STIRRING VEGETABLE SOUP Adrian Martin Warwick Turbulence Symposium: Workshop March 2006 "Environmental Turbulence from Clouds through the Ocean"

Coccolithopore Emiliania huxleyi

100 Gt C y -1 60% land, 40% water

Scales of Interest Mesoscale and sub-mesoscale 1km-500km 1d-few months Rules of thumb: eddy size ~20-150km rotation period ~1-4d max.current speed ~1m/s lifetime ~weeks-months phytoplankton doubling time ~1d

Horizontal velocityVertical velocity Data from PRIME cruise, June 1996

Data from Dundee Satellite Receiving Station Processed by Steve Groom, RSDAS, PML

Given that phytoplankton and physical forcing of phytoplankton are `patchy’… What effect do stirring and mixing have on production? Suppose that upwelling and ambient regions are isolated. How sensitive is the difference to A = upwelling fraction of region? I = ratio of upward nitrate fluxes? m = rate of horizontal mixing? Is the total production for the area more or less than if the two regions were being mixed?

Parameter values A0.025, 0.05, 0.12, 0.25 I s~0.006d -1 background s~1.6d -1 upwelling m0-10d -1

139% increase in total primary production Martin et al., Global Biogeochemical Cycles, 2002

208% increase in total primary production Martin et al., Global Biogeochemical Cycles, 2002

C. Pasquero, Geophysical Research Letters, 32, L17603, 2005

Conclusions Turbulence strongly affects plankton ecology and plays a major role in controlling regional primary production at the mesoscale. Lateral turbulent stirring and mixing is just as important as the vertical supply of nutrients. Correlations between coherent structures and upwelling regions can exert a very strong influence on production. Use of standard effective diffusivities may result in significant overestimates of production Global Carbon Cycle Models may incur significant errors in ignoring the effect of mesoscale turbulence on biology.

May “[Encountered coloured water] extending about two miles from North to South and about six to eight hundred fathoms from West to East. The colour of the water was yellow.” Don Antonio de Ulloa ( )

Approach two-box model examine sensitivity to fundamental parameters of system Twin-pronged turbulence model explore the effect of mixing in more detail in particular the influence of coherent structures Same biological model in each case.

Ecosystem Model Oschlies and Garcon, 1999

Two Box Model

Base value (I=1,m=0): 0.076mMol N /m 3 /d

Use same biological model Range of spatial distributions for forcing, with A constant Two-box model: Advantage: Clearest demonstration of sensitivity to m, I and A Disadvantage: Very crude representation of mixing Motivation for turbulence model: Explicit modelling of mixing due to mesoscale turbulence Sensitivity to distribution of upwelling Role of coherent structures

Forced barotropic quasigeostrophic turbulence Dq/Dt=F+D 1  8 q+D 2  -2 q q=  2  -  /R 2 +f R=1/5 Pseudospectral for vorticity Finite difference for tracers Domain size:512km Resolution: 2km Typ.eddy size:40-80km Typ.eddy vel.:0.6m/s

29% increase in total primary production A