Forced bars induced by variations of channel width: Implications for incipient bifurcation

Abstract

In this study we investigate forced bars that form in a channel with periodic width variations. A depth‐averaged two‐dimensional (2‐D) model incorporating a simplified correction for the helical flows induced by streamline curvature is used to obtain analytical solution of bed deformation. Flume experiments are conducted to verify the model results. With the correction included, the 2‐D model will be comparable to the 3‐D model. Because the no‐slip condition is relaxed at the sidewalls, the model gives distorted results in the near‐bank region, particularly at narrow sections, but the bed topography is satisfactory for the major part of the channel. The forced bars are classified into four types according to the locations of peak deformations. Transition from one type to another is controlled mainly by the aspect ratio β. Increasing the value of β exhibits sequentially the purely central bars (mode 1), transverse bars (central mode 1), side bars, and transverse bars (central mode 2). The analytical solution is used to derive a criterion for central bar formation, which implies a condition required for incipient bifurcation. Given the bank profile, flow, and sediment conditions, the central bars of mode 1 would develop for β < βc1 (a lower critical value), the central bars of mode 2 would develop for β > βc2 (an upper critical value), whereas side bars would form for βc1 < β < βc2. Such criteria for formation of different bar patterns are necessary but not sufficient conditions for establishing stable regimes.