Simple analytic solutions for tidal oscillations in estuaries, such as that of the Thames, are discussed in terms of linearized theory. It is shown that progressive waves of constant speed (gh)1/2 are peculiar to channels of constant cross section, and cannot be regarded as adequate approximations in slowly diverging estuaries as is frequently supposed.The effect of friction is principally to cause a change of phase along an estuary giving a progression in high-water times, the phase difference between current and elevation remaining essentially that of a classical standing wave. Measurements in the Thames support this conclusion. Recent publications treating these tides as progressive waves are therefore disputed. The theory is shown to predict several of the observed features of the tide in the Thames when the friction coefficient is given the value K = 0.0024. These are the speed of high-water from Southend to Hammersmith, the variation in tidal range and the high-waterlslackwater interval from Southend to Greenwich.It is suggested that the classical frictionless terms-"progressive wave" and "standing wave"-can be applied to a frictional situation only with considerable caution.
Fine sediment is carried in suspension by turbulent flow under steady conditions, provided that similar material is present on the bed. An equation is deduced for the variation with depth of the sediment concentration for two-dimensional flow. It is found necessary to take account of the volume occupied by the sediment, this being particularly important near the bed. The result agrees with recent observations by Vanoni (1946). A velocity distribution obtained by Kármán, using a linear variation of shear with depth, is generalized by omitting the infinite velocity gradient condition at the bed and is found to be in good agreement with Vanoni’s measurements. A slight difference is found between the mean sediment velocity in the direction of flow and that of the water.
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