Authors: Ori Saporta-Katz, Edriss S. Titi, Hezi Gildor and Vered Rom-Kedar
We propose a phenomenological model for studying the effects of a general prescribed unsteady 3D flow on a density-driven velocity component through temperature and salinity transport. The model contains an incompressible velocity that couples two advection-diffusion equations for the two tracers. Instead of solving the Navier-Stokes equations for the velocity, we consider a prescribed flow, composed of several spatially predetermined modes. One of the modes models the density-driven flow (e.g. the AMOC), and its strength is determined dynamically by averaged density differences. The other modes are pre-determined by either kinematic models, observations, or simulations. The result is a hybrid kinematic-dynamic model, formulated as a non-linear, weakly coupled system of two non-local PDEs, which, as we prove, is well posed. In one limit the model coincides with the traditional dynamical Stommel Box model, and admits its bi-stable regime. In another limit it coincides with the traditional kinematic model of uncoupled advection-diffusion equations, with the underlying chaotic advection mechanism of mixing. We suggest that this model may be utilized to study spatially dependent feedback processes in the ocean.
Journal of Nonlinear Science 33 (1), 1, 2023.