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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 three-dimensional (3D) turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In the 3D case on the contrary, the chain is extended even in vortical regions, which suggests that the chain 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 three dimensions, 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 two dimensions is considerably reduced. In three dimensions, 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. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

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There is a relation between space and time, which is called space-time continuum. With the help of some mathematical equations, we can establish an alternative relation between space-time and mass, treating mass as a fifth dimension. There is the concept about mass being a property of any inertial or gravitational object in space. Mass can create distortion in space. As a result of that, space-time curvature will be bent towards the massive object.