From Stirring to Mixing in a Stratified Ocean

Over fifty years ago, Carl Eckart described the sequence of processes as a passive scalar is stirred and mixed in a turbulent flow (Eckart, 1948).At first, during the stirring phase, the variance of the scalar gradient is greatly increased, but later, during the mixing phase, the gradients become sufficiently sharp that molecular diffusion becomes important and the gradient variance rapidly decreases.The process is of great practical importance in many engineering situations as well as being familiar from adding cream to coffee.The interplay of stirring and mixing is also important in the ocean for temperature, salinity, chlorophyll and other naturally occurring tracers as well as for introduced material.The situation is complicated by the numerous physical processes that can cause stirring and by the interplay of processes that act along isopycnals (surfaces of constant mean density, where "mean" requires careful definition) with diapycnal processes acting across the density surfaces.The Twelfth 'Aha Huliko'a Hawaiian Winter Workshop was convened from 15 to 19 January 2001 to review this theme, with the support of the Office of Naval Research, the Joint Institute for Marine and Atmospheric Research, and the participation of 25 invited speakers.The general topics included in presentations and discussions were (1) mesoscale eddy parameterization, (2) general approaches to stirring, including the application of ideas from dynamical systems theory, (3) inertial instability, submesoscale motions and vortical motions, (4) the interplay of isopycnal and diapycnal processes, (5) processes in the surface mixed layer, (6) the stirring and mixing of nonconservative, particularly biological, tracers, (7) mixing efficiency, i.e., the fraction of energy lost from the mean flow which produces a vertical buoyancy flux, and (8) differential mixing of heat and salt in doubly-stable environments as well as those which permit double diffusion.Before summarizing the discussions on these topics, we first review the general approach to parameterizing unresolved processes.