scholarly journals Predicting vortex merging and ensuing turbulence characteristics in shear layers from initial conditions

2019 ◽  
Vol 878 ◽  
Author(s):  
Anirban Guha ◽  
Mona Rahmani
Keyword(s):  
Initial Conditions ◽  
Shear Layers ◽  
Late Time ◽  
Initial State ◽  
Effective Measure ◽  
Form Complex ◽  
Turbulence Characteristics ◽  
Vortex Merging ◽  
Highly Nonlinear ◽  
Turbulence Mixing

Unstable shear layers in environmental and industrial flows roll up into a series of vortices, which often form complex nonlinear merging patterns such as pairs and triplets. These patterns crucially determine the subsequent turbulence, mixing and scalar transport. We show that the late-time, highly nonlinear merging patterns are predictable from the linearized initial state. The initial asymmetry between consecutive wavelengths of the vertical velocity field provides an effective measure of the strength and pattern of vortex merging. The predictions of this measure are substantiated using direct numerical simulations. We also show that this measure has significant implications in determining the route to turbulence and the ensuing turbulence characteristics.

The role of transverse secondary instabilities in the evolution of free shear layers

1989 ◽  
Vol 202 ◽  
pp. 367-402 ◽  
Author(s):  
G. P. Klaassen ◽  
W. R. Peltier
Keyword(s):  
Linear Stability ◽  
Initial Conditions ◽  
Shear Layers ◽  
Nonlinear Flow ◽  
Stability Analyses ◽  
Vortex Merging ◽  
Theoretical Predictions ◽  
High Reynolds ◽  
Secondary Instabilities ◽  
Stuart Vortices

Linear stability analyses and nonlinear flow simulations reveal several important features of transverse secondary instabilities of two-dimensional Kelvin–Helmholtz billows and Stuart vortices. Vortex pairing is found to be the most rapidly amplified mode in a continuous spectrum of vortex merging instabilities. In certain not uncommon circumstances it is possible for more than two vortices to amalgamate in a single interaction, demonstrating that the phenomenon that has become known as the pairing resonance in fact has a rather low quality factor. Another form of merging instability in which a vortex is deformed and drained by its neighbours has been revealed by our linear stability analyses of nonlinear shear-layer disturbances. It appears, however, that this vortex draining instability may be important only in unstratified or very weakly stratified flows, since in moderately stratified Kelvin–Helmholtz flow, it is replaced by a highly localized instability which leads to a temporary distortion of the braids. Nonlinear simulations of vortex merging events in moderately stratified, high-Reynolds-number shear layers are compared to the theoretical predictions of our stability analyses. We investigate and quantify the sensitivity of merging events to variations in the initial conditions. The character of the flow after merging instability saturates and the nonlinear aspects of multiple merging events are also considered.

Predicting extreme events using dynamics based machine learning. 

2021 ◽  
Author(s):  
Dario Lucente ◽  
George Miloshevich ◽  
Corentin Herbert ◽  
Freddy Bouchet
Keyword(s):  
Markov Chain ◽  
Heat Waves ◽  
Initial Conditions ◽  
Original System ◽  
Initial Condition ◽  
Initial State ◽  
Probability Of Occurrence ◽  
Effective Dynamics ◽  
Highly Nonlinear ◽  
Low Dimensional

<p>Many phenomena in the climate system lie in the gray zone between weather and climate: they are not amenable to deterministic forecast, but they still depend on the initial condition. A natural example is medium-range forecasting, which is inherently probabilistic because it lies beyond the predictability time of the atmosphere. Similarly, one may ask the probability of occurrence of an El Niño event several months ahead of time or the probability of occurrence of a heat wave a few weeks in advance based on the observed atmospheric circulation. In this talk, we introduce a quantity which corresponds precisely to this type of prediction problem: the committor function is the probability for an event to occur in the future, as a function of the current state of the system.<span> </span></p><p>In the first part of this presentation, we explain the main mathematical properties of this probabilistic concept, and compute it in the case of a low-dimensional stochastic model for El-Niño, the Jin and Timmerman model. This example allows us to show that the ability to predict the probability of occurrence of the event of interest may differ strongly depending on the initial state: in some regions of phase space, the committor function is smooth (intrinsic probabilistic predictability) and in some other regions, it depends sensitively on the initial condition (intrinsic probabilistic unpredictability).<span>  </span>We stress that this predictability concept is markedly different from the deterministic unpredictability arising because of chaotic dynamics and exponential sensivity to initial conditions.<span> </span></p><p>The second part of the talk is about how to efficiently compute the committor function from data through several data-driven approaches, such as direct estimates, kernel-based methods and neural networks. We discuss two examples: a) the computation of committor function for the Jin and Timmerman model, b) the computation of committor function for extreme heat waves. Both systems are highly nonlinear but, considering the dimensionality of the two, their level of complexity is profoundly different. This therefore allows us to explore and discuss the performance and limits of the different methods proposed.<span> </span></p><p>Finally, we propose a method for learning effective dynamics by introducing a Markov chain on the data. Using the Markov chain we are able to quickly and easily compute many interesting quantities of the original system, including the committor function. The goal is to overcome some of the limitations of the methods introduced previously and to develop a robust algorithm that can be useful even in the lack of data.</p>

scholarly journals Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2471
Author(s):  
Tommaso Bradde ◽  
Samuel Chevalier ◽  
Marco De Stefano ◽  
Stefano Grivet-Talocia ◽  
Luca Daniel
Keyword(s):  
Dynamical Systems ◽  
Power System ◽  
System Dynamics ◽  
Real Time ◽  
Initial Conditions ◽  
Test System ◽  
Initial State ◽  
Power System Dynamics ◽  
Vector Fitting ◽  
Time Modeling

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

scholarly journals PNA Predictability at Various Time Scales

2013 ◽  
Vol 26 (22) ◽  
pp. 9090-9114 ◽  
Author(s):  
Waqar Younas ◽  
Youmin Tang
Keyword(s):  
Time Scales ◽  
Initial Conditions ◽  
Prediction Skill ◽  
Multiple Model ◽  
Coupled Models ◽  
Potential Predictability ◽  
Effective Measure ◽  
Dispersion Component ◽  
Significant Difference ◽  
Better Than

Abstract In this study, the predictability of the Pacific–North American (PNA) pattern is evaluated on time scales from days to months using state-of-the-art dynamical multiple-model ensembles including the Canadian Historical Forecast Project (HFP2) ensemble, the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) ensemble, and the Ensemble-Based Predictions of Climate Changes and their Impacts (ENSEMBLES). Some interesting findings in this study include (i) multiple-model ensemble (MME) skill was better than most of the individual models; (ii) both actual prediction skill and potential predictability increased as the averaging time scale increased from days to months; (iii) there is no significant difference in actual skill between coupled and uncoupled models, in contrast with the potential predictability where coupled models performed better than uncoupled models; (iv) relative entropy (REA) is an effective measure in characterizing the potential predictability of individual prediction, whereas the mutual information (MI) is a reliable indicator of overall prediction skill; and (v) compared with conventional potential predictability measures of the signal-to-noise ratio, the MI-based measures characterized more potential predictability when the ensemble spread varied over initial conditions. Further analysis found that the signal component dominated the dispersion component in REA for PNA potential predictability from days to seasons. Also, the PNA predictability is highly related to the signal of the tropical sea surface temperature (SST), and SST–PNA correlation patterns resemble the typical ENSO structure, suggesting that ENSO is the main source of PNA seasonal predictability. The predictable component analysis (PrCA) of atmospheric variability further confirmed the above conclusion; that is, PNA is one of the most predictable patterns in the climate variability over the Northern Hemisphere, which originates mainly from the ENSO forcing.

scholarly journals Implicit large eddy simulation of shock-driven material mixing

2013 ◽  
Vol 371 (2003) ◽  
pp. 20120217 ◽  
Author(s):  
F. F. Grinstein ◽  
A. A. Gowardhan ◽  
J. R. Ristorcelli
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Mixing ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Late Time ◽  
Eddy Simulation ◽  
Geometrical Complexity ◽  
Planar Shock ◽  
Large Eddy ◽  
Implicit Large Eddy Simulation

Under-resolved computer simulations are typically unavoidable in practical turbulent flow applications exhibiting extreme geometrical complexity and a broad range of length and time scales. An important unsettled issue is whether filtered-out and subgrid spatial scales can significantly alter the evolution of resolved larger scales of motion and practical flow integral measures. Predictability issues in implicit large eddy simulation of under-resolved mixing of material scalars driven by under-resolved velocity fields and initial conditions are discussed in the context of shock-driven turbulent mixing. The particular focus is on effects of resolved spectral content and interfacial morphology of initial conditions on transitional and late-time turbulent mixing in the fundamental planar shock-tube configuration.

scholarly journals Study of the influence of initial-state fluctuations on hydrodynamic simulations

2020 ◽  
Vol 245 ◽  
pp. 06005
Author(s):  
Marcin Słodkowski ◽  
Patryk Gawryszewski ◽  
Dominik Setniewski
Keyword(s):  
Initial Conditions ◽  
Graphics Processing Unit ◽  
Heavy Ion ◽  
Processing Unit ◽  
Initial State ◽  
Final State ◽  
Hydrodynamic Simulation ◽  
Hydrodynamic Simulations ◽  
Cartesian Coordinate ◽  
Ion Collision

In this work, we are focusing on assessing the contribution of the initial-state fluctuations of heavy ion collision in the hydrodynamic simulations. We are trying to answer the question of whether the hydrodynamic simulation retains the same level of fluctuation in the final-state as for the initial stage. In another scenario, the hydrodynamic simulations of the fluctuation drowns in the final distribution of expanding matter. For this purpose, we prepared sufficient relativistic hydrodynamic program to study A+A interaction which allows analysing initial-state fluctuations in the bulk nuclear matter. For such an assumption, it is better to use high spatial resolution. Therefore, we applied the (3+1) dimensional Cartesian coordinate system. We implemented our program using parallel computing on graphics cards processors - Graphics Processing Unit (GPU). Simulations were carried out with various levels of fluctuation in initial conditions using the average method of events coming from UrQMD models. Energy density distributions were analysed and the contribution of fluctuations in initial conditions was assessed in the hydrodynamic simulation.

Nonlinear Measure for Nonlinear Dynamic Processes Using Convergence Area: Typical Case Studies

2021 ◽  
Author(s):  
Joanofarc Xavier ◽  
S.K. Patnayak ◽  
Rames Panda
Keyword(s):  
Phase Portrait ◽  
Case Studies ◽  
Initial Conditions ◽  
Operating Point ◽  
Linear Approximations ◽  
Promising Tool ◽  
Highly Nonlinear ◽  
Phase Portrait Analysis ◽  
Nonlinear Dynamic Processes ◽  
Nonlinear Measure

Abstract Several industrial chemical processes exhibit severe nonlinearity. This paper addresses the computational and nonlinear issues occurring in many typical industrial problems in aspects of its stability, strength of nonlinearity and input output dynamics. In this article, initially, a prospective investigation is conducted on various nonlinear processes through phase portrait analysis to understand their stability status at different initial conditions about the vicinity of the operating point of the process. To estimate the degree of nonlinearity, for input perturbations from its nominal value, a novel nonlinear measure is put forward, that anticipates on the converging area between the nonlinear and their linearized responses. The nonlinearity strength is fixed between 0 and 1 to classify processes to be mild, medium or highly nonlinear. The most suitable operating point, for which the system remains asymptotically stable is clearly identified from the phase portrait. The metric can be contemplated as a promising tool to measure the nonlinearity of Industrial case studies at different linear approximations. Numerical simulations are executed in Matlab to compute , which conveys that the nonlinear dynamics of each Industrial example is very sensitive to input perturbations at different linear approximations. In addition to the identified metric, nonlinear lemmas are framed to select appropriate control schemes for the processes based on its numerical value of nonlinearity..

Entrainment and growth of vortical disturbances in the channel-entrance region

2021 ◽  
Vol 927 ◽  
Author(s):  
Pierre Ricco ◽  
Claudia Alvarenga
Keyword(s):  
Initial Conditions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Analytical Description ◽  
Reynolds Numbers ◽  
Boundary Region ◽  
Shear Layers ◽  
Base Flow ◽  
Open Boundary ◽  
Classical Stability

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

scholarly journals Effect of Spheroidization Annealing on Pearlite Banding

2019 ◽  
Vol 949 ◽  
pp. 40-47 ◽  
Author(s):  
Sergey Guk ◽  
Eva Augenstein ◽  
Maksim Zapara ◽  
Rudolf Kawalla ◽  
Ulrich Prahl
Keyword(s):  
Empirical Model ◽  
Initial Conditions ◽  
The Other ◽  
Experimental Investigations ◽  
Initial State ◽  
Ferritic Matrix ◽  
Other Hand ◽  
Initial States ◽  
Hot Rolled

The present paper deals with the influence of the duration of isothermal spheroidization annealing on the evolution of pearlite bands in various initial states. In this study, two initial conditions of the steel 16MnCrS5 are considered: a) industrially hot-rolled pearlite structures in their ferritic matrix and b) a specifically adjusted microstructure in the lab condition. Based on the experimental investigations and quantitative microstructural analyses, an empirical model for the prediction of pearlite banding within a broad range of annealing durations could be derived. Both, experiment and model, agree that pronounced pearlite bands in the initial state almost disappear after 25 h of spheroidization annealing. On the other hand, a marginal degree of pearlite banding in the initial state increases slightly during annealing. This fact could be explained by inhomogeneous cementite formation inside and outside the primary segregation regions of manganese.

DISCRETE TIME QUANTUM WALK ON A LINE WITH TWO PARTICLES

2006 ◽  
Vol 04 (03) ◽  
pp. 573-583 ◽  
Author(s):  
L. SHERIDAN ◽  
N. PAUNKOVIĆ ◽  
Y. OMAR ◽  
S. BOSE
Keyword(s):  
Discrete Time ◽  
Relative Phase ◽  
Initial Conditions ◽  
Quantum Walk ◽  
Degree Of Freedom ◽  
Initial State ◽  
Time Quantum

We introduce the idea of a quantum walk with two particles and study it for the case of a discrete time walk on a line. We consider both separable and maximally entangled initial conditions, and show how the entanglement and the relative phase between the states describing the coin degree of freedom of each particle will influence the evolution of the quantum walk. In particular, these factors will have consequences for the distance between the particles and the probability of finding them at a given point, yielding results that cannot be obtained from a separable initial state, be it pure or mixed. Finally, we review briefly proposals for implementations.

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