Abstract
In three dimensions when water flows around a bend, instead of flowing straight, it spirals around the bend in a loose helical pattern. This pattern is commonly known as secondary circulation or secondary flow. The driving forces behind curvature induced secondary circulation are a stream-wise velocity shear due to bottom friction and centripetal acceleration. The velocity shear decreases the velocity towards the bottom resulting in an imbalance in the centripetal acceleration. This drives the flow radially outwards near the surface, and radially inwards near the bottom, creating a loose helical flow pattern around the curve. Secondary circulation plays an important role in nature, this includes mixing, erosion and formation of banks in rivers and estuaries, and localized up-welling at coastal headlands.
Observations from the curved tidal channel of the Otago Harbour show secondary flows up to 20 % of the primary flow and vertical velocity inferred from secondary flow that is up to 1% of the primary flow. Linear regression shows the cross-channel distribution of the observed secondary flow can be resolved from the horizontal ADCP measurements well enough to be able to infer the vertical velocity using mass continuity, rp = 0.95. The pattern of this vertical velocity is upwards on the inside and downwards on the outside of the curve. Observed around the curved tidal channel is the radially outwards movement of the depth averaged velocity maxima due to advective momentum transport and this movement is contrasted between the flood and ebb tide.
Observations from a sharper curvature bend in the Clutha river delta show flattening and deformation of the vertical profile of the primary flow due to the advection of momentum by secondary circulation and associate a counter rotating outer-bank cell of secondary circulation with this deformation. A visual explanation for this outer bank cell is proposed, based around the forces of plane equilibrium and the deformation of the vertical profile of the primary flow.
At Cape Saunders, a coastal headland, the vertical velocity inferred from horizontal ADCP measurements show a significant localized up-welling synchronized with the tidal cycle of up to 0.007 ms−1. Concurrent CTD measurements show up-welling of up to 0.002 ms−1 are correlated with the vertical velocity inferred from secondary flow, rp = 0.65, supporting the concept of inferring vertical velocity from the horizontal measurements. This up-welling equates to ≈ 7 m per hour meaning the entire water column is replacing itself with nutrient rich deep waters at least once during a tidal cycle.