Predictability of the Northeast Monsoon Forecasts by the Educational Global Climate Model

2015 ◽  
Vol 804 ◽  
pp. 243-246
Author(s):  
Sunisa Saiuparad ◽  
Dusadee Sukawat
Keyword(s):  
Lyapunov Exponent ◽  
Prediction Model ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Weather Prediction ◽  
Finite Size ◽  
Largest Lyapunov Exponent ◽  
Northeast Monsoon ◽  
Finite Time Lyapunov Exponent

The predictability by an atmospheric prediction model is determined by the uncertainties in the initial condition and the imperfection of the model. It is difficult to provide accurate weather prediction and determines the predictability of a model. Atmospheric prediction model efficiency is obtained from the analysis of predictability measurement. Five existing predictability measurements; Lyapunov exponent, finite size Lyapunov exponent, finite time Lyapunov exponent, local Lyapunov exponent and largest Lyapunov exponent are used to measure predictability of the northeast monsoon (winter monsoon) by the Educational Global Climate Model (EdGCM) and to test sensitivity of the model to small initial perturbations. The EdGCM is run for 142-year predictions from the year 1958 to 2100. However, only the outputs of geopotential height at 500hPa of December from 2012 to 2100 are used for predictability measurement. The results show that the EdGCM predictability for the northeast monsoon forecast is about 120 years.

scholarly journals The Finite Size Lyapunov Exponent and the Finite Amplitude Growth Rate

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 348
Author(s):  
Thomas Meunier ◽  
J. H. LaCasce
Keyword(s):  
Growth Rate ◽  
Lyapunov Exponent ◽  
Velocity Structure ◽  
Initial Conditions ◽  
Mathematical Formulation ◽  
Finite Size ◽  
Finite Amplitude ◽  
Computational Method ◽  
Finite Time Lyapunov Exponent ◽  
Amplitude Growth

The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here, we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second-order velocity structure function.

scholarly journals The Finite Size Lyapunov Exponent and the Finite Amplitude Growth Rate

2021 ◽  
Author(s):  
Thomas Meunier ◽  
J.H. LaCasce
Keyword(s):  
Growth Rate ◽  
Lyapunov Exponent ◽  
Velocity Structure ◽  
Initial Conditions ◽  
Mathematical Formulation ◽  
Finite Size ◽  
Finite Amplitude ◽  
Computational Method ◽  
Finite Time Lyapunov Exponent ◽  
Amplitude Growth

The Finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990’s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second order velocity structure function.

An Experimental Study of the Forced Response of Pre- and Post-Critical Plates

1995 ◽  
Author(s):  
Kevin D. Murphy ◽  
Lawrence N. Virgin ◽  
Stephen A. Rizzi
Keyword(s):  
Experimental Study ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Small Amplitude ◽  
Narrow Band ◽  
Power Spectra ◽  
Forced Response ◽  
Acoustic Excitation ◽  
Rectangular Plates ◽  
Auto Correlation

Abstract Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-correlation functions, small amplitude vibrations are considered about both the pre- and post-critical states. These techniques are then employed to investigate the snap-through response. The results for snap-through suggest that the motion is temporally complex and a Lyapunov exponent calculation confirms that the motion is chaotic. Finally, a snap-through boundary is mapped in the (ω, SPL) parameter space separating the regions of snap-through and no snap-through.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

scholarly journals Shape Coherence and Finite-Time Curvature Evolution

2015 ◽  
Vol 25 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Tian Ma ◽  
Erik M. Bollt
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Coherent Structures ◽  
Finite Time ◽  
Large Curvature ◽  
Nonautonomous Dynamical Systems ◽  
Finite Time Lyapunov Exponent ◽  
Close Proximity ◽  
Definition Of ◽  
Curvature Growth

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-Time Lyapunov Exponent (FTLE) computation, often used to indicate hyperbolic material curves as Lagrangian Coherent Structures (LCS). We show that often the FTC troughs are in close proximity to the FTLE ridges, but in other scenarios, the FTC indicates entirely different regions.

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