Reynolds stresses from ADCPs and modelling of internal tides
Date
2003
Authors
Stringer, Steven Ross
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Abstract
Two separate studies are presented. In the first, Reynolds stresses from both a standard four-beam ADCP (Janus) and a modified four-beam ADCP with one vertical and three oblique beams (Cyclops) are analysed algebraically and observationally. Mathematically, the stresses are expressed in terms of the variances of the beam velocities and other unknown components of the stress tensor. It is noted that a deployment condition with zero tilt significantly improves the stress estimates of both instruments. In the presence of tilt, the Janus ADCP provides better estimates of the Reynolds stress than does the Cyclops using the beam variance technique, though the Cyclops ADCP is able to resolve other quantities which the Janus cannot; namely the turbulent kinetic energy and the anisotropy ratio, both of which require a vertical beam for measurement. Further comparisons are made to the data products which can be resolved from a three-beam and a five-beam ADCP which show that a three-beam system cannot recover Reynolds stresses without significant bias from unknown stress tensor components and that a five-beam system can resolve both Reynolds stresses as well as the turbulent kinetic energy. Data from both four-beam ADCPs were gathered during an August 2000 cruise, where both instruments were deployed in Sansum Narrows, off Vancouver Island. The data support the analtyic results, which find that unknown stress tensor components ( e.g. u'2 , v'2 , etc.) that are not multiplied by a tilt angle significantly contaminate the Reynolds stress estimates.
Next, the generation of internal tides by abrupt topography is considered. The tidal generation at a step is examined numerically and compared to an earlier shelf study. The assumption made in the former work of negligible shelf-side internal waves is confirmed for shallow shelves, but is shown to be increasingly unrealistic with decreasing step height. The energy flux generated by the step is compared with the estimate from linear theory for the energy flux from an arctan function and they are found to be equal for vanishing step heights, but the energy flux from the step increasingly exceeds that based on linear theory as the step height increases. Also, the energy flux generated from a knife-edge ridge is calculated and compared to the linear theory prediction for a "Witch of Agnesi" ridge. For vanishing step heights, the knife-edge ridge produces twice the energy flux of the witch, and the ratio increases with step height. Realistic parameter values which are representative of the Hawaiian Ridge are applied to the knife-edge ridge, resulting in reasonable estimates of energy flux (20GW) as compared to those made in observational studies (Egbert and Ray 2000), despite the simplicity of the knife-edge model.