Effect of initial spanwise perturbations on the dynamics and mixing of planar gravity currents

Fully resolved three-dimensional simulations of planar gravity currents are conducted to investigate the influence of imposed spanwise perturbations on flow evolution and mixing at two Reynolds numbers ( $ \textit{Re}=3450$ and 10 000). The initial perturbations consist of sinusoidal waves with a varying number of repeating waves, $k_y$ , with simulations spanning $0 \leqslant k_y \leqslant 8$ . At low- $ \textit{Re} $ , cases with perturbations ( $k_y \gt 0$ ) exhibit a more rapid breakdown of spanwise coherence compared with the unperturbed case ( $k_y = 0$ ), although the resulting structures retain spatial periodicity and remain relatively ordered. This earlier disruption leads to greater front propagation distances beyond the self-similar inertial phase compared with the unperturbed case. Notably, imposed perturbations exhibit minimal influence on the flow transition; all cases follow the slumping velocity reported in the literature, with the transition into the inertial phase occurring at comparable times across different $k_y$ values at both $ \textit{Re} $ . The increased propagation speed is accompanied by reduced mixing efficiency due to the premature disruption of coherent Kelvin–Helmholtz (K–H) billows, which play a key role in maintaining multi-scale mixing. At high- $ \textit{Re} $ , the influence of initial spanwise perturbations diminishes, as three-dimensional turbulence induces a more chaotic, fine-scale breakdown of spanwise coherence across all $k_y$ cases, overriding the effects of the initial perturbations. Consequently, the dominant stirring mechanism shifts from K–H billows to vortices within the current head. Nevertheless, the unperturbed case maintains comparatively higher mixing efficiency at both low- and high- $ \textit{Re} $ . This is attributed to the persistence of recognisable K–H billow structures, which, despite undergoing chaotic breakdown at high- $ \textit{Re} $ , still contribute to effective stirring by stretching and folding the density interface. These results highlight the dual role of K–H billows: they promote efficient mixing, yet the enhanced mixing reduces the density difference between the current and the ambient fluid, weakening buoyancy and slowing front propagation despite stronger stirring. These findings are supported by consistent trends in streamwise density distribution and ‘local’ energy exchange analyses.