The impact of the spatial variability in bottom roughness on tidal dynamics and energetics, a case study: the M 2 surface tide in the North European Basin

A modified version of the 3D finite-element hydrostatic model QUODDY-4 is used to quantify the changes in the dynamics and energetics of the M ₂ surface tide in the North European Basin, induced by the spatial variability in bottom roughness. This version differs from the original one, as it introduces a module providing evaluation of the drag coefficient in the bottom boundary layer (BBL) and by accounting for the equilibrium tide. The drag coefficient is found from the resistance laws for an oscillatory rotating turbulent BBL over hydrodynamically rough and incompletely rough underlying surfaces, describing how the wave friction factor as well as other resistance characteristics depend on the dimensionless similarity parameters for the BBL. It is shown that the influence of the spatial variability in bottom roughness is responsible for some specific changes in the tidal amplitudes, phases, and the maximum tidal velocities. These changes are within the model noise, while the changes in the averaged (over a tidal cycle) horizontal wave transport and the averaged dissipation of barotropic tidal energy may be of the same orders of magnitude as are the above energetic characteristics as such. Thus, contrary to present views, ignoring the spatial variability in bottom roughness at least in the North European Basin is only partially correct: it is valid for the tidal dynamics, but is liable to break down for the tidal energetics.     

Ice-induced seasonal variability of tidal constants in the Arctic Ocean

The results for three-dimensional (3D) winter and summer tidal flows in the homogeneous Arctic Ocean, obtained with the use of a modified version of the 3D finite-element hydrothermodynamic model QUODDY-4, are presented. It is shown that seasonal variability of the M₂ tidal constants (amplitudes and phases of tidal sea surface level elevations) in the Central and Canadian parts of the Arctic Ocean is less than the error in the predicted tidal sea surface level elevations. This means that the seasonal variability can be neglected at least as a first approximation. A different situation is encountered in the Siberian continental shelf, where seasonal changes of tidal amplitude are ±5 cm, while those of tidal phase vary from 15° to several tens of degrees.     

Influence of Horizontal Nonuniformity of Stratification on Internal Tides and Their Induced Diapycnal Diffusion in the Ice-Free Kara Sea

Oceanology - Abstract—The 3D finite-element hydrostatic model QUODDY-4 is used to study the influence of horizontally nonuniform stratification on internal tides and their induced diapycnal...     

Influence of the White Sea on tides in adjacent marginal seas of the North European Basin

An investigation into the interaction of surface M ₂ tides in the system of marginal seas of the North European Basin is carried out using the three-dimensional finite-element hydrostatic model QUODDY-4. Three numerical experiments are performed for this purpose. In the first (control), the model equations are solved in the system of the Norwegian, Greenland, Barents, and White seas; thereby the interaction of the tides in these seas is explicitly taken into account. In the second experiment, the White Sea is excluded from consideration and the no-flux condition is posed at the entrance to the sea. The third experiment uses an approach in which the observed tidal elevations that determine the existence of a finite horizontal transport of barotropic energy to the White Sea are specified at the open boundary of the White Sea. It is shown that changes in tidal dynamics represented by changes in the amplitudes and phases of tidal elevations and in the barotropic tidal velocity ellipse parameters are within the model noise in experiments 2 and 3 when compared with the control experiment. On the contrary, changes in energy characteristics (the horizontal wave transport, density, and dissipation rate of barotropic tidal energy) are equal to or greater (in order of magnitude) than the energy characteristics themselves.     

A method of accounting for tidal changes in regional climates of a water basin under conditions of an ice-free Barents Sea

To account for tidal variations in the regional climate of a water basin, we propose adding up the vertical eddy diffusivity, determined by wind and thermohaline forcings, and the diapycnal diffusivity, determined from the solution to the problem of the internal tidal wave (ITW) dynamics. This approach agrees with the approximation of “weak interaction” between turbulence of various origins. Then, the hydrothermodynamics equations are integrated with and without regard for ITW-induced diapycnal diffusion until a quasistationary solution is reached. Next we compare these solutions, found by using the 3D finite-element hydrostatic model QUODDY-4. This comparison shows that the contribution of tides to the formation of the Barents Sea climate in summer is not negligible with respect to certain hydrological characteristics. We present the fields of the dynamic topography of a free surface, surface current velocities, and seawater temperature and salinity at the depth of the pycnocline in the sea to illustrate the occurrence of tidal effects.