Vladimir S. Maderich

Interaction of a large amplitude interfacial solitary wave of depression with a bottom step

This paper is devoted to the study of the transformation of a finite-amplitude interfacial solitary wave of depression at a bottom step. The parameter range studied goes outside the range of weakly nonlinear theory (the extended Korteweg–de Vries or Gardner equation), and we describe various scenarios of this transformation in terms of the incident wave amplitude and the step height. The dynamics and energy balance of the transformation are described. Several numerical simulations are carried out using the nonhydrostatic model based on the fully nonlinear Navier–Stokes equations in the Boussinesq approximation. Three distinct runs are discussed in detail. The first simulation is done when the ratio of the step height to the lower layer thickness after the step is about 0.4 and the incident wave amplitude is less than the limiting value estimated for a Gardner solitary wave. It shows the applicability of the weakly nonlinear model to describe the transformation of a strongly nonlinear wave in this case. In the second simulation, the ratio of the step height to the lower layer thickness is the same as that in the first run but the incident wave amplitude is increased and then its shape is described by the Miyata–Choi–Camassa solitary wave solution. In this case, the process of wave transformation is accompanied by shear instability and the billows that result in a thickening of the interface layer. In the third simulation, the ratio of the step height to the thickness of the lower layer after the step is 1.33, and then the same Miyata–Choi–Camassa solitary wave passes over the step, it undergoes stronger reflection and mixing between the layers although Kelvin–Helmholtz instability is absent. The energy budget of the wave transformation is calculated. It is shown that the energy loss in the vicinity of the step grows with an increase of the ratio of the incident wave amplitude to the thickness of the lower layer over the step.

Internal solitary wave transformation over a bottom step: Loss of energy

In this paper, we extend the numerical study of Maderich et al. [“Interaction of a large amplitude interfacial solitary wave of depression with a bottom step,” Phys. Fluids 22, 076602 (2010)10.1063/1.3455984] on the interaction of an interfacial solitary wave with a bottom step, considering (i) the energy loss of solitary waves of both polarities interacting with a bottom step and (ii) features of the transformation of a large-amplitude internal solitary waves at the step. We show that the dependence of energy loss on the step height is not monotonic, but has different maximum positions for different incident wave polarities. The energy loss does not exceed 50% of the energy of an incident wave. The results of our numerical modeling are compared with some recent results from laboratory tank modeling.

Inter-comparison of dynamic models for radionuclide transfer to marine biota in a Fukushima accident scenario.

We report an inter-comparison of eight models designed to predict the radiological exposure of radionuclides in marine biota. The models were required to simulate dynamically the uptake and turnover of radionuclides by marine organisms. Model predictions of radionuclide uptake and turnover using kinetic calculations based on biological half-life (TB1/2) and/or more complex metabolic modelling approaches were used to predict activity concentrations and, consequently, dose rates of (90)Sr, (131)I and (137)Cs to fish, crustaceans, macroalgae and molluscs under circumstances where the water concentrations are changing with time. For comparison, the ERICA Tool, a model commonly used in environmental assessment, and which uses equilibrium concentration ratios, was also used. As input to the models we used hydrodynamic forecasts of water and sediment activity concentrations using a simulated scenario reflecting the Fukushima accident releases. Although model variability is important, the intercomparison gives logical results, in that the dynamic models predict consistently a pattern of delayed rise of activity concentration in biota and slow decline instead of the instantaneous equilibrium with the activity concentration in seawater predicted by the ERICA Tool. The differences between ERICA and the dynamic models increase the shorter the TB1/2 becomes; however, there is significant variability between models, underpinned by parameter and methodological differences between them. The need to validate the dynamic models used in this intercomparison has been highlighted, particularly in regards to optimisation of the model biokinetic parameters.

A new comparison of marine dispersion model performances for Fukushima Dai-ichi releases in the frame of IAEA MODARIA program.

A detailed intercomparison of marine dispersion models applied to the releases from Fukushima Dai-ichi nuclear power plant was carried out in the frame of MODARIA program, of the IAEA. Models were compared in such a way that the reasons of the discrepancies between them can be assessed (i.e., if they are due to the hydrodynamic part, the dispersion part, and the ultimate reasons). A sequential chain of dispersion exercises was carried out with this purpose. The overall idea is to harmonize models, making them run with the same forcing in a step-by-step procedure, in such a way that the main agent in producing discrepancy between models can be found. It was found that the main reason of discrepancies between models is due to the description of the hydrodynamics. However, once this has been suppressed, some variability between model outputs remains due to intrinsic differences between models (as numerical schemes). The numerical experiments were carried out for a perfectly conservative radionuclide and for (137)Cs (including water/sediment interactions). Model outputs for this radionuclide were also compared with measurements in water and sediments.

A comparison of marine radionuclide dispersion models for the Baltic Sea in the frame of IAEA MODARIA program.

Four radionuclide dispersion models have been applied to simulate the transport and distribution of (137)Cs fallout from Chernobyl accident in the Baltic Sea. Models correspond to two categories: box models and hydrodynamic models which solve water circulation and then an advection/diffusion equation. In all cases, interactions of dissolved radionuclides with suspended matter and bed sediments are included. Model results have been compared with extensive field data obtained from HELCOM database. Inventories in the water column and seabed, as well as (137)Cs concentrations along 5 years in water and sediments of several sub-basins of the Baltic, have been used for model comparisons. Values predicted by the models for the target magnitudes are very similar and close to experimental values. Results suggest that some processes are not very relevant for radionuclide transport within the Baltic Sea, for instance the roles of the ice cover and, surprisingly, water stratification. Also, results confirm previous findings concerning multi-model applications.

Modelling of marine radionuclide dispersion in IAEA MODARIA program: Lessons learnt from the Baltic Sea and Fukushima scenarios☆

State-of-the art dispersion models were applied to simulate (137)Cs dispersion from Chernobyl nuclear power plant disaster fallout in the Baltic Sea and from Fukushima Daiichi nuclear plant releases in the Pacific Ocean after the 2011 tsunami. Models were of different nature, from box to full three-dimensional models, and included water/sediment interactions. Agreement between models was very good in the Baltic. In the case of Fukushima, results from models could be considered to be in acceptable agreement only after a model harmonization process consisting of using exactly the same forcing (water circulation and parameters) in all models. It was found that the dynamics of the considered system (magnitude and variability of currents) was essential in obtaining a good agreement between models. The difficulties in developing operative models for decision-making support in these dynamic environments were highlighted. Three stages which should be considered after an emergency, each of them requiring specific modelling approaches, have been defined. They are the emergency, the post-emergency and the long-term phases.

3-D numerical modelling of mud and radionuclide transport in the Chernobyl Cooling Pond and Dnieper - Boog Estuary

The 3-D model THREETOX, that includes modules of hydrodynamics, sediment and pollutant transport, was developed to simulate the radionuclide fate in a deep stratified water body. This paper describes the methodology and results of simulation of the radionuclide transport and fate in the cooling pond of the Chernobyl Nuclear Power Plant and in the Dnieper – Boog Estuary. The analysis of the efficiency of the chosen sediment transport model is based on the use of radionuclides from the Chernobyl accident as tracer.

Internal breather-like wave generation by the second mode solitary wave interaction with a step

The transformation of an internal second mode solitary wave over a bottom step in a computational tank filled with a three-layer stratified fluid was studied. The convex waveforms were generated by a collapse mechanism for stratification with a thin mid-layer. The wave transformation depends on the blocking parameter B which is a ratio of the amplitude of the incident wave to the thickness of the lower water layer over the step. Three regimes of second mode wave transformation over the step are identified. In regime I (2 6. In regime II (0.5 < B < 2) the mode-2 wave is permanently disintegrated, generating a chain of waves of mode-1 ahead of wave of mode-2 and tail of short waves of mode-1 behind the wave. In regime III (B < 0.5) only waves of elevation of mo...

Numerical Simulations of the Nonhydrostatic Transformation of Basin-Scale Internal Gravity Waves and Wave-Enhanced Meromixis in Lakes

The processes of the transformation of basin-scale internal waves are simulated by a numerical three-dimensional nonhydrostatic model that is applied to a sequence of idealized problems, namely the transformation and degeneration of basin-scale internal waves in a rectangular basin, in a basin with a sloping bottom, in a basin with a sill and a cross-section constriction, and finally in a small, elongated lake. The results of the simulations are compared with laboratory experiments and with field observations, when they are available.

The marine kd and water/sediment interaction problem

The behavior of marine distribution coefficients is analyzed with the help of numerical experiments and analytical solutions of equations describing kinetic models for uptake/release of radionuclides. The difficulties in measuring true kd in a marine environment perturbed by an external radionuclide source are highlighted. Differences between suspended matter and bed sediment kd are analyzed. The performances of different kinetic models (1-step/2step; single-layer/multi-layer) are studied in model/model and model/experiment comparisons. Implications for the use of models to assess radioactive contamination after an emergency are given; as well as recommendations when kd data are compiled in order to create a useful database.