A Numerical Study of the Internal Tide in Upper Loch Linnhe

Abstract

Data has been analysed from two independent investigations into the dynamics of
Upper Loch Linnhe. The first data set, collected between February 1991 and
February 1992 by Fisheries Research Services (FRS), was made available by the
British Oceanographic Data Centre. The second set of data was collected between
November 1992 and June 1993 by G. Allen. Comparison with the earlier data backs up the original conclusions of Allen (1995) that an energetic mode l internal tide is present in the basin. Further the residual flows during a renewal event have also been found to compare favorably with those taken from the current meter moorings of the earlier FRS data during a similar renewal event.
The dynamics of the mode 1 internal tide have been simulated using two differing numerical models. The hydrostatic model of Gillibrand (1993) has been compared with a model developed for this study based around the non-hydrostatic model presented in Bourgault and Kelley (2004). The hydrostatic model fails to reproduce the phase of the internal tide, in error by approximately 180°. The non-hydrostatic model reproduces this internal tidal stream within the error bounds of the harmonic analysis at the surface and bed. The errors in the middle of the water column were larger, at 60m the disagreement was 33° ± 15. The gross lack of agreement of the hydrostatic model with the data was found to be due to its inability to simulate flow separation from the lee of the sill.
Subsequently the non-hydrostatic model was used to investigate the flows during
renewal events. The deep depression in the isopycnals, attributed by Allen and
Simpson (2002) to a baroclinic adjustment to the density gradients at slack water,
has been reproduced by this model, showing its generation is due to several flood streams advecting dense water over the sill.
Further analysis of this model output is suggestive of three processes that can lead to the formation of an internal tidal response in a jet fjord. Firstly Bernoulli forcing involves a low pressure created in the lee of the sill drawing deep waters seaward during a flood. The second process is the vertical advection of the density gradient up the slope at the northern end of the basin. This has been termed aspirational forcing. The third and most significant mechanism has been identified as time variant density, caused by density variations over the tidal cycle in the waters overflowing the Corran sill.
It is proposed that these processes go someway to explaining the conundrum posed by Stigebrandt (1999b); how can a jet fjord create an internal tide?

Date of Award	Mar 2007
Original language	English
Awarding Institution	University of Wales, Bangor
Sponsors	Ministry of Defence
Supervisor	John Simpson (Supervisor)