Analytical Modeling of Hydraulic Jumps Induced by River Plume’s Lateral-Boundary Constriction

In this paper, we present an analytical two-layer model to demonstrate the basic dynamics in the formation of an internal hydraulic jump. In particular, we want to determine downstream conditions with known upstream conditions and a prescribed constriction angle, which is defined as the change of mean flow direction across the front face of the hydraulic jump. The analytical model conserves mass in each individual layer and the flow force across the jump front. The closure problem is approached by assuming that the layer Bernoulli functions remain constant along streamlines. Our model clearly indicates the existence of an oblique front for the limiting case when the constriction angle \(\theta \) and internal disturbance amplitude \({h}_{1}^{\prime}-{h}_{1}\) are both infinitesimal, and the predicted front angle is perfectly consistent with that derived from a so-called Froude angle theory. We also detected another solution branch which it not noticed before. Our model also holds for finite \(\theta \) cases, and the solution existence is proved. Simple calculations show that the predicted front angle agrees well with in-situ observation, and increases approximately linearly with the constriction angle for small \(\theta \) . Comparison of analytical solutions with high-resolution numerical results will be presented in the near future.