Lagrangian Time Scale of Passive Rotation for Mesoscale Particles in Turbulence

Abstract

Turbulence induces rotation in the living and the non-living materials in the ocean. The time scale of rotation for a living organism is important in understanding an organism's feeding efficiency, mating, prey capture rate, etc. This time scale is also crucial for understanding the migration of non-living materials such as microplastics. Herein, we investigate the tumbling motion of mesoscale particles that resemble organisms of intermediate size, such as zooplankton that appear in the ocean. Using time-resolved measurements of the orientation of rigid inertial fibers in a turbulence-tank, we analyze the autocorrelation of their tumbling rate. The correlation time (τ d ) is well-predicted by Kolmogorov inertial-range scaling based on the fiber length (L) when the fiber inertia can be neglected. For inertial fibers, we propose a simple model considering fiber inertia (measured by a tumbling Stokes number) and a viscous torque which accurately predicts both the correlation time and the variance of the tumbling rate. Our measurements and the theoretical model provide a basic understanding of the rotational response of an intermediately sized organism to the surrounding turbulence in its non-active state.

Spinning and tumbling of long fibers in isotropic turbulence

“…Main statistical quantities of turbulence in the volume of measurement are given in Table I. These values have been validated during our previous studies [9,23] by comparing the evolution of the normalized variance and the correlation time of the tumbling rate, which are in good agreement with other studies.…”

“…Given that the variance of the spinning rate of a fiber scales with the fiber diameter (d/η K ) and not the fiber length (L/η K ), the goal here is to probe if such scaling also exists for the correlation time of the spinning rate. Following the method described in Bordoloi et al [23], we compute two timescales, namely, the zero-crossing time (τ 0 ) and the integral time (τ i ), based on the mean autocorrelation of the spinning and the tumbling rates from approximately 1500 trajectories. The details of this computation can be found in Bordoloi et al [23].…”

Long non-axisymmetric fibres in turbulent channel flow

“…Moreover, we observe that the tumbling rate increases with the wall-normal coordinate y + . The studies investigating particle tumbling behaviour currently available in the literature are related to straight rods (Parsa et al 2012;Marcus et al 2014;Sabban et al 2017;Bounoua et al 2018;Kuperman et al 2019;Bordoloi et al 2020;Jiang et al 2020). For long and neutrally buoyant straight rods in HIT conditions, the magnitude of mean squared tumbling rate is observed to be approximately 0.1 (Parsa et al 2012;.…”

“…with particle size larger than the smallest scale of the flow. Following the same approach, a modified scaling for the tumbling rate of rod-like particles was provided in subsequent works by Bordoloi & Variano (2017), Bounoua, Bouchet & Verhille (2018), Kuperman, Sabban & van Hout (2019) and Bordoloi, Variano & Verhille (2020). Recently, Jiang, Calzavarini & Sun (2020) investigated the rotation of oblate and prolate spheroids in a Rayleigh–Bénard flow.…”

“…916 A3-3 Marcus et al (2014) Jack and cross Rigid [2] 91 [1] 10 NA [3] 6 H I T / 3 D -T Rod Rigid [2] Bounoua et al (2018) Rod Rigid [2] 350-610 2.5-80 [1] 0.016-2.8 22-850 CTT/3D-T Pujara et al (2018) Cube, cuboid, cone, rod Rigid [2] 261 1-3.72 NA [2] 13-55 HIT/S-PIV Hejazi, Krellenstein & Voth (2019) Triads Flexible [2] 198 [2] 10 NA [3] 39.28 VWBCF/3D-T Zhao et al (2019) Rod Rigid [2] Di Benedetto et al (2019) Rod and disk Rigid [4] 46-66 0.16-7.8 NA NA SGWF/2D-T Bordoloi et al (2020) Rod Rigid [2] 350-610 2-80 [2] 0.014-2.68 51.1-858.9 HIT/3D-T Jiang et al (2020) Rod and disk Rigid [5] 1. Summary of experimental investigations of anisotropic particle-laden flows available in the literature.…”