Dataset: Simulation of the Turbulent Graetz Problem with Neumann Boundary Conditions at Two Reynolds and Prandtl Numbers

Data are provided as tar archives of .zarr version 3 files (https://zarr.dev/), created with Xarray (https://xarray.dev/).

The different scalars are present on the "isc" axis; where the bc_index axis corresponds to the boundary condition used.

• 0: azimuthally uniform heat flux
• 2: half-sinusoidal heat flux: q_w = pi*sin(phi) if phi < np.pi; 0 otherwise
• 3: q_w = sin(phi)
• 4: q_w = sin(2*phi)

The following statistics, averaged in time, are contained in the dataset:

Primary Variables:

• p
• t
• u
• v
• w

Correlations:

• p*p
• u*u
• v*v
• w*w
• www
• www*w
• u*v
• u*w
• v*p
• v*w
• w*p
• t*t
• ttt
• t*u
• t*v
• t*w
• u*p
• ttu
• ttv
• ttw

Derivatives and their products determined using SEM differentiation:

• d(t)dx
• d(t)dy
• d(t)dz
• d(t)dx*d(t)dx
• d(t)dx*d(t)dy
• d(t)dy*d(t)dx
• d(t)dy*d(t)dy
• d(t)dz*d(t)dz

For each Reynolds number, three datasets are provided:

1. tavg_t.zarr(.tar) contains the time-averaged data on the original NekRS grid (i.e. coordinates are isc, element, i, j, k). Data are chunked along isc and element for easier access on memory-constrained machines.
2. tavg_t.interp.zar(.tar) contains polar-interpolated data (i.e. coordinates are isc, r, phi, z). Interpolation points are concentrated near the start of the heated region to resolve the high mean gradients occurring in this region. Interpolation was performed using the gfldr utility in nek5000.
3. monitor.zar(.tar) contains runtime statistics like TMax, TMin, TBulk, uMax, wMax over the entire domain.

In addition, two Python entrypoints are provided, as an example on how to work with the data:

1. azimuthal_decomp.py computes the Nusselt number decomposition according to J. Neuhauser et al 2026 J. Phys.: Conf. Ser. 3173 012040; extended for azimuthally inhomogeneous heat flux.
2. development_length_turb.py evaluates the development length of the mean (modal) temperature, and plots r-z contours of it (stored as pgfplot prepared contourplot).

Averaging times in eddy turnover times (t_avg * u_tau / D) after decay of the initial transient:
Re_b = 5300: 199.7
Re_b = 19000: 10.5
Statistics were sampled every five timesteps to account for the short integral timestep of local statistics in a 3D-inhomogeneous setting.

Simulations were performed on the national supercomputer HPE Cray EX4000 Hunter at the High Performance Computing Center Stuttgart (HLRS) under the grant number ctbctpf.