The Motion of a Solid Sphere in an Oscillating Flow: An Evaluation of Remotely Sensed Doppler Velocity Estimates in the Sea

Abstract

Several popular techniques employed to remotely sense oceanic velocity fields utilize the Doppler shifts of backscattered radiation (such as sound or light) from suspended particles to estimate fluid velocities. Implicit in this use is the assumption that the motion of the particles and the fluid parcels about them is identical. Here, a simple dynamical model of a solid sphere in a unidirectional oscillating flow is used to evaluate the effects of differential particle motion on remotely sensed Doppler velocity estimates. The analysis indicates that typical oceanic particles will move with the fluid if their density is equal to the fluid's density or if the oscillation frequency (?) is less than a critical frequency (?c≡0.1?a?2; where ? is the kinematic viscosity of the fluid and a is the particle radius). For oscillation frequencies greater than ?c, the particle and flow velocities diverge significantly from each other. Particle motion will be amplified for particles less dense than the fluid and reduced for relatively heavy particles. The motions of particles and the fluid may have significant phase differences as well. Critical frequencies are estimated for some common oceanic particles enabling the performance of several Doppler velocity measurement techniques to be evaluated. The present results indicate that for some oceanographic applications the Doppler sensing of fluid velocities using particulate backscatter may be limited by the inability of the particles to follow the fluid motion. The model results suggest that it is possible to correct for the velocity differences between the particle and its fluid parcel if the size and relative density of the backscattering material is known. This strongly indicates that a greater emphasis must be placed on the characterization of the materials that are producing the backscattered signals.