Distribution of vertical velocity inferred from secondary flow in a curved tidal channel

Abstract

High-resolution observations from the curved tidal channel of the Otago Harbour shows secondary flows up to 20% of the primary flow and vertical velocity inferred from secondary flow up to 1% of the primary flow. This vertical velocity is inferred on a much finer scale than previous works. The spatial pattern of this vertical velocity is upward on the inside and downward on the outside of the bend, consistent with previous laboratory flume measurements. Linear regression, rp = 0.95, shows the cross-channel distribution of the observed secondary flow can be resolved from the horizontal ADCP measurements well enough to be consistent with the cross-channel distribution of secondary flow derived from the observed primary flow using the model of Kalkwijk and Booij (1986). Linear regression, rp = 0.80, shows the vertical velocity inferred from observed secondary flow is consistent with vertical velocity derived from the observed primary flow using the model of Kalkwijk and Booij (1986). This also shows the cross-channel distribution of the observed secondary flow is resolved well enough from the horizontal ADCP measurements to be able to infer the vertical velocity from mass continuity. The required horizontal resolution is made possible by Radial Basis Function (RBF) smoothing and spatial interpolation that allows for continuity of the spatial derivatives. Modeling trajectories using channel dimensions and velocity field values equivalent to the observations show that 3-dimensional secondary circulation forms a loose helical flow pattern.