# Dynamical dispersion in turbulent plumes

## TL;DR

This paper introduces a model for axial dispersion in turbulent plumes with time-dependent buoyancy fluxes, validated by experiments showing self-similar transitions and quantifying dispersion effects.

## Contribution

The paper develops a new axial dispersion model for turbulent plumes with variable buoyancy fluxes, extending classical steady-state models to dynamic conditions.

## Key findings

- Dispersion coefficient  Ub with  between 0.70 and 0.88
- Transition between buoyancy states is self-similar
- Model aligns with classical plume theory for steady fluxes

## Abstract

Experimental observations of turbulent buoyant plumes, produced by a constant source of buoyancy, have been described with great success using a horizontally averaged model for the conservation of mass, momentum and buoyancy flux. However, experimental observations of plumes with time-dependent buoyancy fluxes has proved more challenging for quantitative models. At each level in the plume, the horizontal variation in velocity leads to an along-axis shear and hence dispersive transport relative to the mean. With a time-dependent source, axial dispersion of the dynamic properties of the plume has a key role in the evolution of the flow. Using ideas of mixing length theory, we introduce a model for this axial dispersion, and test the model by comparison with experimental observations of plumes in which the buoyancy flux is suddenly decreased or suddenly increased. In both cases, we show the transition from one buoyancy flux to another is self-similar, and using the data, we find the axial dispersion may be expressed as \beta Ub where \beta\ lies in the range 0.70-0.88 and U and b are respectively the horizontally averaged vertical velocity and radius of the plume at height z and time t. Our model also reduces to that of a classical plume when the buoyancy flux is steady.