Laboratory of numerical experiments in ocean dynamics

Impact of the spatial inhomogeneity of the bottom hydrodynamic roughness on tidal dynamics and energetics in the Barents and Kara seas
Head: Prof. B. Kagan

Fig. 1. Absolute value of the average (over a tidal cycle) normalized bottom friction stress for a constant drag coefficient (a) and difference between it and the value obtained at a variable drag coefficient (b) in the Barents and Kara seas.

The QUODDY-4 three-dimensional finite-element hydrostatic model is modified by including a module for the drag coefficient calculated from external determining parameters of the bottom boundary layer (BBL). The drag coefficient is either taken to be constant (5 x 10^-3) or calculated by new resistance laws obtained in (Kagan, 2003, 2005) by matching asymptotic expansions for velocity in the bottom logarithmic layer and the external part of the BBL.

The modified model is used to evaluate changes in dynamic characteristics (the amplitude and phases of tidal elevations and the maximum barotropic tidal velocity), as well as some components of the barotropic tidal energy budget in the Barents and Kara Seas, induced by the spatial variability in the drag coefficient. It has been shown that the changes in all tidal characteristics, except for the direction of the averaged (over a tidal cycle) horizontal wave transport of barotropic tidal energy, are significant in the sense that they are either greater than the rms absolute vector error or have identical (or near-identical) orders of magnitude when compared to the tidal characteristics themselves (Kagan and Timofeev, 2015).

Moreover for average (over tidal cycle) bed shear stress these changes are the same order or slightly less than the absolute values of the bottom stress. These findings imply that the concept of a "constant drag coefficient" should be revised.

Fig. 2. Ellipses and velocities of tidal currents on the surface

Fig.3. The amplitudes of internal tidal waves on the pycnocline’s depth in the Strait of Kara Gate at the combined forcing

Modeling of the stationary circulation and semidiurnal surface and internal tides in the Strait of Kara Gates
Kagan and Timofeev, 2015

The finite element mesh of the Strait has horizontal resolution from 0.5 to 2 km. The 3-D QUODDY-4 model if forced by either stationary difference of the free surface level at the open boundaries of the study domain, or by tidal elevations at the same boundaries, or by means of both concurrently.

Forcing is caused either by stationary differences in the free surface elevation at the open boundaries, or by tidal elevation oscillations at the same boundaries, or both (combined forcing). It is shown that the amplitude of internal tidal waves predicted by the model in this strait is of the order of 10-16 m at medium spring-neap conditions.

Also the maximum internal tidal waves' amplitudes are detected where internal tidal waves propagate against the stationary flow.

Effect of the tidal mixing on the average climatic characteristics of the Barents Sea
Kagan & Sofina, 2015

Fig. 4. Vertical profiles of average (by the sea area) values of the vertical turbulent diffusion coefficient (a) and the buoyancy frequency (b) when specifying the total (solid curve) and combined (dashed line) forcings.

The results of two numerical experiments on the determination of the climate of the Barents Sea obtained using the 3D finite element model hydrostatic model QUODDY-4 are presented. One of the experiments is carried out with the total (wind + thermohaline + tidal) forcing, while the second is conducted without taking into account the tidal component (combined forcing). It is shown that the climate in the Barents Sea is experiencing significant changes associated with the tidal forcing. Thus, maximum differences between two solutions are approximately ±1.0°C for the temperature and ±0.4‰ for seawater salinity at the pycnocline depth.

The same conclusion follows from the comparison of the diapycnal diffusion coefficient that characterizes the influence of internal tidal waves and the “background” diffusion coefficient determined by total forcing (including tidal forcing).

Predicted values of the background diffusion coefficient are of the same order of magnitude as the ones observed by microstructural measurements of shear in velocity, temperature, and electrical conductivity of sea water in the centers of intense mixing in the marginal zone of the sea ice in the Barents Sea.

Non-hydrostatic dynamics in straits of the World Ocean
Voltzinger and Androsov, 2013 - 2016

Fig. 5. Bathymetry inStrait of Gibraltar

Fig. 6. Significance of non-hydrostatic effects (?~О(1)) over M2-tidal period T in zones of the Strait of Gibraltar.

A numerical models of strait dynamics are developed to assess the significance of the non-hydrostatic effects and classification of the Straits from the perspective of a rational approach for modeling non-hydrostatic dynamics, facilitating the choice between increasing the accuracy of the model and reducing the computation costs. The method was applied to simulate the non-hydrostatic barotropic-baroclinic interaction over seamount in the straits of Messina, Gibraltar and Bab-el-Mandeb (see figs. 5 and 6 in case of the strait of Gibraltar).

Nonlinear internal waves in the White sea according to simulation results and observations
D. Romanenkov in collaboration with A. Zimin, I. Kozlov and B. Chapron

Fig. 9. Nonlinear internal waves in the White Sea. Above in the center - the reanalysis of the radar satellite image of the of IW packets manifestations on the sea surface. Bottom fragment - the result of modeling the evolution of a two-wave packet of nonlinear IW along the density interface after 6 days of calculation; the A-F symbols indicate the positions of the packets as on a satellite image. The left upper fragment – recorded oscillations of isotherms with a period of 10-20 min at the polygon. Right fragment – IR image of the sea surface.

The possibility of estimating the kinematic parameters of nonlinear internal waves (IW) using the results of modeling and partially observational data in the White Sea is studied.

The results of calculations performed by two-layer models of internal waves in the framework of weakly-nonlinear approximation with variable sea water properties and arbitrary bathymetry are presented.

Numerical implementation of models allowed us to estimate the evolution and transformation of the initial wave disturbances arising after their generation by barotropic tide in the area of the hydrological thermohaline front. The simulation results are compared with the measured data, and they are also used for the interpretation of spaceborne radar images (see figure and Kozlov et al., 2014).

Mega-tsunami in the Lituya Bay, 1958 г.

Fig. 7. Passage of the tsunami wave across the axis of the bay (blue line) after the descent of the coastal landslide (red line). The maximum height of the splash is 360 m.

Рис. 8. The maximum wave height reaches 160 m. (According to sources: Singerland et al., 1979 - 158м; Fritz et al., 2001 - 152м.; Fritz et al., 2010 - 180 m)

Modeling of non-hydrostatic hydrodynamics in case of catastrophic natural coastal destruction
Androsov et al., 2014; Voltzinger and Androsov, 2015

Landslide dynamics is considered in the framework of a two-layer system involving water and landslide material. The problem is formulated both in the Cartesian coordinates and in a generalized form relying on curvilinear boundary-fitted coordinates.

An essential element of landslide dynamics is the account for non-hydrostatic pressure component defined by the solution of the nonlinear dispersive Boussinesq equation. A numerical implementation for curvilinear coordinates uses the second-order difference splitting scheme with restriction on the grid size only imposed by advection, and includes a module for computing draining in the shallow zone.

The results of extensive series of numerical experiments simulating changing physical and energetic characteristics of landslide in function of slope angle are presented together with modeling results for coastal wave dynamics generated by a landslide as well as estimation of the impact of non-hydrostatic effects.

The model is verified by comparing its simulation results with the results of laboratory experiments for three events: a tsunami wave at the Japan coast, wave passage over a submarine barrier and a gravity wave generated by a landslide. As a practical model application simulations of the flow generated by the Alaska mega-landslide (1958) are presented.