Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions |
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Authors: | Alan M Davies Jiuxing Xing Jarle Berntsen |
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Institution: | (1) Proudman Oceanographic Laboratory, 6 Brownlow Street, Liverpool, L3 5DA, UK;(2) Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway; |
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Abstract: | A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing
the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill
regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing
the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear
terms in the energy flux become increasingly important as the sill Froude Number (F
s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close
to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee
wave generation and the non-linear contribution to the energy flux. Calculations show that as F
s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The
importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the
buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as
the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these
calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions. |
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