Relationships between vertical mixing and photoadaptation of phytoplankton: similarity criteria

In their natural environment, phytoplankton are exposed to fluctuations in incident irradiance due to vertical displacements in the water column induced by turbulent fluid motion. Physiological adaptation to these fluctuations results in variation in a number of measurable quantities (e.g. parameters of P-I curves, fluorescence yield, chemical composition), each of which have different time-scales of adaptation. A reaction-diffusion model is analyzed to determine the physical conditions under which a given physiological adaptation would be of ecological importance and thus may show variation in the photoadaptive variable with depth in a mixing layer. Two non-dimensional numbers control the dynamics. KJP2y expresses the ratio of the mixing rate to the photoadaptation rate (K, is the eddy diffusion coefficient, l' is the mixing length, and y is the photoadaptation rate constant for given variable). k,t' is the ratio of the mixing length scale to the optical length scale (k, is the attenuation coefficient for scalar irradiance). When KJP2y is low and k,P is high, photoadaptation proceeds fast enough to create variations in depth in the photoadaptive variable and conversely, when &/P&( is high and k,t' is low, turbulent fluid motion dissipates any depth variation. By observing the variation in depth of several photoadaptive variables, each with a different photoadaptation time-scale, the mixing rate of the water can be estimated. Data from laboratory and field experiments are used to illustrate applications.