# The physics behind a physics scheme

When I joined the Met Office (or, as it was then, The Meteorological Office), I was posted to the boundary layer group. I spent a number of years investigating the atmospheric boundary layer, using data from aircraft and tethered balloons. The justification for the work was to increase our understanding of the boundary layer, which would hopefully lead to improvements in the parametrization of the boundary layer in forecast models. Fast forwarding to the present, I now work on the boundary layer that forms below the surface of the ocean, using high resolution large eddy models, instead of autonomous underwater vehicles (AUVs) and gliders.  The aim of the work remains the same, to develop better parametrizations.

Figure 1. The sea surface in a North Pacific Storm. Photo credit – NOAA

A simple approach to parametrizing the ocean boundary layer is to use parametrizations developed for the cloud-free, atmosphere boundary layer, but upside down (making appropriate changes to account for different densities and heat capacities of air and water). This is a reasonable strategy, but it turns out that there is more to the ocean boundary layer than this, and unsurprisingly the source of the difference between the oceanic and atmospheric boundary layers is the boundary condition.

The possible effects of the surface waves, one of the more striking features of the ocean surface, is an obvious difference between the oceanic and atmospheric boundary layers. Breaking waves, and the interaction between turbulent currents and the Stokes drift of the surface waves (a Lagrangian drift which arises from the non-linearity of the Navier-Stokes equations) has dramatic effect on the properties of the turbulence in the boundary layer.

A more fundamental difference between the oceanic and atmospheric boundary layers is the effect that the surface stress has on the boundary layer flow. In the atmospheric boundary layer momentum is transferred to the surface, so that the surface exerts a drag on the atmosphere. Along with the transport of momentum to the surface, there is also a transport of the mean kinetic energy of the flow (not to be confused with turbulent kinetic energy) from the outer region of the boundary layer towards the surface. This flux of mean kinetic energy maintains the flow near the surface, and supplies the energy needed for the large dissipation rates that occur in the surface layer. The ultimate source of this kinetic energy flux is the work done by the pressure gradient.

In the oceanic boundary layer, the momentum transferred from the atmosphere to the surface acts to generate the mean current. Along with the transfer of momentum into the ocean there is, again, a transfer of mean kinetic energy, but now it is directed away from the surface into the ocean.  This energy flux supports the generation of turbulence at the base of the well-mixed portion of the boundary layer, and turbulent mixing in the stratified layer below. The turbulent mixing in the stratified layer is an important feature of the upper ocean, but is poorly represented in current parametrizations.

To improve parametrizations of the mixing in the stratified layer we need to understand in more detail the process outlined above, and large-eddy simulation can be used to make detailed studies of this and other processes. By understanding the fundamental physics that lies behind the physics scheme we can hopefully improve the parametrization of the surface boundary layer in ocean models.

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