Summer 2013

This summer I have been examining a phenomenological model of the flow in a rotating can, which may be analogous to submesoscale ocean eddy flow. I hope to spend the rest of the summer investigating the effect the overturning rate has on modeled phytoplankton growth through a simple quadratic NPZ model using the rotating can flow. Read on for more of what's been done so far.
My advisor, Larry Pratt, devised a phenomenological model of flow in a can which is rotating about its center and the lid of the can is rotating at a different speed. This model is analytic, laminar, uses the Ekman number (a measure of how much deep the can is compared to the depth to which velocities induced by wind stress matters, usually about 20m), and conforms to continuity (conservation of volume). In the limit of infinite radius, the flow is dynamically consistent- it is a solution to the Navier-Stokes equations. For any radius, the flow of individual water parcels is along a toroidal shape, with upwelling in the center and downwelling toward the sides. One special torus is a single periodic loop at half the depth and half the radius, where water simply flows around a circle; this is a fixed point in the radial and vertical plane. As the Ekman number changes, more tori of this type are found; new appearances are called bifurcations.

 If the rotation of the lid is off-center, some of the tori break up into chaotically mixing regions and some twist, creating folded shapes. The number of 'islands' formed by twisted tori (something like the number of times it is twisted) changes with the Ekman number, initially decreasing as the Ekman number decreases from one but increasing again as the Ekman number diminishes beyond about 1/500. This qualitatively matches results from a full Navier-Stokes simulation.

The unique quality of this model flow is that it is fully 3 dimensional: the vertical velocity and the vertical derivative of the vertical velocity are of first-order importance as compared to the horizontal velocities and their horizontal derivatives. Often oceanographers assume that the vertical velocities (and/or their derivatives) are much smaller than the horizontal, which is true on large spatial and time scales. However, the importance of smaller-scale (eddy) motions is increasingly evident, especially for nutrient cycling. Hopefully I will gain some understanding of how nutrient cycling in 3D oceanographic features could affect productivity (phytoplankton growth).