A direct approach to solving the hydrodynamic oseenlet

TL;DR

This paper introduces a novel direct method for deriving the Green's function of the Oseen equations, simplifying the solution and making inertial effects more transparent compared to traditional approaches.

Contribution

A new direct approach to derive the Oseenlet that does not rely on assumed initial solutions, resulting in a simplified and more interpretable form.

Findings

Derived a simplified Green's function for the Oseen equations

The solution clearly separates inertial contributions

Provides a more accessible form similar to the Stokeslet tensor

Abstract

We present a new direct approach to obtain the Green's function of the Oseen equations, also known as the oseenlet. This approach is different in that it does not assume an initial form of the solution to begin with. The final solution is expressed in a new, simplified form that resembles the Oseen-Burger's tensor of the stokeslet equations, from which the contributions due to inertia are easily appreciable.