Horst Malchow1, Nanako Shigesada2
1Dept. of Water Modelling & Wadden Sea Research, Inst. of Physics, GKSS Research Centre, Max-Planck-Strasse, D-21502 Geesthacht, Germany
2Dept. of Information and Computer Sciences, Nara Women's University, Kita-Uoya Nisihimachi, Nara 630, Japan
Tóm tắt
Abstract. Due to the local and global impacts of algae blooms and patchiness on water quality, carbon cycling and climate, models of plankton dynamics are of current interest. In this paper, the temporal and spatial patterns in natural plankton communities are interpreted as transient and stationary nonequilibrium solutions of dynamical nonlinear interaction-diffusion-advection systems. A simple model of phytoplankton-zooplankton dynamics (Scheffer, 1991) is presented in space and time. After summarizing the local properties as multiple stability and oscillations, the emergence of spatial and spatio- temporal patterns is considered, accounting also for diffusion and weak advection. In order to study the emergence and stability of these structures under hydrodynamic forcing, the interaction- diffusion-advection model is coupled to the hydrodynamic equations. It is shown, that the formation of nonequilibrium spatio-temporal density patterns due to the interplay of the deterministic nonlinear biological interactions and physical processes is a rare occurrence in rapidly flowing waters. The two-timing perturbation technique is applied to problems with very rapid single-directed steady flows. A channel under tidal forcing serves as and example for a system with a relatively high detention time of matter. Generally, due to the different time and length scales of planktic interactions, diffusion and transport, initial nonequilibrium plankton patches are simply moved through the system unless the strong hydrodynamic forces do not destroy them before.
