Numerical simulation of hydrobiological processes during the spring thermal bar on the basis of the nutrient–phytoplankton–zooplankton model

In this paper, a mathematical model for simulating the hydrodynamic and hydrobiological processes in a temperate water body during the evolution of the spring riverine thermal bar is described. A thermal bar is a narrow zone in a lake where the water, which has a maximum density, sinks from the surface to the bottom. Numerical simulation of the dynamics of plankton ecosystems in case of Kamloops Lake (British Columbia, Canada) is accomplished by using the nutrient–phytoplankton–zooplankton model of Franks et al. (1986). The hydrodynamic model, which includes the Coriolis force due to Earth's rotation, is written in the Boussinesq approximation with the continuity, momentum, energy, and salinity equations. Closure of the simultaneous equation system is performed with a two-parameter Wilcox $k-\omega$ turbulence model and algebraic relations for the coefficients of turbulent diffusion. The convection–diffusion equations are solved by a finite volume method to satisfy the integral conservation laws. The numerical algorithm for the flow and temperature fields' indication is based on a Crank Nicolson difference scheme. In the equations, the convective terms are approximated with the QUICK second-order upstream scheme. The systems of grid equations are solved by the under-relaxation method at each time step. The data from numerical experiments have shown qualitative agreement with results obtained by Holland et al. (2003). Simulations with the variable values of the concentrations of the biological components, coming from the Thompson River, have demonstrated that the high riverine nutrient concentrations do not play a significant role in dynamics of the phytoplankton and zooplankton biomasses; increasing of the phytoplankton in the river leads to a reduction of the nutrient at the location of the thermal bar, and the monotone growth of the riverine zooplankton incoming has a negative impact on the phytoplankton population.