Time and space scales of vertical mixing and advection of phytoplankton in the upper ocean

The dependence of phytoplankton photosynthesis on light intensity may be altered by the range and frequency of variations in light intensity recently experienced by the organisms. A major source of the fluctuations in light intensity experienced by phytoplankton in the upper ocean is vertical motion. We estimate time and space scales for vertical displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes. In the surface layer, depending on windspeed, current shear and stratification, we find that time scales for cycling of phytoplankton by turbulent eddies and mixing vary from about 0.5 h to hundreds of hours for vertical displacements of the order of 10 m. In the seasonal thermocline, turbulent diffusive time scales for displacements as small as several meters are weeks to months, whereas similar displacements by internal waves occur over periods of several minutes to several hours, according to the strength of the density stratification, and are then dominant. Langmuir cells seem to scale as the large turbulent eddies and need not be treated separately, and double diffusive processes seem to be of minor importance. The formulation used here of a vertical turbulent diffusion coefficient K z as a function of observable quantities—ε the rate of dissipation of turbulent kinetic energy, arid N the local buoyancy frequency—should also be useful for estimating vertical fluxes of nutrients. In addition, this formulation is reversible in time and can be used to estimate the recent depth and light history of phytoplankton taken from the upper ocean.