The Mathematical Modelling of Mixing in Natural Streams

Abstract

<p> A method of modelling the mixing phenomenon in natural streams is presented. A wide range of mixing situations can be characterized using a lumped parameter model consisting of a network of ideally mixed components. The components represent two ideal states of mixing: complete mixing of the total component volume, and the other extreme where no mixing occurs in the direction of flow through the component volume. The use of frequency response techniques to match the mathematical model to the real situation is also discussed.</p> <p> Experimental work was carried out on a small natural stream to illustrate how the method is to be applied. The frequency response was obtained using sinusoidal, pulse, and impulse inputs and fluorometric dye tracing techniques. The non-linear model parameters were evaluated using the principles of least squares. The mathematical model chosen for this particular stream illustrates how the phenomenon of stagnant or slow moving regions can be included. The necessary data was collected on several days under different flow conditions to show how the model can be made a function of stream flow.</p>