Thermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional ...premixed flame in a duct via numerical simulations of a
$G$
-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle–Takens–Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.
Atmospheric rivers (ARs) are now widely known for their association with high‐impact weather events and long‐term water supply in many regions. Researchers within the scientific community have ...developed numerous methods to identify and track of ARs—a necessary step for analyses on gridded data sets, and objective attribution of impacts to ARs. These different methods have been developed to answer specific research questions and hence use different criteria (e.g., geometry, threshold values of key variables, and time dependence). Furthermore, these methods are often employed using different reanalysis data sets, time periods, and regions of interest. The goal of the Atmospheric River Tracking Method Intercomparison Project (ARTMIP) is to understand and quantify uncertainties in AR science that arise due to differences in these methods. This paper presents results for key AR‐related metrics based on 20+ different AR identification and tracking methods applied to Modern‐Era Retrospective Analysis for Research and Applications Version 2 reanalysis data from January 1980 through June 2017. We show that AR frequency, duration, and seasonality exhibit a wide range of results, while the meridional distribution of these metrics along selected coastal (but not interior) transects are quite similar across methods. Furthermore, methods are grouped into criteria‐based clusters, within which the range of results is reduced. AR case studies and an evaluation of individual method deviation from an all‐method mean highlight advantages/disadvantages of certain approaches. For example, methods with less (more) restrictive criteria identify more (less) ARs and AR‐related impacts. Finally, this paper concludes with a discussion and recommendations for those conducting AR‐related research to consider.
Key Points
The large number of atmospheric river identification/tracking methods produces large uncertainty related to AR climatology and impacts
Uncertainty is quantified using the same data (MERRA v2), time period (1980–2017), region (global where possible), and common metrics
This study presents recommendations regarding the advantages/disadvantages of certain approaches based on science application
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There is currently large uncertainty over the impacts of climate change on precipitation trends over the US west coast. Atmospheric rivers (ARs) are a significant source of US west coast ...precipitation and trends in ARs can provide insight into future precipitation trends. There are already a variety of different methods used to identify ARs, but many are used in contexts that are often difficult to apply to large climate datasets due to their computational cost and requirement of integrated vapor transport as an input variable, which can be expensive to compute in climate models at high temporal frequencies. Using deep learning (DL) to track ARs is a unique approach that can alleviate some of the computational challenges that exist in more traditional methods. However, some questions still remain regarding its flexibility and robustness. This research investigates the consistency of a DL methodology of tracking ARs with more established algorithms to demonstrate its high‐level performance for future studies.
Plain Language Summary
Atmospheric rivers (ARs) are long corridors of water vapor in the lower atmosphere that are associated with a large amount of precipitation on the US west coast. They are important to investigate in future climate change scenarios. To further understand them in climate change scenarios, they must be tracked in large datasets. We demonstrate the efficiency, effectiveness, and flexibility of a machine learning tracking method by comparing it to more established existing tracking methods. This method applies particularly well to large climate datasets and can be useful for future studies.
Key Points
CG‐Climate is an effective and efficient way to track atmospheric rivers in large datasets
CG‐Climate is flexible with varying spatial resolutions and domains
Human hand labels are effective in identifying atmospheric river events in the correct location, but have a spatial area bias
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•Confirmed statistics-conforming property of GANs for modeling dynamical systems.•Highlighted the lack of robustness of GANs and need of explicit physical constraints.•Improved training robustness of ...GANs by explicitly enforcing statistical constraints.•Demonstrated merits of statistics-informed GANs on modeling Rayleigh-Bénard convection.
Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Although the advancement of high performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, reliable and accurate closure models for the unresolved physics remains an important requirement for many computational physics problems, e.g., turbulence simulation. Recently, several researchers have adopted generative adversarial networks (GANs), a novel paradigm of training machine learning models, to generate solutions of PDEs-governed complex systems without having to numerically solve these PDEs. However, GANs are known to be difficult in training and likely to converge to local minima, where the generated samples do not capture the true statistics of the training data. In this work, we present a statistical constrained generative adversarial network by enforcing constraints of covariance from the training data, which results in an improved machine-learning-based emulator to capture the statistics of the training data generated by solving fully resolved PDEs. We show that such a statistical regularization leads to better performance compared to standard GANs, measured by (1) the constrained model's ability to more faithfully emulate certain physical properties of the system and (2) the significantly reduced (by up to 80%) training time to reach the solution. We exemplify this approach on the Rayleigh-Bénard convection, a turbulent flow system that is an idealized model of the Earth's atmosphere. With the growth of high-fidelity simulation databases of physical systems, this work suggests great potential for being an alternative to the explicit modeling of closures or parameterizations for unresolved physics, which are known to be a major source of uncertainty in simulating multi-scale physical systems, e.g., turbulence or Earth's climate.
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Open-loop forcing is known to be an effective strategy for controlling self-excited thermoacoustic oscillations, but the details of this synchronization process have yet to be comprehensively ...explored. In this study, we experimentally examine the synchronization dynamics of a laminar conical premixed flame in a tube combustor subjected to periodic acoustic forcing. We compare the response of this forced self-excited system with that of a forced Duffing–van der Pol oscillator, and find many similarities but also some differences. The similarities include (i) a torus-birth bifurcation from periodicity to quasiperiodicity at low forcing amplitudes, producing a stable ergodic T2 torus attractor in phase space; (ii) a transition from T2 quasiperiodicity to lock-in above a critical forcing amplitude, which increases linearly as the forcing frequency ff deviates from the natural frequency f1; (iii) two distinct routes to lock-in, one via a torus-death bifurcation if ff is far from f1 and one via a saddle-node bifurcation if ff is close to f1; and (iv) asynchronous quenching (AQ), which coincides with a torus-death bifurcation to lock-in and reduces the oscillation amplitude – by up to 90% in the combustor. There are, however, quantitative differences between the two systems, which pertain mainly to (i) the magnitude of the amplitude reduction achieved by AQ and (ii) the size of the AQ region in the ff/f1–forcing-amplitude plane.
This study has three main contributions. First, it shows that studying open-loop control from a synchronization perspective can provide valuable insight into the optimal forcing conditions. Second, it shows that the optimal forcing condition for weakening thermoacoustic oscillations is that which causes the onset of lock-in via a torus-death bifurcation, as this is where AQ occurs. Third, it shows that the synchronization dynamics of a real combustor can be qualitatively modelled with a low-order universal oscillator. This suggests that it may be possible to develop and test new control strategies by analyzing the solutions to such an oscillator.
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Synchronization is a universal concept in nonlinear science but has received little attention in thermoacoustics. In this numerical study, we take a dynamical systems approach to investigating the ...influence of harmonic acoustic forcing on three different types of self-excited thermoacoustic oscillations: periodic, quasi-periodic and chaotic. When the periodic system is forced, we find that: (i) at low forcing amplitudes, it responds at both the forcing frequency and the natural (self-excited) frequency, as well as at their linear combinations, indicating quasi-periodicity; (ii) above a critical forcing amplitude, the system locks in to the forcing; (iii) the bifurcations leading up to lock-in and the critical forcing amplitude required for lock-in depend on the proximity of the forcing frequency to the natural frequency; (iv) the response amplitude at lock-in may be larger or smaller than that of the unforced system and the system can exhibit hysteresis and the jump phenomenon owing to a cusp catastrophe; and (v) at forcing amplitudes above lock-in, the oscillations can become unstable and transition to chaos, or switch between different stable attractors depending on the forcing amplitude. When the quasi-periodic system is forced at a frequency equal to one of the two characteristic frequencies of the torus attractor, we find that lock-in occurs via a saddle-node bifurcation with frequency pulling. When the chaotic system is forced at a frequency close to the dominant frequency of its strange attractor, we find that it is possible to destroy chaos and establish stable periodic oscillations. These results show that the open-loop application of harmonic acoustic forcing can be an effective strategy for controlling periodic or aperiodic thermoacoustic oscillations. In some cases, we find that such forcing can reduce the response amplitude by up to 90 %, making it a viable way to weaken thermoacoustic oscillations.
There is growing interest in data-driven weather prediction (DDWP), e.g., using convolutional neural networks such as U-NET that are trained on data from models or reanalysis. Here, we propose three ...components, inspired by physics, to integrate with commonly used DDWP models in order to improve their forecast accuracy. These components are (1) a deep spatial transformer added to the latent space of U-NET to capture rotation and scaling transformation in the latent space for spatiotemporal data, (2) a data-assimilation (DA) algorithm to ingest noisy observations and improve the initial conditions for next forecasts, and (3) a multi-time-step algorithm, which combines forecasts from DDWP models with different time steps through DA, improving the accuracy of forecasts at short intervals. To show the benefit and feasibility of each component, we use geopotential height at 500 hPa (Z500) from ERA5 reanalysis and examine the short-term forecast accuracy of specific setups of the DDWP framework. Results show that the spatial-transformer-based U-NET (U-STN) clearly outperforms the U-NET, e.g., improving the forecast skill by 45 %. Using a sigma-point ensemble Kalman (SPEnKF) algorithm for DA and U-STN as the forward model, we show that stable, accurate DA cycles are achieved even with high observation noise. This DDWP+DA framework substantially benefits from large (O(1000)) ensembles that are inexpensively generated with the data-driven forward model in each DA cycle. The multi-time-step DDWP+DA framework also shows promise; for example, it reduces the average error by factors of 2–3. These results show the benefits and feasibility of these three components, which are flexible and can be used in a variety of DDWP setups. Furthermore, while here we focus on weather forecasting, the three components can be readily adopted for other parts of the Earth system, such as ocean and land, for which there is a rapid growth of data and need for forecast and assimilation.
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Tracking and predicting extreme events in large-scale spatio-temporal climate data are long standing challenges in climate science. In this paper, we propose Convolutional LSTM (ConvLSTM)-based ...spatio-temporal models to track and predict hurricane trajectories from large-scale climate data; namely, pixel-level spatio-temporal history of tropical cyclones. To address the tracking problem, we model time-sequential density maps of hurricane trajectories, enabling to capture not only the temporal dynamics but also spatial distribution of the trajectories. Furthermore, we introduce a new trajectory prediction approach as a problem of sequential forecasting from past to future hurricane density map sequences. Extensive experiment on actual 20 years record shows that our ConvLSTM-based tracking model significantly outperforms existing approaches, and that the proposed forecasting model achieves successful mapping from predicted density map to ground truth.
Numerous facets of scientific research implicitly or explicitly call for the estimation of probability densities. Histograms and kernel density estimates (KDEs) are two commonly used techniques for ...estimating such information, with the KDE generally providing a higher fidelity representation of the probability density function (PDF). Both methods require specification of either a bin width or a kernel bandwidth. While techniques exist for choosing the kernel bandwidth optimally and objectively, they are computationally intensive, since they require repeated calculation of the KDE. A solution for objectively and optimally choosing both the kernel shape and width has recently been developed by Bernacchia and Pigolotti (2011). While this solution theoretically applies to multidimensional KDEs, it has not been clear how to practically do so.
A method for practically extending the Bernacchia–Pigolotti KDE to multidimensions is introduced. This multidimensional extension is combined with a recently-developed computational improvement to their method that makes it computationally efficient: a 2D KDE on 105 samples only takes 1 s on a modern workstation. This fast and objective KDE method, called the fastKDE method, retains the excellent statistical convergence properties that have been demonstrated for univariate samples. The fastKDE method exhibits statistical accuracy that is comparable to state-of-the-science KDE methods publicly available in R, and it produces kernel density estimates several orders of magnitude faster. The fastKDE method does an excellent job of encoding covariance information for bivariate samples. This property allows for direct calculation of conditional PDFs with fastKDE. It is demonstrated how this capability might be leveraged for detecting non-trivial relationships between quantities in physical systems, such as transitional behavior.
•A multidimensional, fast, and robust kernel density estimation is proposed: fastKDE.•fastKDE has statistical performance comparable to state-of-the-science kernel density estimate packages in R.•fastKDE is demonstrably orders of magnitude faster than comparable, state-of-the-science density estimate packages in R.•A Python-based implementation of fastKDE is available at https://bitbucket.org/lbl-cascade/fastkde.
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While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and ...inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call Turbulent-Flow Net, is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.
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