navier-stokes-v1

Scientist: denario-2 Date: 2026-09-13

Navier-Stokes Synthetic Dataset Description

This dataset contains a synthetic 2D incompressible flow field generated from the Taylor-Green vortex initial condition at time t=0. The flow is periodic in both x and y directions.

File Inventory (absolute paths)

• /home/node/work/projects/navier-stokes-v1/velocity_u.npy — x‑component of velocity, shape (64, 64), dtype float64
• /home/node/work/projects/navier-stokes-v1/velocity_v.npy — y‑component of velocity, shape (64, 64), dtype float64
• /home/node/work/projects/navier-stokes-v1/pressure.npy — pressure field, shape (64, 64), dtype float64
• /home/node/work/projects/navier-stokes-v1/coordinates.npy — spatial coordinates (x, y) for each grid point, shape (64, 64, 2), dtype float64

Variable Definitions

• velocity_u (u): x‑component of velocity, units of m/s (non‑dimensional). Range approx [-1, 1]. Represents horizontal flow.
• velocity_v (v): y‑component of velocity, units of m/s (non‑dimensional). Range approx [-1, 1]. Represents vertical flow.
• pressure (p): pressure field, units of Pa (non‑dimensional). Derived from the incompressible Navier‑Stokes equations for the Taylor‑Green vortex.
• coordinates: (x, y) positions in meters (non‑dimensional, domain [0, 2π] × [0, 2π]).

Data Generating Process

The Taylor‑Green vortex is an exact solution of the incompressible Navier‑Stokes equations with periodic boundary conditions. At t=0:

• u(x, y) = sin(x) * cos(y)
• v(x, y) = -cos(x) * sin(y)
• p(x, y) = -(cos(2x) + cos(2y)) / 4

The domain size is L = 2π in each direction, discretized with N = 64 grid points per dimension (uniform grid). No noise is added; the field is deterministic.

Known Properties and Caveats

• The flow is incompressible (∂u/∂x + ∂v/∂y = 0) up to machine precision.
• The velocity field is divergence‑free.
• The dataset is ideal for testing numerical solvers, vortex dynamics, and energy cascades.
• No temporal evolution is included; only a single snapshot is provided.

Suggested Analyses

• Compute kinetic energy spectrum and enstrophy.
• Verify incompressibility and compute vorticity field (∂v/∂x - ∂u/∂y).
• Use as initial condition for a Navier‑Stokes solver to study temporal evolution.
• Perform proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD) on ensembles generated by varying Reynolds number (not included here).