Morón, Daniel; Vela-Martín, Alberto; Avila, Marc (2025): Predictability assessment of turbulence decay events with massive ensembles of simulations [dataset]. PANGAEA, https://doi.pangaea.de/10.1594/PANGAEA.977819 (DOI registration in progress)
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Published: 2025-03-06
Abstract:
Linearly stable shear flows first transition to turbulence in the form of localized turbulent patches. At low Reynolds numbers these turbulent patches tend to suddenly decay, following a memory less process. There is no satisfactory explanation as to why turbulence decays in these flows, nor how far in advance decay can be forecasted. Using massive ensembles of simulations of pipe flow and a reduced order model of shear flows we monitor how predictable different initial conditions are to decay events. In this database we include the GPU-codes we use to perform the massive ensembles of direct numerical simulations of pipe and a reduced order model of shear flows. Additionally the database includes time series of the predictability and main variables of many base flow trajectories, and classifications between predictable and unpredictable states. We also include a simple but still accurate model of reduced order model decays.
Parameter(s):
| # | Name | Short Name | Unit | Principal Investigator | Method/Device | Comment |
|---|---|---|---|---|---|---|
| 1 | Binary Object | Binary | Morón, Daniel | Numerical simulated | ||
| 2 | Figure | Fig | Morón, Daniel | Numerical simulated | ||
| 3 | Title | Title | Morón, Daniel | Numerical simulated | ||
| 4 | File name | File name | Morón, Daniel | Numerical simulated | ||
| 5 | Binary Object (File Size) | Binary (Size) | Bytes | Morón, Daniel | Numerical simulated | |
| 6 | Variable | Variable | Morón, Daniel | Numerical simulated | ||
| 7 | File format | File format | Morón, Daniel | Numerical simulated | ||
| 8 | Description | Description | Morón, Daniel | Numerical simulated |
License:
Creative Commons Attribution 4.0 International (CC-BY-4.0)
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Data
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| 1 Binary | 2 Fig | 3 Title | 4 File name | 5 Binary (Size) [Bytes] | 6 Variable | 7 File format | 8 Description |
|---|---|---|---|---|---|---|---|
| CODE1_nsPipe_CUDA.zip | Code for the direct numerical simulation (DNS) of the Navier-Stokes equations NSE | CODE1_nsPipe_CUDA.zip | 33 kBytes | Sources of the Fourier pseudospectral DNS code solving the NSE in a rigid pipe. See github.com for more information about the methods. This version integrates the ensembles of simulations used to characterize the predictability to decay events. It integrates a turbulent puff until it detects a decay event. It saves the instantaneous states of the puff at different times before decay and launches ensembles of simulations using as initial condition these puffs. | |||
| CODE2_MFE_CUDA.zip | Code for the massive ensemble of simulations of the MFE model | CODE2_MFE_CUDA.zip | 29.4 kBytes | Sources of the CUDA code used to integrate the MFE model in time. It integrates the model using a low-storage Runge Kutta method of 4th order. This version integrates the ensembles of simulations used to characterize the decay events. It first integrates a huge number of base cases that have a decay event at a given time. It saves states at different times before decay and uses these states as initial conditions for massive ensembles of simulations of the model. | |||
| CODE3_DECAY_PREDICTOR.zip | Code to predict decay events of the MFE model using predictability | CODE3_DECAY_PREDICTOR.zip | 5.4 kBytes | Sources of the MATLAB code that, integrates a reduced order MFE model trajectory, and computes the probability to decay as the indicator Ind as the trajectory evolves. Ind is equal to 1 when the predictor predicts inminent decay and smaller otherwise. | |||
| Fig1.zip | 1 | Description of transitional puffs and the MFE model | Fig1.zip | 8.6 MBytes | Time series of puffs and model variables, and life-time statistics | mat, txt and .m files | "It includes the time series of the cross-section averaged kinetic energy Q, and the model variables; and the lifetime statistics of both systems. Has the MATLAB function to generate Fig1 of the paper." |
| Fig2.zip | 2 | Description of the method to characterize predictability: Kullback-Leibler divergence (KLD) | Fig2.zip | 2.8 MBytes | Time series of puff variables, life-time statistics and metric of predictability. | mat, txt and .m files | Example of a puff trajectory before decay, as denoted by the time-dependent volume-averaged cross section kinetic energy. It includes the conditioned life-time statistics of massive ensembles of puffs initialized close to a given known state. It also includes the metric to measure predictability (before normalizing it). Find inside the MATLAB functions required to produce Figure 2 in the paper. |
| Fig3.zip | 3 | Trajectory averaged Kullback-Leibler divergence (KLD) as a measure of puff and MFE decay predictability | Fig3.zip | 23.5 MBytes | KLD of puff and MFE decay | mat, txt and .m files | Kullback-Leibler divergence as a measure of predictability for puffs and MFE model. It is computed as the difference between the conditional probability of different puff/MFE states compared with the exponential expected value. It includes MATLAB functions to generate Fig 4 of the paper. |
| Fig4.zip | 4 | Statistics of the KLD, defect of mean profile and cross-flow fluctuations in the MFE model | Fig4.zip | 389.5 kBytes | KLD, E1 and Ej (as the streamwise and cross-flow fluctuations) in the MFE model | mat, txt and .m files | Statistics of the time evolution of the KLD, E1 (as the defect of the energy of the mean profile) and Ej (as the energy of the cross-flows) of the MFE model, depending on whether trajectories are considered as predictable or unpredictable. Includes MATLAB functions to generate Figure 4 in the paper. |
| Fig5.zip | 5 | Regions of phase space according to predictability of MFE decay | Fig5.zip | 112 kBytes | KLD, E1 and Ej (as the streamwise and cross-flow fluctuations) in the MFE model | mat, txt and .m files | Colormaps of the projected phase space of the MFE model in the two variables E1 and Ej. The color corresponds to statistics of predictability in equispaced bins of the projected phase space. Includes MATLAB functions to generate figure 5 of the paper. |
| Fig6.zip | 6 | Assessment of the MFE decay predictor. | Fig6.zip | 19.8 MBytes | KLD, E1 and Ej (as the streamwise and cross-flow fluctuations) in the MFE model | mat, txt and .m files | Time series of the MFE decay predictor ability, in the case of a extremely rare MFE trajectory. It includes MATLAB functions to generate Figure 6 of the paper. |
| Fig7.zip | 7 | Statistics of the KLD, defect of center-line velocity and cross-flow fluctuations in puffs | Fig7.zip | 379.5 kBytes | KLD, Q as the cross flow energy and Uc as the defect of centerline velocity in puffs | mat, txt and .m files | Statistics of the time evolution of the KLD, Uc (as the defect of centerline velocity) and Q (as the energy of the cross-flows) of puffs, depending on whether trajectories are considered as predictable or unpredictable. Includes MATLAB functions to generate Figure 7 in the paper. |
| Fig8.zip | 8 | Regions of phase space according to predictability of puff decay | Fig8.zip | 56.5 kBytes | KLD, Q as the cross flow energy and Uc as the defect of centerline velocity in puffs | mat, txt and .m files | Colormaps of the projected phase space of the puffs in the two variables Q and Uc. The color corresponds to statistics of predictability in equispaced bins of the projected phase space. Includes MATLAB functions to generate figure 8 of the paper. |
| Fig9.zip | 9 | Assessment of the robustness of computation of the metric of predictability | Fig9.zip | 7.1 MBytes | KLD of puff and MFE decay | mat, txt and .m files | Statistics of puff and MFE KLD depending on the shape of the initial perturbations used in the ensembles and the number of members per ensemble. Includes MATLAB functions to create figure 9 of the paper. |
| Fig10.zip | 10 | Assessment of the effect of the uncertainty on the metric of predictability | Fig10.zip | 204 MBytes | KLD of MFE decay | mat, txt and .m files | Trajectory averaged KLD of MFE decay events, computed using different magnitudes of uncertainty (epsilon 0). It includes MATLAB functions to generate figure 10 of the paper. |
| Fig11.zip | 11 | Predictability of MFE extreme events | Fig11.zip | 31 MBytes | KLD of MFE extreme events | mat, txt and .m files | Description and assessment of the predictability of a different but also extreme event of the MFE model. Includes the MATLAB functions to generate figure 11 |
| Fig12.zip | 12 | Assessment of the MFE decay predictor. | Fig12.zip | 181.9 kBytes | KLD, E1 and Ej (as the streamwise and cross-flow fluctuations) in the MFE model | mat, txt and .m files | Time series of the MFE decay predictor ability, in the case of a decaying MFE trajectory. It includes MATLAB functions to generate Figure 6 of the paper. |