Volume 29, Issue 2

The problem of ship route optimization is studied in the paper. A functional is introduced so that it includes the terms corresponding to the deviation of the ship trajectory from the preliminary route and to the risk of crossing for the trajectories of the ship and a dynamically moving dangerous object. Theminimization problem of the introduced functional is posed to determine the optimal route of the ship. The problem is studied for the solvability, the existence, and uniqueness conditions are obtained for the solution. Results of numerical experiments are presented.

The joint hydrodynamic model of mesoscale atmospheric processes and transfer of multicomponent gas admixtures and aerosols in the atmosphere is considered taking into account the photochemical transformation, nucleation, condensation/evaporation, and coagulation. Numerical calculations have been performed for given levels of emissions of gas admixtures and aerosols from combustion sources. The paper also describes the mechanisms of formation of organic substances in the atmosphere and their transition into a condensed phase and back, which leads to formation of organic aerosol. The spatio-temporal variability of concentrations of gas admixtures of natural and anthropogenic origin is studied in the case of combustion of biomass from forest and peat fires. Based on the results of numerical calculations, the variability of concentration of an organic aerosol is studied depending on the spectrum of particle sizes.

The paper is focused on the formulation, study, and solution of the problem of oil pollution risk control in the Baltic Sea. The main emphasis is placed on the development of the risk control methodology and the model of oil spill motion is taken the most simple, i.e., the oil spill is considered undeformable and the oil evolution processes are not taken into account. It is assumed that the spill appears at a certain spatial point, but the time of its occurrence is a random variable. The methodology developed here is based on a ‘dual representation’ of the cost functional and on minimization of damage for any possible time of spill appearance. It can be also used in conjunction with more complex models of oil evolution for solution of practical problems.

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The operator of the model, and hence the optimal solution, depend on the parameters which may contain uncertainties. A response function is considered as a functional of the solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the parameters of the model is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The solvability of the non-standard problem is studied. Numerical algorithms for solving the problem are developed. The results are applied for 2D hydraulic and pollution models. Numerical examples on computation of the gradient of the response function are presented.

The problem of mathematical modelling of the large-scale circulation of the Baltic Sea is considered. Marine hydrodynamics equations are written in the spherical coordinate system with a displaced point of the North Pole. The geographical North Pole is shifted to the vicinity of St. Petersburg to increase the spatial resolution of the Gulf of Finland. The free surface, sigma-coordinate primitive equation model under the Boussinesq, continuity, and hydrostatic assumptions is solved numerically. The problem of estimation of the pollution of some ‘protected’ marine sub-area by a passive tracer by means of the introducing an adjoint equation for the sensitivity function is formulated. The sensitivity function specifies the contribution of each basin point to the total pollution of the ‘protected area’.