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-ю 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.
Keywords
планктон,
термобар,
математическая модель,
численный эксперимент,
озеро Камлупс,
plankton,
thermal bar,
mathematical model,
numerical experiment,
Kamloops LakeAuthors
| Tsydenov Bair Olegovich | Tomsk State University | btsydenov@gmail.com |
Всего: 1
References
Forel F.A. La congelation des lacs Suisses et savoyards pendant l'hiver 1879-1880. Lac Leman. L'Echo des Alpes. 1880. No. 3. P. 149-161.
Тихомиров А.И. О термическом баре в Якимварском заливе Ладожского озера // Изв. ВГО. 1959. № 91(5). C. 424-438.
Шерстянкин П.П. Динамика вод Селенгинского мелководья в начале лета по данным распределения оптических характеристик и температуры воды // Элементы гидрометеорологического режима озера Байкал. М.-Л.: Наука, 1964. Т. 5(25). C. 29-37.
Blokhina N.S., Ordanovich A.E., Savel'eva O.S. Model of formation and development of spring thermal bar // Water Resources. 2001. No. 28(2). P. 201-204.
Naumenko M.A., Gyzivaty V.V., Karetnikov S.G., Petrova T.N., Protopopova E.V., Kryuchkov A.M. Natural experiment "Thermal Front in Lake Ladoga, 2010" // Doklady Earth Sciences. 2012. No. 444(1). P. 601-605.
Tsvetova E.A. Mathematical modelling of Lake Baikal hydrodynamics // Hydrobiologia. 1999. No. 407. P. 37-43.
Rodgers G.K. A Note on thermocline development and the thermal bar in Lake Ontario // Symposium of Garda, Int. Assoc. Scientific Hydrology. 1966. No. 1(70). P. 401-405.
Holland P.R., Kay A., Botte V. Numerical modelling of the thermal bar and its ecological consequences in a river-dominated lake // J. Mar. Syst. 2003. No. 43(1-2). P. 61-81.
Farrow D.E. A model for the evolution of the thermal bar system // EJAM. 2013. No. 24(2). P. 161-177.
Parfenova V.V., Shimaraev M.N., Kostornova T.Y., Domysheva У.М., Levin L.A., Dryukker V.V., Zhdanov A.A., Gnatovskii R.Y., Tsekhanovskii V.V., Logacheva N.F. On the vertical distribution of microorganisms in Lake Baikal during spring deep-water renewal // Microbiology. 2000. No. 69. P. 357-363.
Mortimer C.H. Lake hydrodynamics // Mitteilugen Int. Ver. Limnol. 1974. No. 20. P. 124-197.
Kelley D.E. Convection in ice-covered lakes: effects on algal suspension // J. Plankton Res. 1997. No. 19(12). P. 1859-1880.
Botte V. , Kay A. A numerical study of plankton population dynamics in a deep lake during the passage of the Spring thermal bar // J. Mar. Sys. 2000. No. 26(3). P. 367-386.
Franks P.J., Wroblewski, J.S., Flierl G.R. Behavior of a simple plankton model with food-level acclimation by herbivores // Marine Biology. 1986. No. 91. P. 121-129.
Цыденов Б.О., Старченко А.В. Численная модель взаимодействия систем «река - озеро» на примере весеннего термобара в озере Камлупс // Вестник Томского государственного университета. Математика и механика. 2013. № 5(25). С. 102-115.
Wilcox D.C. Reassessment of the scale-determining equation for advanced turbulence models // AIAA Journal. 1988. No. 26(11). P. 1299-1310.
Цыденов Б.О., Старченко А.В. Применение двухпараметрической k-ю-модели турбулентности для исследования явления термобара // Вестник Томского государственного университета. Математика и механика. 2014. № 5(31). C. 104-113.
Chen C.T., Millero F.G. Precise thermodynamic properties for natural waters covering only limnologies range // Limnol. Oceanogr. 1986. No. 31(3). P. 657-662.
Mayzaud P., Poulet S.A. The importance of the time factor in the response of zooplankton to varying concentrations of naturally occurring particulate matter // Limnol. Oceanogr. 1978. No. 23(6). P. 1144-1154.
Tsydenov B.O., Starchenko A.V. To the selection of heat flux parameterization models at the water-air interface for the study of the spring thermal bar in a deep lake // Proc. SPIE 9680, 21st International Symposium Atmospheric and Ocean Optics: Atmospheric Physics, 2015. P. 1-8.
Orlanski I. A simple boundary condition for unbounded hyperbolic flows // J. Comput. Phys. 1976. No. 21(3). P. 251-269.
Patankar S. Numerical heat transfer and fluid flow. CRC Press, 1980. 214 p.
Leonard B. A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation // Computer Methods in Applied Mechanics and Engineering. 1979. No. 19(1). P. 59-98.
Цыденов Б.О., Старченко А.В. Алгоритм SIMPLED согласования полей скорости и давления для численного моделирования термобара в глубоком озере // Седьмая Сибирская конференция по параллельным и высокопроизводительным вычислениям: материалы конференции. Томск: Изд-во Том. ун-та, 2014. C. 109-113.
Цыденов Б.О. Численное моделирование эффекта весеннего термобара в глубоком озере: дис.. канд. физ.-мат. наук. Томск, 2013. 145 с.
