What question did this study set out to answer?

This research aims to validate the Cartan-Biot-Savart inequality through simulations in the 3D Navier-Stokes framework and establish a corresponding empirical scale law.

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May 25, 2026Open Access

NXE Program: Cartan-Biot-Savart Inequality and Morphological Scale Law in 3D Navier-Stokes — Data and Code Repository

Key Points

This research aims to validate the Cartan-Biot-Savart inequality through simulations in the 3D Navier-Stokes framework and establish a corresponding empirical scale law.
Conducted four pseudospectral simulations using 128³ grid points and RK4 integration.
Set initial conditions of anti-parallel vortices, with Reynolds numbers ranging from 2481 to 25279.
Utilized python verification code to reproduce results in under 30 seconds.
Found a scale law represented as C_median ~ Re^(-3/8) with r²=0.985, p=0.007.
Confirmed the Cartan-Biot-Savart inequality with 0 violations across 41 timesteps.

Abstract

DNS data and verification code for the NXE preprint. Four pseudospectral simulations (N=128³, RK4, anti-parallel vortex initial condition, Re=2481–25279) establishing the empirical scale law Cₘedian ~ Re^ (-3/8) with r²=0. 985, p=0. 007, and confirming the Cartan-Biot-Savart inequality (0 violations / 41 timesteps). Run python verifyᵣesults. py --datadir. /data to reproduce Table 3 of the preprint in under 30 seconds.

NXE Program: Cartan-Biot-Savart Inequality and Morphological Scale Law in 3D Navier-Stokes — Data and Code Repository

Key Points

Abstract

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