The long-time dynamics of large particles trapped in two nonhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one-dimensional stochastic model of an overdamped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially nonhomogeneous fluctuations and a suited confinement strength.

The existence of energy cascades as signatures of conserved magnitudes is one of the universal characteristics of turbulent flows. In homogeneous 3D turbulence, the energy conservation produces a direct cascade from large to small scales, although in 2D, it produces an inverse cascade pointing towards small wave numbers. In this Letter, we present the first evidence of an inverse cascade in a fully developed 3D experimental turbulent flow where the conserved magnitude is the angular momentum. Two counterrotating flows collide in a central region where very large fluctuations are produced, generating a turbulent drag that transfers the external torque between different fluid layers. DOI: 10.1103/PhysRevLett.110.124501 PACS numbers: 47.27.De, 47.27.wj In his seminal work of 1941 [1,2], Kolmogorov postulated a mechanism for the transfer of energy from the injection scales towards the small scales, where it is finally dissipated [3]. This direct cascade with the now classical exponent of À5=3 has been verified in very different 3D flows, whether homogeneous or not. But there are many topics that remain open; one of these is the creation and origin of coherent structures, with typical scales usually much larger than the injection scales. In 2D turbulence [4] where the vortices cannot be stretched, Kraichnan [5] proposed a new cascade in 1967: he introduced the concept of an inverse cascade where the energy was transported towards the large scales, whereas a direct cascade transported enstrophy to the small scales. Other particular cases of inverse cascades have been found in some special configurations, as in quantum fluids [6], in wave turbulence [7,8], through the coupling of different modes in a Korteweg-de Vries model [9], in the transport of helicity in inviscid fluids [10,11], or inspired on the magnetic field generation in turbulent flows, the anisotropic kinetic alpha effect [12].We analyze the behavior of a fluid in a closed cavity where two inhomogeneous and strongly turbulent flows collide in a thin region. Depending on the spatial position, different cascades have been found. Far from the collision layer, a classical Kolmogorov scenario is found, but in the shear region, inverse cascades appear. These cascades, that have been observed both in spatial and temporal spectra, correspond to the conservation of the axial angular momentum. A similar behavior may be present in any situation where large coherent structures are relevant and appear on the top of very turbulent colliding flows, as, for example, in atmospheric circulations [13], large scale currents and vortices in oceans [14], MRI instabilities and accretion disks [15][16][17], dynamo action in MHD [18,19], mixing problems [20], and industrial applications, to name a few.

We present a method to improve the accuracy of velocity measurements for fluid flow or particles immersed in it, based on a multi-timestep approach that allows for cancellation of noise in the velocity measurements. Improved velocity statistics, a critical element in turbulent flow measurements, can be computed from the combination of the velocity moments computed using standard Particle Tracking Velocimetry or Particle Image Velocimetry techniques for data sets that have been collected over different values of time intervals between images. This method produces Eulerian velocity fields and Lagrangian velocity statistics with much lower noise levels compared to standard PIV or PTV measurements, without the need of filtering and/or windowing. Particle displacement between two frames are computed for multiple different timestep values between frames in a canonical experiment of homogeneous isotropic turbulence. The second order velocity structure function of the flow is computed with the new method, and compared to results from traditional measurement techniques in the literature. Increased accuracy is also demonstrated by comparing the dissipation rate of turbulent kinetic energy measured from this function against previously validated measurements.

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