Fluid Flows driven by Oscillating Body Force

TL;DR

This paper derives a general averaged equation for inviscid incompressible fluid flows driven by oscillating body forces using a two-timing method, with potential broad applications.

Contribution

It provides a new, simple form of averaged Euler's equations for oscillating body force-driven flows without additional assumptions.

Findings

Derived a general averaged flow equation

Used two-timing method for analysis

Equation applicable to various fluid flow scenarios

Abstract

In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing method. Our main result is the general and simple form of the equation describing the averaged flows, which are derived without making any additional assumptions. The presented results can have many interesting applications.