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Register a new userSwimmer dynamics in externally-driven fluid flows: The role of noise
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We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally-driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e. sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmers Fokker-Planck equation. Using the semiclassical technique, we compute (i) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (ii) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.
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Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $fproptotextrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $textrm{Re}^{-1/4}$. For large Re, $f sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.
We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a new first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible, Navier-Stokes equation, we obtain the time $t_R$ at which a tracer, initially at the origin of a sphere of radius $R$, crosses the surface of the sphere textit{for the first time}. We obtain the probability distribution function $mathcal{P}(R,t_R)$ and show that it displays two qualitatively different behaviors: (a) for $R ll L_{rm I}$, $mathcal{P}(R,t_R)$ has a power-law tail $sim t_R^{-alpha}$, with the exponent $alpha = 4$ and $L_{rm I}$ the integral scale of the turbulent flow; (b) for $l_{rm I} lesssim R $, the tail of $mathcal{P}(R,t_R)$ decays exponentially. We develop models that allow us to obtain these asymptotic behaviors analytically. We show how to use $mathcal{P}(R,t_R)$ to develop social-distancing guidelines for the mitigation of the spreading of airborne aerosols with viruses such as SARS-CoV-2.
A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.
We develop a framework to study the role of variability in transport across a streamline of a reference flow. Two complementary schemes are presented: a graphical approach for individual cases, and an analytical approach for general properties. The spatially nonlinear interaction of dynamic variability and the reference flow results in flux variability. The characteristic time-scale of the dynamic variability and the length-scale of the flux variability in a unit of flight-time govern the spatio-temporal interaction that leads to transport. The non-dimensional ratio of the two characteristic scales is shown to be a a critical parameter. The pseudo-lobe sequence along the reference streamline describes spatial coherency and temporal evolution of transport. For finite-time transport from an initial time up to the present, the characteristic length-scale of the flux variability regulates the width of the pseudo-lobes. The phase speed of pseudo-lobe propagation averages the reference flow and the flux variability. In contrast, for definite transport over a fixed time interval and spatial segment, the characteristic time-scale of the dynamic variability regulates the width of the pseudo-lobes. Generation of the pseudo-lobe sequence appears to be synchronous with the dynamic variability, although it propagates with the reference flow. In either case, the critical characteristic ratio is found to be one, corresponding to a resonance of the flux variability with the reference flow. Using a kinematic model, we demonstrate the framework for two types of transport in a blocked flow of the mid-latitude atmosphere: across the meandering jet axis and between the jet and recirculating cell.
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