Intermittent turbulence in inclined gravity currents

Abstract

Inclined gravity currents on shallow slopes can exhibit pronounced turbulence intermittency. Using direct numerical simulations, we investigate this behaviour for a temporal gravity current over a range of initial Reynolds numbers $Re_0$. For $Re_0=2500$ and a slope angle of $0.5^\circ$, the outer layer of the current exhibits large excursions in turbulence intensity and repeated transitions between turbulent and weakly turbulent states. Analysis of the flow energetics reveals that the intermittency is associated with a finite delay between shear production and dissipation of turbulent kinetic energy. During transitional phases, this delay permits a transient amplification of turbulence, which significantly weakens the mean shear by extracting kinetic energy from the mean flow and promoting entrainment-driven layer growth, ultimately leading to relaminarisation. Increasing $Re_0$ reduces the delay and progressively suppresses intermittency, steering the flow towards a more sustained turbulent state. Motivated by these observations, we develop an autonomous delay-differential model based on the coupled evolution of the mean and turbulent kinetic energies. The model reproduces the observed transition from intermittent to sustained turbulence as the delay is reduced and predicts an increased tendency towards intermittency at larger flux Richardson numbers. The results support an interpretation of intermittent turbulence in inclined gravity currents as a delay-induced oscillation arising from the finite adjustment time of turbulence to changes in the mean flow.