polymathic-ai/rayleigh_taylor_instability

This Dataset is part of The Well Collection.

How To Load from HuggingFace Hub

1. Be sure to have the_well installed (pip install the_well)
2. Use the WellDataModule to retrieve data as follows:

from the_well.data import WellDataModule

# The following line may take a couple of minutes to instantiate the datamodule
datamodule = WellDataModule(
    "hf://datasets/polymathic-ai/",
    "rayleigh_taylor_instability",
)
train_dataloader = datamodule.train_dataloader()

for batch in dataloader:
    # Process training batch
    ...

Rayleigh-Taylor instability

One line description of the data: Effect of spectral shape and component phases on development of Rayleigh-Taylor turbulence.

Longer description of the data: We consider the Rayleigh-Taylor instability for a range of Atwood numbers and initial perturbations, all of which have a log—normal horizontal energy spectrum with random phase. The dataset examines how varying the mean, standard deviation and the disparity of the random phase effects the transition to and statistics of the ensuing turbulent flow.

Associated paper: Paper.

Domain experts: Stefan Nixon, University of Cambridge, Romain Watteaux, CEA DAM, Suart B. Dalziel, University of Cambridge.

Code or software used to generate the data: TurMix3D.

Equation:The flow is governed by equations for continuity, momentum and incompressibility in the case of miscible fluids with common molecular diffusivity:

Here, $\rho \backslash rho$ is density, $\vec{u}\backslash vec\{u\}$ is velocity, $pp$ is pressure, $\vec{g}\backslash vec\{g\}$ is gravity, $\kappa \backslash kappa$ is the coefficient of molecular diffusivity and $\vec{\tau }\backslash vec\{\backslash tau\}$ is the deviatoric stress tensor

$$\vec{\tau }=\rho \nu (\mathrm{\nabla }\vec{u}+{\left(\mathrm{\nabla }\vec{u}\right)}^T-\frac{2}{3}(\mathrm{\nabla }\cdot \vec{u})\vec{I}),\backslash vec\{\backslash tau\}=\; \backslash rho\backslash nu\backslash left(\backslash nabla\backslash vec\{u\}+\backslash left(\backslash nabla\backslash vec\{u\}\backslash right)^T-\backslash frac\{2\}\{3\}\backslash left(\backslash nabla\backslash cdot\backslash vec\{u\}\; \backslash right)\backslash vec\{I\}\backslash right),$$

where $\nu \backslash nu$ is the kinematic viscosity and $\vec{I}\backslash vec\{I\}$ is the identity matrix.

Dataset	FNO	TFNO	Unet	CNextU-net
rayleigh_taylor_instability (At = 0.25)	>10	>10	>10	>10

Table: VRMSE metrics on test sets (lower is better). Best results are shown in bold. VRMSE is scaled such that predicting the mean value of the target field results in a score of 1.

About the data

Dimension of discretized data: 60 time-steps of 128 $\times \backslash times$ 128 $\times \backslash times$ 128 cubes.

Fields available in the data: Density (scalar field), velocity (vector field).

Number of trajectories: 45 trajectories.

Estimated size of the ensemble of all simulations: 255.6 GB.

Grid type: uniform grid, cartesian coordinates.

Initial conditions: Initial conditions have been set by imposing a log—normal profile for the shape of energy spectrum in wavenumber space, such that:

$$A(k)=\frac{1}{k\sigma \sqrt{2\pi }}\exp (-\frac{(\ln (k)-\mu {)}^2}{2{\sigma }^2})\text{with}k=\sqrt{k_x^2+k_y^2}A(k)\; =\; \backslash frac\{1\}\{k\backslash sigma\backslash sqrt\{2\backslash pi\}\}\; \backslash exp\backslash Big(-\backslash frac\{(\backslash ln\; (k)\; -\; \backslash mu)^2\}\{2\backslash sigma^2\}\backslash Big)\; \backslash quad\backslash textrm\{with\}\backslash quad\; k\; =\; \backslash sqrt\{k^2\_x+k^2\_y\}$$

where $\mu \backslash mu$ is the mean and $\sigma \backslash sigma$ is the standard deviation of the profile. Furthermore, we have imposed a random phase to the corresponding complex Fourier component (i.e. a random value for the argument of the complex Fourier component) between zero and a varied maximum (\(\phi_{max}\)), finally after Fourier transforming to physical space the mean of the resulting profile is normalized to ${3.10}^{5}3.10^5$ to ensure comparable power.

Boundary conditions: Periodic boundary conditions on sides walls and slip conditions on the top and bottom walls.

Simulation time-step: $\mathrm{\Delta }t\backslash Delta\; t$ is set such that the maximum Courant number is $\frac{1}{2}(CF{L}_{max}=0.5)\backslash frac12(CFL\_\{max\}=0.5)$. Therefore, the time step decreases as the flow accelerates.

Data are stored separated by ( $\mathrm{\Delta }t\backslash Delta\; t$): varies with the Atwood number.

Total time range ( $t_{min}t\_\{min\}$ to $t_{max}t\_\{max\}$): Varies from $t_{min}=0t\_\{min\}=0$ to $t_{max}t\_\{max\}$ between $\sim 30s\backslash sim\; 30s$ and $\sim 100s\backslash sim\; 100s$, depending on Atwood number.

Spatial domain size ( $L_{x}L\_x$, $L_{y}L\_y$, $L_{z}L\_z$): $[0,1]\times [0,1]\times [0,1][0,1]\backslash times[0,1]\backslash times[0,1]$.

Set of coefficients or non-dimensional parameters evaluated: We run simulations with 13 different initializations for five different Atwood number values $At\in \{\frac{3}{4},\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16}\}At\backslash in\; \backslash \{\backslash frac34,\; \backslash frac12,\; \backslash frac14,\; \backslash frac18,\; \backslash frac\{1\}\{16\}\backslash \}$. The first set on initial conditions considers varying the mean $\mu \backslash mu$ and standard deviation $\sigma \backslash sigma$ of the profile $A(k)A(k)$ with $\mu \in 1,4,16\backslash mu\backslash in\{1,\; 4,\; 16\}$ and $\sigma \in \{\frac{1}{4},\frac{1}{2},1\}\backslash sigma\backslash in\backslash \{\backslash frac14,\; \backslash frac12,\; 1\backslash \}$, the phase (argument of the complex Fourier component) $\varphi \backslash phi$ was set randomly in the range $[0,2\pi )[0,2\backslash pi)$. The second set of initial conditions considers a fixed mean ( $\mu =16\backslash mu=16$) and standard deviation ( $\sigma =0.25\backslash sigma\; =0.25$) and a varieed range of random phases (complex arguments $\varphi \in [0,{\varphi }_{max}\backslash phi\backslash in[0,\backslash phi\_\{max\}$)) given to each Fourier component. The four cases considered are specified by ${\varphi }_{max}\in \{\frac{\pi }{128},\frac{\pi }{8},\frac{\pi }{2},\pi \}\backslash phi\_\{max\}\backslash in\; \backslash \{\; \backslash frac\{\backslash pi\}\{128\},\; \backslash frac\{\backslash pi\}\{8\},\; \backslash frac\{\backslash pi\}\{2\},\; \backslash pi\backslash \}$.

Approximate time to generate the data: 1 hour on 128 CPU cores for 1 simulation. 65 hours on 128 CPU cores for all simulations.

Hardware used to generate the data: 128 CPU core on the Ocre supercomputer at CEA, Bruyères-le-Châtel, France.

What is interesting and challenging about the data:

What phenomena of physical interest are catpured in the data: In this dataset, there are three key aspects of physical interest. Firstly, impact of coherence on otherwise random initial conditions. Secondly, the effect of the shape of the initial energy spectrum on the structure of the flow. Finally, the transition from the Boussinesq to the non-Boussinesq regime where the mixing width transitions from symmetric to asymmetric growth.

How to evaluate a new simulator operating in this space:

From a fundamental standpoint, we would expect the density field to be advected and mixed rather than created or destroyed to give appropriate statistics. From a qualitative perspective, given that the underlying simulations are of comparable spatial resolution to the simulations run by the alpha group (Dimonte et. al. 2003), we would consider a good emulator to produce a comparable value for α as reported in their paper for an appropriately similar set of initial conditions. This parameter is derived by considering the flow after the initial transient. At this stage, the width of the turbulent mixing zone, $LL$, is self-similar and grows as $L=\alpha \ast At\ast g\ast t^{2}L=\; \backslash alpha\; *\; At\; *\; g\; *\; t^2$. They reported a value of $\alpha \backslash alpha$=0.025±0.003. In addition, during this self-regime, we would expect to observe energy spectra with a similar shape to those reported in Cabot and Cook 2006, specifically exhibiting an appropriate $k^{-\frac{5}{3}}k^\{-\backslash frac53\}$ cascade. From a structural perspective, we would expect that for an initialization with a large variety of modes in the initial spectrum to observe a range of bubbles and spikes (upward and downward moving structures), whereas in the other limit (where this only on mode in the initial spectrum) we expect to observe a single bubble and spike. In addition, a good emulator would exhibit symmetric mixing with for low Atwood numbers in the Boussinesq regime (defined as $AtAt$ < 0.1 by Andrews and Dalziel 2010) and asymmetries in the mixing with for large Atwood number.

Please cite the associated paper if you use this data in your research:

@article{cabot2006reynolds,
  title={Reynolds number effects on Rayleigh--Taylor instability with possible implications for type Ia supernovae},
  author={Cabot, William H and Cook, Andrew W},
  journal={Nature Physics},
  volume={2},
  number={8},
  pages={562--568},
  year={2006},
  publisher={Nature Publishing Group UK London}
}