Navier-Stokes and tracer conservation equations
Oceananigans.jl solves the incompressible Navier-Stokes equations and an arbitrary number of tracer conservation equations. Physics associated with individual terms in the momentum and tracer conservation equations –- the background rotation rate of the equation's reference frame, gravitational effects associated with buoyant tracers under the Boussinesq approximation[1], generalized stresses and tracer fluxes associated with viscous and diffusive physics, and arbitrary "forcing functions" –- are determined by the whims of the user.
- 1Named after Boussinesq (1903) although used earlier by Oberbeck (1879), the Boussinesq approximation neglects density differences in the momentum equation except when associated with the gravitational term. It is an accurate approximation for many flows, and especially so for oceanic flows where density differences are very small. See Vallis (2017, section 2.4) for an oceanographic introduction to the Boussinesq equations and Vallis (2017, Section 2.A) for an asymptotic derivation. See Kundu (2015, Section 4.9) for an engineering introduction.