How inappropriate to call this planet Earth when it is quite clearly Ocean.

Arthur C. Clark

Just beneath the ocean surface...

Wind, rain, sun, ice, and waves drive turbulence that churns the surface ocean, mediating the exchange of quantities like heat, carbon, and momentum between the atmosphere and ocean interior. Models that approximate the effects of atmospheric forcing on turbulence and turbulent mixing in the upper ocean are critical components in ocean circulation models and coupled climate models.

The basic idea

OceanTurb.jl implements one-dimensional partial differential equations that model these processes –- namely, turbulent mixing, convection, and transport in the ocean surface boundary layer associated with boundary layer currents, surface waves, atmospheric fluxes, and solar radiation. It's purpose is the exploration and development of ocean turbulence schemes intended for use in models of ocean circulation and Earth's climate.


Open julia, press ] at the Julian prompt to enter package manager mode, and type

pkg> add OceanTurb

Use help mode by typing ? to find information about key functions:

help?> time_step!

which produces

time_step!(model; Δt, Nt)

Step model forward in time for Nt steps with step size Δt.


Step forward m by Δt with the backward Euler method.


Modules and models

Solvers for various turbulence models are implemented in submodules of OceanTurb.jl. For example, our simplest module solves the 1D diffusion equation. A diffusion Model is instantiated by writing

using OceanTurb

# 100-grid point model with height 1.0 and diffusivity 0.01.
model = Diffusion.Model(grid = UniformGrid(N=100, L=1.0), parameters = Parameters(K=0.01))

Setting an initial condition is done by writing

c₀(z) = exp(-(z + 0.5)^2 / 0.005)
model.solution.c = c₀

Time stepping a model forward looks like

time_step!(model, Δt=0.01, Nt=100)

This example, and more, can be found in the /examples directory.

In addition to simple diffusion we have models for

  • The K-Profile-Parameterization proposed by Large et al (1994).

  • A 'modular', and therefore generic, $K$-profile parameterization that has multiple models for diffusivity, diffusivity shapes and profiles, nonlocal fluxes including a diagnostic plume model, and mixing depth.

  • A model for stress-driven mixing that uses a prognostic turbulent kinetic energy variable.

  • The Pacanowski-Philander parameterization.


Gregory L. Wagner.