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A Lagrangian Approach to the Role of Turbulence in Biological Physical Interactions
Louis Goodman, and Allan R. Robinson
School for Marine Science and Technology University of Massachusetts Dartmouth
lgoodman@umassd.edu(Abstract received 04/11/2005 for session B)
ABSTRACT
An extension is made of the Robinson NPZ model (Proc. R. Soc., Lond., A, 1999, 455, 1813-1828) of the role of advective upwelling of nutrients and seed plankton into the euphotic zone to include the effect of turbulence. The formalism is based on the usage of the probability density function associated with the Fokker-Plank equations. First and second order moment expressions for both the biological N, P, Z and physical variables are derived. Equivalence of the probability density function with that of the direct solution of the inhomogeneous Fokker-Plank equation for the case of turbulence embedded in an arbitrary advective velocity field is established. Application is made to two simple models - open ocean and coastal upwelling of nutrient and seed plankton into a turbulent euphotic zone. Both the case of a uniform deep reservoir of nutrients and that of a deep nutricline are considered. Inclusion of turbulence in the Robinson advection model of open ocean upwelling model in a linear strain rate field results in a broadening of the phytoplankton vertical profile maximum. The degree of this broadening is shown to be related to a turbulent Reynolds number criteria.
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2005 LAPCOD Meeting, Lerici, Italy, June 13-17, 2005