Patchy alignment pervades magnetohydrodynamic (MHD) turbulence, yet its role in the turbulent cascade remains unclear. Using net- and no-net-flux compressible simulations with up to $10,368^3$ grid cells, we uncover two distinct alignment laws. Our constant-flux model of departures from locally aligned states predicts the measured velocity-magnetic and velocity-vorticity angle scalings, ${\lambda }^{1/8}$ and ${\lambda }^{1/16}$, over resolved inertial scales $\lambda$. These laws change the predicted shapes of turbulent eddies and raise the theoretical threshold for magnetic reconnection to control the flow of energy across scales.

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• Astrophysical fluid dynamics
• Compressible flows
• Flow instability
• Magnetohydrodynamic turbulence
• Magnetohydrodynamics
• Scaling laws of complex systems
• Space & astrophysical plasma
• Turbulence