Long-time fate of intermittency at small slope angles

Determine whether the outer layer of an inclined gravity current at relatively small slope angles and larger flux Richardson numbers remains permanently intermittent, settles into a laminar regime, or eventually transitions into the dynamically equilibrated turbulent regime.

Background

The direct numerical simulations show that, at a slope angle of 0.5 degrees, the outer layer can undergo repeated transitions between turbulent bursts and relaminarisation, whereas higher Reynolds numbers promote a more sustained turbulent state. The delay-differential model likewise predicts a transition between oscillatory and statistically steady behaviour as the delay and flux Richardson number vary.

The paper does not establish the asymptotic behaviour at still smaller slope angles, where stronger stratification and larger flux Richardson numbers may produce qualitatively different long-time states. The unresolved alternatives are permanent intermittency, eventual laminarisation, or eventual convergence to the dynamically equilibrated turbulent regime.

References

Several questions, however, remain open. At relatively small slope angles (larger $\hat{Ri_f}$), the long-time behaviour is uncertain: it is not yet clear whether the outer layer may remain permanently intermittent, settle into a laminar regime as suggested by , or eventually transition into the dynamically equilibrated regime reported by .

— Intermittent turbulence in inclined gravity currents  (2608.16683 - Cui et al., 17 Aug 2026) in Conclusion, Section 5

It also remains to be tested whether the same delay-controlled mechanism persists in spatially developing gravity currents and more realistic geophysical settings.

— Intermittent turbulence in inclined gravity currents  (2608.16683 - Cui et al., 17 Aug 2026) in Conclusion, Section 5