Effects of ocean turbulence on the large-scale stratification and Small-Scale Particle Distributions

Part I: “The Middepth Ocean.” Away from polar regions, the ocean stratification from 1–3 km depth exhibits little horizontal variability and a strikingly exponential vertical structure. The stratification is maintained by a large-scale balance between the upwelling of cold water from the abyss and the downward mixing of heat by turbulence. At smaller scales, however, the upwelling and mixing exhibit tremendous spatial variability, belying the simple structure of the stratification. Observations of mixing are too sparse to extrapolate accurately to large scales, and the millennial timescales associated with diapycnal mixing render it challenging to constrain with models. By studying the basin-averaged buoyancy budget in light of what is known about the stratification and overturning, we deduce that the vertical profile of the isopycnal-averaged turbulent diffusivity must increase with depth, but it must do so more slowly than the stratification decays. In recognition of the importance of the distribution of mixing to the stratification and upwelling, we then extend theoretical models of middepth dynamics to account for structure in the turbulent diffusivity profile. We develop a fully predictive theory for the stratification and upwelling profiles that explains why bottom-enhanced mixing is essential to the observed exponential stratification. The upshot is that as long as the mixing is appreciably bottom-enhanced, the basin-averaged diapycnal upwelling will vary roughly linearly with depth and the stratification will be exponential; conversely, without any structure in the mixing, the stratification will not be exponential. This result tightens constraints on the large-scale distribution of mixing and implies that the vertical structure of mixing is important to characterize correctly in ocean models. Part II: “Inertial Particles.” The motion of solid objects in the ocean such as plastic debris or freely floating oceanographic instruments may differ from that of the surrounding fluid due to differences in inertia. The details of the deviations of inertial particle trajectories from the fluid velocity field depend on small-scale fluctuations in the fluid velocity that are typically unresolved in oceanographic contexts. We introduce a framework for modeling distributions of inertial particles in noisy oceanographic flows. Turbulence is modeled as a white noise force acting on the particle, and the resulting stochastic equations are reduced via perturbation analysis to a single advection-diffusion equation for the spatial distribution of particles. We verify and test the resulting model in several sample flows and begin to quantify the many inertial and stochastic effects affecting particle motion.