The Gareloch is a Scottish fjord that is 7.5 km long, 1 km wide and up to 45 m deep with a sill at the mouth, dredged to a depth of 16 m. Unlike the circulation in the adjacent Clyde Sea, flow in the Gareloch is dominated by short period (1-6 hours) baroclinic oscillations superimposed on the tidal (predominantly M₂) forcing. The aim of this study was to quantify and explain the baroclinic circulation through data collection and analysis, and by performing numerical model simulations. Three different models were applied to the Gareloch and a further objective was to see how the models compared in terms of their accuracy, efficiency and application to the study area.
Field observations taken over the last 16 years from the Gareloch (including two
surveys for the present study) have been presented and analysed. A tidal and density-driven jet was observed over the sill reaching speeds of 0.6 m/s during spring tides. The basin was permanently stratified with two distinct layers that were 180° out of phase at the tidal frequency and pulsated (unlike the sinusoidal modulation of the elevation) with speeds an order of magnitude greater than expected from the barotropic tide. However, the most important finding was that the short period oscillations ( observed in both the velocity and temperature data from 1998-2006) were higher harmonics of the semi-diurnal frequency. The first 5 harmonics were clearly isolated by the analyses and the amplitude of the first harmonic (M₄) was as great as the forcing (M₂) harmonic.
Three numerical, hydrostatic models were developed for the study area: a one-dimensional, two-layered model (ONED); a two-dimensional width-averaged model (SLICE); and a three-dimensional model (ECOMSED). Many aspects of the
baroclinic circulation were poorly simulated with ONED due to the impenetrable
interface between the two layers. The across-loch symmetry of the Gareloch meant that SLICE produced realistic hydrodynamics. SLICE was also an order of magnitude more efficient than ECOMSED. However, it was shown that accurate simulations can only be achieved with three-dimensional models and with high resolution density and wind data.
The models predicted a 1 ^st mode barotropic seiche period of 35 minutes which was consistent with the theory. Only odd-mode solutions were simulated as elevations were clamped to zero at the boundary ( over the sill) to emulate the realistic condition of infinitesimal ocean outside the basin. SLICE and ECOMSED simulated a 1^st mode internal seiche wave with a period of 8.5 hours which was comparable to vertical modal calculations and some observations. The models reproduced the higher harmonics in the internal wave field and showed that their generation was attributed to the non-linear distortion of the internal tide, governed by water depth, stratification, barotropic flux and the shape of the basin, including the presence of the sill. It was shown that when the internal Froude number, F ( controlled by barotropic flux, stratification and water depth) was less than unity, a linear internal tide was produced. As F was increased, a quasi-nonlinear state occurred where higher harmonics were generated. The internal tide was further modified by wave reflection and interaction off steep boundaries, and by flow over the sill leading to a fully non-linear state where
cnoidal waves can develop. It is important to note that the hydrostatic models used in this project cannot reproduce non-hydrostatic effects, such as solitary waves and nonhydrostatic overturning, which are inherent in shelf seas. Lee waves were simulated with SLICE and ECOMSED on the lee slope of the sill when the amplitude of the flow exceeded 0.3 m/s.