Jets with Reversing Buoyancy

TL;DR

This paper derives an exact analytical expression for the maximum height time of buoyant jets, applicable to both laminar and turbulent flows with or without swirl, enhancing understanding of buoyant fluid dynamics.

Contribution

It introduces a novel exact analytical formula for the maximum height time of buoyant jets, valid across laminar and turbulent regimes with or without swirl.

Findings

Derived an exact expression for maximum height time $t_i$

Applicable to laminar and turbulent buoyant jets

Valid for flows with or without swirl

Abstract

A jet of heavy fluid is injected upwards, at time $t=0$, into a lighter fluid and reaches a maximum height at time $t=t_i$ and then flows back around the upward flow. A similar flow situation occurs for a light fluid injected downward into a heavy one. In this paper an exact analytical expression for $t_i$ is derived. The expression remains valid for laminar and turbulent buoyant jets with or without swirl.