THE OCCURRENCE OF CRITICAL FLOW AND HYDRAULIC JUMPS IN A MULTI-LAYERED FLUID SYSTEM

Abstract

With use of the speed of long waves of infinitesimal amplitude as the criterion for critical flow, general expressions are obtained for critical conditions in a fluid system of n layers, where velocity as well as density vary from layer to layer. It is shown that at critical flow, energy per unit volume in each layer, total energy transfer, and total momentum transfer are all minima. The multi-layered system is in this respect a simple extension of the one-fluid regime, since the fluid system cannot pass through critical flow in steady state over a horizontal surface without occurrence of a finite surface or internal hydraulic jump. These principles are illustrated by a detailed analysis of a two-layer system, and it is shown that momentum and energy considerations are insufficient to specify conditions below a standing hydraulic jump when all upstream parameters are known. The implications of this concept are discussed in connection with the changes a real two-fluid system will undergo when momentum and energy are abstracted by friction.