The Effect of Channel Length on the Residual Circulation in Tidally Dominated Channels

With an analytic model, this paper describes the subtidal circulation in tidally dominated channels of different lengths, with arbitrary lateral depth variations. The focus is on an important parameter associated with the reversal of the exchange flows. This parameter (δ) is defined as the ratio between the channel length and one-quarter of the tidal wavelength, which is determined by water depth and tidal frequency. In this study, a standard bottom drag coefficient, CD = 0.0025, is used. For a channel with δ smaller than 0.6–0.7 (short channels), the exchange flow at the open end has an inward transport in deep water and an outward transport in shallow water. This situation is just the opposite of channels with a δ value larger than 0.6–0.7 (long channels). For a channel with a δ value of about 0.35–0.5, the exchange flow at the open end reaches the maximum of a short channel. For a channel with a δ value of about 0.85–1.0, the exchange flow at the open end reaches the maximum of a long channel, with the inward flux of water occurring over the shoal area and the outward flow in the deep-water area. However, near the closed end of a long channel, the exchange flow appears as that in a short channel—that is, the exchange flow changes direction along the channel from the head to the open end of the channel. For a channel with a δ value of about 0.6–0.7, the tidally induced subtidal exchange flow at the open end reaches its minimum when there is little flow across the open end and the water residence time reaches its maximum. The mean sea level increases toward the closed end for all δ values. However, the spatial gradient of the mean sea level in a short channel is much smaller than that of a long channel. The differences between short and long channels are caused by a shift in dynamical balance of momentum or, equivalently, a change in tidal wave characteristics from a progressive wave to a standing wave.