A note on waveless subcritical flow past symmetric bottom topography

Abstract

This paper re-examines the problem of the flow of a fluid of finite depth over two Gaussian-shaped obstructions on the stream bed. A weakly nonlinear analysis in the form of the Korteweg–de Vries equation is used to compare with the results of the fully nonlinear problem. The main focus is to find waveless subcritical solutions, and contours showing the obstruction height and separation values that result in waveless solutions are found for different Froude numbers and different obstruction widths.

Ideal Planar Fluid Flow Over a Submerged Obstacle: Review and Extension

“…Several more recent papers have also examined the accuracy of KdV theory against the predictions of fully nonlinear inviscid free-surface hydrodynamics. Holmes and Hocking [28] found that KdV theory was only accurate for flow over topography when , which is entirely consistent with the approximation used in the derivation of that theory. Tam et al [44] used both KdV theory and fully nonlinear models to solve the (inverse) problem in which the free-surface elevation is assumed known, for a critical flow, and the bottom bump shape then calculated.…”

“…Later, Holmes et al [29] and Hocking et al [27] carried out similar and more accurate computations for steady flow over a system of two bottom bumps, and confirmed the existence of sets of separation distances between the bumps for which wave-free solutions exist; furthermore, they allowed these bumps to have either positive or negative heights, and obtained an elaborate lattice of waveless solutions in a parameter space consisting of the separation distance and height of the two bumps. These results were extended by Holmes and Hocking [28], who also compared the fully nonlinear solutions with the predictions of weakly nonlinear theory.…”

Interference of internal waves due to two point vortices: linear analytical solution and nonlinear interaction

“…An elaborate description of solution branches in the parameter with respect to the heights and the separation distance of two topographies was provided, in which every point on the branch represents a waveless solution. Then Holmes & Hocking [ 25 ] used KdV theory to re-examine this problem and compared the results from nonlinear methods, KdV theory and linearized methods. Besides, contours in parameter space of separation distances and heights of obstructions are depicted under different widths of the obstruction and Froude numbers.…”