Low-Reynolds-number turbulence with active vortex stretching in three-dimensional cryogenic sloshing

Two-dimensional simulations of liquid sloshing underpredict damping by two orders of magnitude. This long-standing discrepancy is traced here to the structure of the energy cascade. Using three-dimensional volume-of-fluid simulations of liquefied natural gas (LNG) sloshing (in a Basilisk framework, up to 5123 effective resolution), we show that the flow occupies a previously uncharacterized regime: an active vortex stretching (ratio 2.67) at a Taylor-scale Reynolds number Reλ∼50–80 (measured directly via multi-scale variance decomposition separating turbulent fluctuations from organized sloshing), below the inertial-range threshold. We prove that both vortex stretching and strain-rate self-amplification (SSA) are the two mechanisms driving the forward energy cascade. The mechanisms vanish identically in two dimensions, establishing a fundamental, not merely quantitative, origin for the simulation failure. Direct measurement of the SSA-to-stretching ratio (3.24±1.22, consistent with the Betchov identity and the Carbone–Bragg prediction of ∼3) confirms that cascade physics operates at these low Reynolds numbers. Second-order velocity structure functions computed from the adaptive mesh refinement data show no inertial plateau, providing direct real-space spectral evidence for the sub-inertial classification. Free-decay analysis reveals anisotropic damping spanning three orders of magnitude with irreducible three-dimensional coupling (R=0.14–0.18,dynamic forces). Under Froude scaling, boundary-layer damping vanishes at the prototype scale (ζBL∼λ−3/4) while cascade damping remains scale-independent (ζ3D∼λ0), with direct implications for full-scale LNG damping prediction.