Ratnesh K. Shukla

A wide array of natural and artificial swimmers and flyers adhere to a seemingly universal relationship between their propulsive kinematics and forward speed. Most commonly expressed through the Strouhal–Reynolds number (St–Re) scaling, this relationship links a locomotor's transverse oscillation frequency and amplitude to its mean forward speed. It has long fascinated researchers and carries broad significance, as it justifies the study of undulatory biolocomotion through relatively simple model systems self-propelled by foil-like oscillating kinematics. In this talk, we examine the energetic and dynamical implications of universality in the St–Re scaling relation. We show that self-propelled systems as distinct as those driven by recoil-based thrust and by leading-edge suction can converge to a common scaling regime under intense flapping, a convergence that arises principally from asymptotic similarities in thrust generation at high reduced frequencies. Crucially, we demonstrate that this apparent scaling consistency does not translate into uniform energetic efficiency: significant differences in locomotory performance emerge across systems governed by a similar St–Re relation.

High efficiency thrust generating foils are extensively being researched for potential use as thrusters in micro air vehicles and biomimetic autonomous underwater vehicles. Here, we propose a simple reduced order model for prediction of thrust generation attributes of foils that are pitched either continuously or intermittently in a periodic and possibly asymmetric fashion. Our model accounts for the distinct thrust contributions from added mass, leading edge suction, quasi steady and wake terms, all deduced from a rigorous generalization of linearized potential theory to foils undergoing small amplitude multimodal flapping motion. Additionally, the model relies on Bone-Lighthill boundary layer thinning hypothesis to account for the pitching motion induced increase in the drag force exerted on the foil. We derive generic forms of the thrust coefficient for prescribed multimodal pitching motions and specifically in the limit of large reduced frequencies, demonstrate a convergence to rather simplified scaling laws that are functions of just the Reynolds number and Strouhal number based on root mean square of the foil’s trailing edge velocity. Comparisons with previously reported experimental and simulation-based investigations demonstrate that the scaling laws capture the influence of imposed pitch on thrust generation characteristics over a range of pitching waveforms ranging from sinusoidal to square or triangular-shaped waveforms and also waveforms corresponding to intermittent pitching. The generalized relations derived in our work and the asymptotic scaling laws deduced from them are applicable to a wide spectrum of self-propulsion enabling and thrust producing waveforms including the ones that can potentially be employed in burst and coast swimming.

We analyze the transport behavior of surface-actuated spheroidal microswimmers that locomote steadily with or without a spatiotemporally uniform external forcing. The surface actuation is in the form of either a tangential surface motion or a zero-net-mass-flux wall-normal transpiration. Starting from a general modal expansion in terms of an appropriate basis set, we link the surface actuation, the force exerted on the spheroid, and its forward speed through a Stokesian representation of the microhydrodynamics. Our analysis is generic and enables a systematic investigation over the complete range of aspect ratios from zero (streamlined needlelike spheroid) to infinity (disc-shaped spheroid). We identify a critical aspect ratio of 1.82 below and above which tangential and wall-normal surface actuations enable transport at minimal energetic cost, irrespective of whether the spheroidal microswimmer is free or forced. Crucially, we find the propulsive performance of a forced spheroidal swimmer to be appreciably higher than the one of an analogous self-propelled swimmer. Most importantly, the optimal energy expenditure minimizing tangential or wall-normal surface actuation for forced transport is passive overall so that the power requirement arises solely from the rate at which work is done by the external forcing. We highlight the complementing roles of external forcing and surface actuation over moderate and extreme aspect ratios and also exemplify the crucial disparities between optimal transport in free and forced environments. Our results indicate that a combination of external forcing and an optimal surface actuation could substantially enhance the transport of generic streamlined and bluff microswimmers.

We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and except in the neighbourhood of the rear stagnation point, behave like a linear perturbation of the inviscid flow. Our theory gives a highly accurate description of these modifications by including the contribution from the most significant viscous term in a correctional perturbation expansion about an inviscid base state. We derive the boundary layer equation for the flow and deduce a similarity transformation that leads to a set of infinite, shear-free-condition-incompatible, self-similar solutions. By suitably combining members from this set, we construct an all-boundary-condition-compatible solution to the boundary layer equation. We derive the governing equation for vorticity transport through the narrow wake region and determine its closed-form solution. The near and far-field forms of our wake solution are desirably consistent with the boundary layer solution and the well-known, self-similar planar wake solution, respectively. We analyse the flow in the rear stagnation region by formulating an elliptic partial integro-differential equation for the distortion streamfunction that specifically accounts for the fully nonlinear and inviscid dynamics of the viscous correctional terms. The drag force and its atypical logarithmic dependence on Reynolds number, deduced from our matched asymptotic analysis, are in remarkable agreement with the high-resolution simulation results. The logarithmic dependence gives rise to a critical Reynolds number below which the viscous correction term, counterintuitively, reduces the net dissipation in the flow field.