Second harmonic generation and vortex shedding by a dipole-quadrupole and a quadrupole-octupole swimmer in a viscous incompressible fluid

TL;DR

This paper investigates vortex shedding and second harmonic generation by specific swimmer models in viscous fluids, analyzing flow dynamics and swimming velocity for applications including bird flight.

Contribution

It introduces models combining dipolar, quadrupolar, and octupolar surface modulations to study vortex shedding and flow patterns in viscous fluids.

Findings

Flow velocity and swimming velocity are calculated to second order in surface modulation amplitude.

Models reveal the generation of second harmonic flow components.

Applications discussed include implications for bird flight dynamics.

Abstract

Vortex shedding by a swimming sphere in a viscous incompressible fluid is studied for surface modulation characterized by a superposition of dipolar and quadrupolar, as well as for quadrupolar and octupolar displacements, varying harmonically in time. The time-dependent swimming velocity and the flow velocity are calculated to second order in the amplitude of surface modulation for both models. The models are also useful for the discussion of bird flight.