Suspension and fall of heavy particles in random two-dimensional flow

Dynamics of phytoplankton blooms in turbulent vortex cells

Turbulence and coherent circulation structures, such as submesoscale and mesoscale eddies, convective plumes and Langmuir cells, play a critical role in shaping phytoplankton spatial distribution and population dynamics. We use a framework of advection-reaction-diffusion equations to investigate the effects of turbulent transport on the phytoplankton population growth and its spatial structure in a vertical two-dimensional vortex flow field. In particular, we focus on how turbulent flow velocities and sinking influence phytoplankton growth and biomass aggregation. Our results indicate that conditions in mixing and growth of phytoplankton can drive different vertical spatial structures in the mixed layer, with the depth of the mixed layer being a critical factor to allow coexistence of populations with different sinking speed. With increasing mixed layer depth, positive growth for sinking phytoplankton can be maintained with increasing turbulent flow velocities, allowing the apparently counter-intuitive persistence of fast sinking phytoplankton populations in highly turbulent and deep mixed layers. These dynamics demonstrate the role of considering advective transport within a turbulent vortex and can help to explain observed phytoplankton biomass during winter in the North Atlantic, where the overturn of deep convection has been suggested to play a critical role in phytoplankton survival.

Microscale patches of nonmotile phytoplankton

Phytoplankton cells have evolved sophisticated strategies for actively responding to environmental signals, most notably to mechanical stresses of hydrodynamic origin. A largely unanswered question, however, is the significance of these cellular responses for the largely heterogeneous spatial distribution of cells found in the oceans. Motivated by the physiological regulation of buoyancy prevalent in nonmotile phytoplankton species, we solve here a minimal model for "active" sinking that incorporates these cellular responses. Within this model, we show how buoyancy regulation leads to intense patchiness for nonmotile species as compared to passive tracers, resulting in important variations in settling speeds and, as a consequence, determining escape rates to the deep ocean.

On the existence and multiplicity of one-dimensional solid particle attractors in time-dependent Rayleigh-Bénard convection

For the first time evidence is provided that one-dimensional objects formed by the accumulation of tracer particles can emerge in flows of thermogravitational nature (in the region of the space of parameters, in which the so-called OS (oscillatory solution) flow of the Busse balloon represents the dominant secondary mode of convection). Such structures appear as seemingly rigid filaments, rotating without changing their shape. The most interesting (heretofore unseen) feature of such a class of physical attractors is their variety. Indeed, distinct shapes are found for a fixed value of the Rayleigh number depending on parameters accounting for particle inertia and viscous drag. The fascinating "sea" of existing potential paths, their multiplicity and tortuosity are explained according to the granularity of the loci in the physical space where conditions for phase locking between the traveling thermofluid-dynamic disturbance and the "turnover time" of particles in the basic toroidal flow are satisfied. It is shown, in particular, how the observed wealth of geometric objects and related topological features can be linked to a general overarching attractor representing an intrinsic (particle-independent) property of the base velocity field.

Ordering of small particles in one-dimensional coherent structures by time-periodic flows

Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional dynamic coherent structures. This effect may take place for particles so small that often they would be expected to behave as passive tracers and be used in PIV measurement technique. We link the particle tendency to form one-dimensional structures to the nonlinear phenomenon of phase locking. We propose that this general mechanism is, in particular, responsible for the enigmatic formation of the "particle accumulation structures" discovered experimentally in thermocapillary flows more than a decade ago and unexplained until now.

Can aerosols be trapped in open flows?

The fate of aerosols in open flows is relevant in a variety of physical contexts. Previous results are consistent with the assumption that such finite-size particles always escape in open chaotic advection. Here we show that a different behavior is possible. We analyze the dynamics of aerosols both in the absence and presence of gravitational effects, and both when the dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent trapping of aerosols much heavier than the advecting fluid is shown to occur in all these cases. This phenomenon is determined by the occurrence of multiple vortices in the flow and is predicted to happen for realistic particle-fluid density ratios.

Signatures of fractal clustering of aerosols advected under gravity

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension D(0) of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.

Delayed transitions between fluid-like and solid-like granular states

Analysis of granular flows has been a significant theoretical challenge over the past several decades. These flows are difficult to analyze largely because they exhibit both solid-like and fluid-like behaviors side-by-side in single experiments. In this paper, we examine two experiments in which the co-existence between these states is especially marked and leads to unique patterns that may serve as signatures for underlying granular dynamics deserving of further scrutiny. In these experiments, we find that when fluidization of grains is prolonged--as can be expected to occur for example under reduced gravity environments or under conditions of strong kinetic forcing (e.g. during earthquakes)--grains can produce residual depositional patterns that are difficult to distinguish from fluvial deposits. This suggests that geological landforms under low gravity (for example on Mars) or influenced by strong forcing (for example during earthquakes) may behave in a fluid-like manner despite being entirely dry.

Dry granular flows can generate surface features resembling those seen in Martian gullies

Over the past decade or more, contradictory evidence of Martian climate, indicating that surface temperatures seldom if ever approach the melting point of water at midlatitudes, and geomorphic features, consistent with liquid flows at these same latitudes, have proven difficult to reconcile. In this article, we demonstrate that several features of liquid-erosional flows can be produced by dry granular materials when individual particle settling is slower than characteristic debris flow speeds. Since the gravitational acceleration on Mars is about one-third that on Earth, and since particle settling speeds scale with gravity, we propose that some (although perhaps not all) Martian geomorphological features attributed to liquid flows may in fact be associated with dry granular flows in the presence of reduced gravity.