Predicting channel bed topography in hydraulic falls

Abstract

We consider inverse methods for predicting the channel bed topography in experiments of hydraulic falls. Nonlinear solutions and weakly nonlinear approximations from Euler-based models are compared to experimental observations. Accurate predictions are obtained for the maximum height of the topography and its constant horizontal level far downstream using the nonlinear method. The weakly nonlinear approximation is shown only to be a good predictor of the maximum height of the topography. The error in the inverse predictions is examined and discussed.

Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

“…We see that there is good agreement between the two theories when 0.8 < F < 1.20. An additional comparison between the weakly nonlinear theory and numerical solutions to solve the full problem with experimental values of the amplitude of forcing is also found in the work of Tam et al [19].…”

“…This is sometimes referred to as the forward problem. Alternatively, one can prescribe η and solve for f , which is referred to as the inverse problem [10,19,35,45,60,61,80], and this is of interest in our ongoing research in this area.…”

“…The latter of these conditions is what makes the full problem difficult to solve because it is a nonlinear and unknown boundary condition which is found as a part of the solution. This defines the potential flow model for the full problem, and fully nonlinear solutions can be computed using boundary integral methods [8,19,26,43,45,49,60,64].…”

“…The study of free-surface flow has also explored energy lost in surface waves as an important component of the overall drag on the disturbance (e.g., the steady wave pattern and drag at the stern of a ship) [7][8][9][10][11][12][13]. The nature of research into free-surface flow has led to experimental studies predominantly in rectangular open channels [14][15][16][17][18][19] (e.g., see Figure 1). Understanding the fundamentals of such flows has been important in applications where there is a desire to protect waterway banks and hydraulic infrastructures, and reduce the wave-drag on a moving disturbance.…”

“…In addition, hybrid problems are also examined in which a combination of the four types of disturbances is considered [33,50,[57][58][59]. [19]. The flow is from left-to-right with uniform flow both far upstream and far downstream.…”