Environmental Engineering Reference
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to modify the 3D finite-element hydrothermodynamic model QUODDY-4,
incorporating the rotated co-ordinate system, which allows us to obviate “the pole
problem”, and supplementing the model with the effects of the equilibrium tide;
to simulate (in the frames of the modified model) the spatial structure of the M 2 ITW;
to use the model results for revealing the ITW generation sites, if any;
to find spatial distributions of the ITW energy budget components, including the
conversion of barotropic tidal energy into baroclinic one and back; and
to map the ITW-induced diapycnal mixing coefficient, determining changes in the
mixing of tidal origin.
The article is organized as follows: in Section 2, a brief description of a modified version
of the 3D finite-element hydrothermodynamic model QUODDY-4 and means of its
implementaton are given; Section 3 is devoted to a discussion of the model results for the M 2
surface and internal tides. At last, Section 4 summarizes the work and setts off one of
problems, which has a bearing on the surface and internal tides in the Arctic Ocean and,
accordingly, on information relative to a contribution of the Arctic Ocean to the global tidal
energy dissipation budget.
2. The Model
The basis for research on the surface and internal tides in the Arctic Ocean forms the
modified 3D finite-element hydrothermodynamic model QUODDY-4, which differs from its
original version [Ip and Lynch, 1995] by introducing the rotated coordinate system (Sein, a
private communication), bypassing “the pole problem”, and describing the effects of the
equilibrium tide. The model contains the system of 3D hydrothermodynamic equations,
namely, primitive equations of motion, written in hydrostatic and Boussinesq approximations,
as well as evolutionary equations for temperature and salinity and equations of continuity and
seawater state. The vertical eddy viscosity and diffusivity are considered to be unknown and
determined using a 2½-level turbulence closure scheme (i.e. kinetic turbulence energy (TKE)
and the turbulence scale are found from the relevant evolutionary equations and the
Kolmogorov approximate similarity relationships). The horizontal eddy viscosity and
diffusivity are computed using the well-known Smagorinsky formulae. The bottom stress is
parameterized by a quadratic resistance law, suggesting that the velocity in the near-bottom
layer is described by the logarithmic law. The heat and salt fluxes at the bottom and ocean
surface are taken as zero, while the corresponding values of TKE and the turbulence scale are
found from the condition of local balance between the TKE generation and dissipation, with
allowance made (in accordance with the law of the wall) for a linear change in the turbulence
scale within the near-bottom layer. It is also assumed that the ocean surface is ice-free. This
assumption is justified by the fact that the influence of ice on surface and internal tides may
be neglected, at least, as a first approximation.
The enumerated boundary conditions, together with the boundary conditions at open and
solid boundaries, are presented and detailly described in [Ip and Lynch, 1995; see also Kagan
and Timofeev, 2005]. Recall that the tidal sea surface level elevations at the open boundary
are specified, and the normal derivation of the tangential (to the boundary) component of the
integral transport is taken as zero. In addition, if the domain under steady is stratified, as with
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