Characterization of the long-time particle-distribution dynamics

Characterize the long-time dynamics and asymptotic particle distribution of weakly inertial, quasi-neutrally buoyant particles in the vertically inhomogeneous convective ocean mixed-layer model, including rare transitions between the thermocline and mixed layer caused by spatially varying turbulent diffusivity.

Background

The paper models particle transport using a one-dimensional stochastic equation with a restoring drift toward the neutral-buoyancy isopycnal, internal-gravity-wave forcing, and turbulent noise. For analytical simplicity, the turbulent diffusivity is treated as spatially constant, although the simulations show that turbulence is much stronger in the mixed layer than in the thermocline.

This spatial variation creates a difficult long-time problem: particles can make rare noise-driven transitions from the thermocline into the mixed layer, where they may remain for long periods, while sufficiently strong fluctuations in the mixed layer may drive reverse transitions back into the thermocline. The simulations are not long enough to fully resolve the resulting asymptotic distribution, especially for small Stokes numbers.

References

Summarizing, while the present approach allows to identify the key mechanisms controlling accumulation and spreading around the reference isopycnal, particle dynamics in the long-time limit seem to be highly complex and remain to be fully characterized.

— Vertical transport and confinement of weakly buoyant particles in a convective ocean mixed-layer model  (2609.18400 - Silva-Torres et al., 16 Sep 2026) in Section 3.4, final paragraph before Fig. 12; Section 4, paragraph beginning “We note, however”

An interesting perspective to address this point could be to consider a stochastic two-layer toy model, which is left for future work.

— Vertical transport and confinement of weakly buoyant particles in a convective ocean mixed-layer model  (2609.18400 - Silva-Torres et al., 16 Sep 2026) in Section 4, paragraph beginning “We note, however”