Plume (fluid dynamics)

Introduction

A plume in the context of fluid dynamics is a column of one fluid moving through another. Several effects control the motion of the fluid, including momentum (inertia), diffusion and buoyancy (density differences). Plumes are used by geologists to study the interior of the Earth.

Types of Plumes

There are different types of plumes, and they can be categorized based on their behavior in the ambient fluid:

Buoyant plumes - Buoyant plumes are driven by density differences in the fluid. This can be caused by a difference in temperature, salinity, or concentration of chemical species. The fluid at the source of the plume is less dense than the ambient fluid, and as a result, it rises.

Forced plumes - Forced plumes, also known as momentum-driven plumes, are driven by the momentum of the fluid source. The fluid is ejected into the ambient fluid at a velocity, and the momentum of the fluid source propels the plume upwards.

Line plumes - Line plumes are a type of forced plume that are elongated in the direction of flow. They are often seen in the ocean where a river discharges into the sea.

Passive plumes - Passive plumes are a type of plume where the fluid source has no initial momentum. The motion of the plume is driven entirely by diffusion.

A column of smoke rising from a source, illustrating the concept of a plume in fluid dynamics.

Mathematical Modelling of Plumes

Mathematical modelling of plumes is used to predict the behavior of plumes in various environments. The governing equations for plume motion are derived from the principles of conservation of mass, momentum, and energy. The complexity of the equations can vary depending on the assumptions made about the plume and the ambient fluid.

Buoyant Plumes

The governing equations for buoyant plumes are derived from the principles of conservation of mass, momentum, and energy, combined with the equation of state for the fluid. The equations are typically written in terms of the plume radius, velocity, and excess temperature or concentration.

Forced Plumes

Forced plumes are modelled using similar principles as buoyant plumes, but the source momentum is included in the momentum equation. The equations are typically written in terms of the plume radius, velocity, and excess temperature or concentration.

Line Plumes

Line plumes are modelled using a simplified set of equations that assume the plume is slender and has a constant shape. The equations are typically written in terms of the plume length, velocity, and excess temperature or concentration.

Passive Plumes

Passive plumes are modelled using diffusion equations. The equations are typically written in terms of the plume radius, and concentration.

Applications of Plume Theory

Plume theory has a wide range of applications in environmental engineering, geophysics, and industrial processes. Some examples include:

Air pollution dispersion - Plume models are used to predict the spread of pollutants from industrial stacks and other sources.

Volcanology - Plume models are used to predict the behavior of volcanic plumes, including the spread of ash and other volcanic materials.

Oceanography - Plume models are used to predict the behavior of plumes in the ocean, such as those created by river outflows or deep-sea vents.

Industrial processes - Plume models are used in the design of industrial processes that involve the release of fluids, such as cooling towers and chemical reactors.