A dynamic-kinematic 3D model for density-driven ocean circulation flows: Construction, global well-posedness and dynamics

TL;DR

This paper introduces a new 3D model for density-driven ocean flows that combines observational data with predefined flow modes, ensuring well-posedness and capturing complex oceanic dynamics.

Contribution

It develops a modular, nonlinear PDE framework that models density-driven flows coupled with temperature and salinity, and proves its mathematical well-posedness.

Findings

Model reproduces North Atlantic dynamics

Recovers simplified oceanic box model in a limit

Links to chaotic advection models

Abstract

Differential buoyancy surface sources in the ocean may induce a density-driven flow that joins faster flow components to create a multi-scale, 3D flow. Potential temperature and salinity are active tracers that determine the ocean's potential density: their distribution strongly affects the density-driven component while the overall flow affects their distribution. We present a robust framework that allows one to study the effects of a general 3D flow on a density-driven velocity component, by constructing a modular observation-based 3D model of intermediate complexity. The model contains an incompressible velocity that couples two advection-diffusion equations, for temperature and salinity. Instead of solving the Navier-Stokes equations for the velocity, we consider a flow composed of several temporally separated, spatially predetermined modes. One of these modes models the density-driven flow: its spatial form describes the density-driven flow structure and its strength is determined dynamically by average density differences. The other modes are completely predetermined, consisting of any incompressible, possibly unsteady, 3D flow, e.g. as determined by kinematic models, observations, or simulations. The model is a non-linear, weakly coupled system of two non-local PDEs. We prove its well-posedness in the sense of Hadamard, and obtain rigorous bounds regarding analytical solutions. The model's relevance to oceanic systems is demonstrated by tuning the model to mimic the North Atlantic ocean's dynamics. In one limit the model recovers a simplified oceanic box model and in another limit a kinematic model of oceanic chaotic advection, suggesting it can be utilized to study spatially dependent feedback processes in the ocean.