Study of interaction and complete merging of binary cyclones using complex networks.

Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru-Kulap and Seroja-Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.

Preventing a global transition to thermoacoustic instability by targeting local dynamics.

The burning of fossil fuels to generate power produces harmful emissions. Lowering such emissions in gas turbine engines is possible by operating them at fuel-lean conditions. However, such strategies often fail because, under fuel-lean conditions, the combustors are prone to catastrophic high-amplitude oscillations known as thermoacoustic instability. We reveal that, as an operating parameter is varied in time, the transition to thermoacoustic instability is initiated at specific spatial regions before it is observed in larger regions of the combustor. We use two indicators to discover such inceptive regions: the growth of variance of fluctuations in spatially resolved heat release rate and its spatiotemporal evolution. In this study, we report experimental evidence of suppression of the global transition to thermoacoustic instability through targeted modification of local dynamics at the inceptive regions. We strategically arrange slots on the flame anchor, which, in turn, reduce the local heat release rate fluctuations at the inceptive regions and thus suppress the global transition to thermoacoustic instability. Our results open new perspectives for combustors that are more environmental-friendly.

Neural ODE to model and prognose thermoacoustic instability.

Thermoacoustic instability in a reacting flow field is characterized by high amplitude pressure fluctuations driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. In a turbulent flow, the transition of a thermoacoustic system from a state of chaos to periodic oscillations occurs via a state of intermittency. During the transition to periodic oscillations, the unsteady heat release rate synchronizes with the acoustic pressure fluctuations. Thermoacoustic systems are traditionally modeled by coupling the model for the heat source and the acoustic subsystem, each estimated independently. The response of the unsteady heat source, i.e., the flame, to acoustic fluctuations is characterized by introducing unsteady external forcing. The forced response of the flame need not be the same in the presence of an acoustic field due to their nonlinear coupling. Instead of characterizing individual subsystems, we introduce a neural ordinary differential equation (neural ODE) framework to model the thermoacoustic system as a whole. The neural ODE model for the thermoacoustic system uses time series of the heat release rate and the pressure fluctuations, measured simultaneously without introducing any external perturbations, to model their coupled interaction. Furthermore, we use the parameters of neural ODE to define an anomaly measure that represents the proximity of system dynamics to limit cycle oscillations and thus provide an early warning signal for the onset of thermoacoustic instability.

Convolutional neural networks to predict the onset of oscillatory instabilities in turbulent systems.

Many fluid dynamic systems exhibit undesirable oscillatory instabilities due to positive feedback between fluctuations in their different subsystems. Thermoacoustic instability, aeroacoustic instability, and aeroelastic instability are some examples. When the fluid flow in the system is turbulent, the approach to such oscillatory instabilities occurs through a universal route characterized by a dynamical regime known as intermittency. In this paper, we extract the peculiar pattern of phase space attractors during the regime of intermittency by constructing recurrence networks corresponding to the phase space topology. We further train a convolutional neural network to classify the periodic and aperiodic structures in the recurrence networks and define a measure that indicates the proximity of the dynamical state to the onset of oscillatory instability. We show that this measure can predict the onset of oscillatory instabilities in three different fluid dynamic systems governed by different physical phenomena.

A cellular automata model for expanding turbulent flames.

Cellular automata models based on population dynamics, introduced by Von Neumann in the 1950s, has been successfully used to describe pattern development and front propagation in many applications, such as crystal growth, forest fires, fractal growth in biological media, etc. We, herein, explore the possibility of using a cellular automaton, based on the population dynamics of flamelets, as a low-order model to describe the dynamics of an expanding flame propagating in a turbulent environment. A turbulent flame is constituted by numerous flamelets, each of which interacts with their neighborhood composed of other flamelets, as well as unburned and burnt fluid particles. This local interaction leads to global flame dynamics. The effect of turbulence is simulated by introducing stochasticity in the local interaction and hence in the temporal evolution of the flamefront. Our results show that the model preserves various multifractal characteristics of the expanding turbulent flame and captures several characteristics of expanding turbulent flames observed in experiments. For example, at low turbulence levels, an increase in global burning rate leads to an increase in the turbulence level, while beyond a critical turbulence level, the expanding flame becomes increasingly fragmented, and consequently, the total burning rate decreases with increasing turbulence. Furthermore, at an extremely high turbulence level, the ignition kernel quenches at its nascent state and consequently loses its ability to propagate as an expanding flame.

Universality in spectral condensation.

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.

Modeling the role of respiratory droplets in Covid-19 type pandemics.

In this paper, we develop a first principles model that connects respiratory droplet physics with the evolution of a pandemic such as the ongoing Covid-19. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time, accounting for droplet cooling, heat and mass transfer, and finally, crystallization of the dissolved salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. The droplet evaporation/desiccation time is, indeed, dependent on ambient temperature and is also a strong function of relative humidity. The multi-scale model thus developed and the firm theoretical underpinning that connects the two scales-macro-scale pandemic dynamics and micro-scale droplet physics-thus could emerge as a powerful tool in elucidating the role of environmental factors on infection spread through respiratory droplets.

Bursting and mixed mode oscillations during the transition to limit cycle oscillations in a matrix burner.

We investigate the route to self-excited thermoacoustic instability in a laminar flow multiple flame matrix burner. With an increase in the equivalence ratio, the thermoacoustic system that is initially quiet (stable operation) transitions to limit cycle oscillations through two distinct dynamical states, namely, bursting oscillations and mixed mode oscillations. The acoustic pressure oscillations transition from quiescence to large amplitudes during bursting oscillations. Such high amplitude bursting oscillations that occur well ahead of the onset of limit cycle oscillations can potentially cause structural damage. The thermoacoustic system exhibits hysteresis. The transition to limit cycle oscillations is replicated in a phenomenological model containing slow-fast time scales.

Interplay between random fluctuations and rate dependent phenomena at slow passage to limit-cycle oscillations in a bistable thermoacoustic system.

We study the impact of noise on the rate dependent transitions in a noisy bistable oscillator using a thermoacoustic system as an example. As the parameter-the heater power-is increased in a quasi-steady manner, beyond a critical value, the thermoacoustic system undergoes a subcritical Hopf bifurcation and exhibits periodic oscillations. We observe that the transition to this oscillatory state is often delayed when the control parameter is varied as a function of time. However, the presence of inherent noise in the system introduces high variability in the characteristics of this critical transition. As a result, if the value of the system variable-the acoustic pressure-approaches the noise floor before the system crosses the unstable manifold, the effect of rate on the critical transition becomes irrelevant in determining the transition characteristics, and the system undergoes a noise-induced tipping to limit-cycle oscillations. The presence of noise-induced tipping makes it difficult to identify the stability regimes in such systems by using stability maps for the corresponding deterministic system.

Flame blowout: Transition to an absorbing phase.

The turbulent flame inside a gas turbine engine is susceptible to local extinction leading to global extinguishment or blowout at fuel lean conditions. Flame blowout is traditionally viewed as a loss of static stability of the combustor. However, flames often exhibit rich dynamics as blowout is approached suggesting that a more comprehensive description of the dynamics of flame blowout, which could lead to reduced order models, is necessary. A turbulent flame can be considered as a collection of a large number of flamelets. The population dynamics of these flamelets could be used to model the overall flame behavior as a contact process. In this context, flame blowout can be viewed as the population of flamelets approaching zero, in other words, extinction of flamelets. In this paper, we employ a cellular automata based model to study the emergent dynamics of the population of such flamelets. We show that the model is able to qualitatively capture interesting dynamics that a turbulent flame inside a combustor exhibits close to flame blowout. Furthermore, we show that flame blowout is similar to a threshold-like transition to an absorbing phase.

Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor.

Thermoacoustic instability is a result of the positive feedback between the acoustic pressure and the unsteady heat release rate fluctuations in a combustor. We apply the framework of the synchronization theory to study the coupled behavior of these oscillations during the transition to thermoacoustic instability in a turbulent bluff-body stabilized gas-fired combustor. Furthermore, we characterize this complex behavior using recurrence plots and recurrence networks. We mainly found that the correlation of probability of recurrence ( C P R ), the joint probability of recurrence ( J P R ), the determinism ( D E T ), and the recurrence rate ( R R ) of the joint recurrence matrix aid in detecting the synchronization transitions in this thermoacoustic system. We noticed that C P R and D E T can uncover the occurrence of phase synchronization state, whereas J P R and R R can be used as indices to identify the occurrence of generalized synchronization (GS) state in the system. We applied measures derived from joint and cross recurrence networks and observed that the joint recurrence network measures, transitivity ratio, and joint transitivity are useful to detect GS. Furthermore, we use the directional property of the network measure, namely, cross transitivity to analyze the type of coupling existing between the acoustic field ( p ' ) and the heat release rate ( q ˙ ' ) fluctuations. We discover a possible asymmetric bidirectional coupling between q ˙ ' and p ' , wherein q ˙ ' is observed to exert a stronger influence on p ' than vice versa.

On the emergence of critical regions at the onset of thermoacoustic instability in a turbulent combustor.

We use complex network theory to investigate the dynamical transition from stable operation to thermoacoustic instability via intermittency in a turbulent combustor with a bluff body stabilized flame. A spatial network is constructed, representing each of these three dynamical regimes of combustor operation, based on the correlation between time series of local velocity obtained from particle image velocimetry. Network centrality measures enable us to identify critical regions of the flow field during combustion noise, intermittency, and thermoacoustic instability. We find that during combustion noise, the bluff body wake turns out to be the critical region that determines the dynamics of the combustor. As the turbulent combustor transitions to thermoacoustic instability, during intermittency, the wake of the bluff body loses its significance in determining the flow dynamics and the region on top of the bluff body emerges as the most critical region in determining the flow dynamics during thermoacoustic instability. The knowledge about this critical region of the reactive flow field can help us devise optimal control strategies to evade thermoacoustic instability.