Transition to the buoyancy dominated regime in a planar temporal forced plume

TL;DR

This paper models and validates the transition from momentum- to buoyancy-dominated regimes in planar temporal forced plumes using a simple entrainment-based model and numerical simulations.

Contribution

It introduces a new analytical model that accurately describes the transition between regimes based on a single entrainment parameter.

Findings

Model accurately predicts transition timing.

Simulations confirm the model's validity.

Buoyancy effects dominate at long times.

Abstract

We study the transition from momentum- to buoyancy-dominated regime in temporal jets forced by gravity. From the conservation of the thermal content and of the volume flux, we develop a simple model which is able to describe accurately the transition between the two regimes in terms of a single parameter representing the entrainment coefficient. Our analytical results are validated against a set of numerical simulations of temporal planar forced plumes at different initial values of Reynolds and Froude numbers. We find that, although the the pure jet-scaling law is not clearly observed in simulations at finite Froude number, the model correctly describe the transition to the buoyancy-dominated regime which emerges at long times.