EFFECT OF CROSS-SECTIONAL SHAPE ON FREE-SURFACE INSTABILITY

The effect of cross-sectional shape on free-surface instability is cha racterized by the dimensionless relative kinematic wave celerity c(drk ), defined as beta - 1, in which beta is the exponent of the normal di scharge-flow area rating Q = alpha A(beta). The value of c(drk) is a f unction of the type of friction (Manning or Chezy) and the cross-secti on parameter delta, the exponent of the wetted perimeter-flow area rel ation P = kappa A(delta). A stable channel is defined as that which fe atures a constant delta. Two types of stable channels are formulated: (1) unconditionally stable, for which delta = 1 and the Vedernikov num ber V = 0 for all Froude numbers; and (2) conditionally stable, for wh ich delta < 1, and V less than or equal to 1 for Froude numbers in the range F less than or equal to F-ns, in which F-ns is a design neutral -stability Froude number. Given a suitable choice of initial hydraulic radius R(o) and F-ns, a stable yet relatively narrow channel cross se ction may be designed following the methodology described here. Provid ed the Froude number remains in the range F less than or equal to F-ns , such a channel should be largely free from roll waves and kinematic shock waves.