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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 1, issue 1
Nonlin. Processes Geophys., 1, 3–11, 1994
https://doi.org/10.5194/npg-1-3-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Including papers presented at the AGU Chapman Conference on...

Nonlin. Processes Geophys., 1, 3–11, 1994
https://doi.org/10.5194/npg-1-3-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  31 Mar 1994

31 Mar 1994

Nonequilibrium plankton community structures in an ecohydrodynamic model system

H. Malchow1 and N. Shigesada2 H. Malchow and N. Shigesada
  • 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

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.

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