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Register a new userSedimenting Elastic Filaments in Turbulent Flows
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We investigate the gravitational settling of a long, model elastic filament in homogeneous isotropic turbulence. We show that the flow produces a strongly fluctuating settling velocity, whose mean is moderately enhanced over the still-fluid terminal velocity, and whose variance has a power-law dependence on the filaments weight but is surprisingly unaffected by its elasticity. In contrast, the tumbling of the filament is shown to be closely coupled to its stretching, and manifests as a Poisson process with a tumbling time that increases with the elastic relaxation time of the filament.
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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.
Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low-Reynolds-number are investigated within the point-particle model. Evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling down. We find that elasticity (which breaks time-reversal symmetry of the motion) significantly affects the systems dynamics. This is remarkable taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length non-periodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbells - their centres of mass move apart from each other horizontally. The shift is fast for moderate values of the spring constant k, and slows down when k tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal time-dependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centre-of-mass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understand general features of systems with larger number of elastic particles, at regular and random configurations.
A string of tracers, interacting elastically, in a turbulent flow is shown to have a dramatically different behaviour when compared to the non-interacting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: an elastic chain is trapped in the vortical regions and not the straining ones. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain, via the number of links that form it, is also examined.
We show and explain how a long bead-spring chain, immersed in a homogeneous, isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of 3D turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In 3D, on the contrary, the chain is extended even in vortical regions, which suggests that it follows axially-stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly-flexible, inextensible chain also shows preferential sampling in 3D, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in 2D is considerably reduced. In 3D, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis.
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.
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