Turbulent flow over an interactive alternating land-water surface

The alternating land-water surface is a challenging surface to represent accurately in weather and climate models, but it is of great importance for the surface energy balance in polar regions. The complexity of this surface lies in the fact that secondary circulations, which form at the boundary of water and land, interact strongly with the surface energy balance. Due to its large heat capacity, the water temperature adapts slowly to the flow, thus the properties of the atmosphere determine the uptake of energy from the water.

In order to study this complex system in a simpler way, retaining only the most essential physics, we have simplified the full surface energy balance including radiation. We have derived a boundary condition that mimics the full balance and can be formulated as a so-called Robin boundary condition: a linear combination of Dirichlet (fixed temperature) and Neumann (fixed temperature gradient) ones. By spatially varying the coefficients, we are able to express land and water using this boundary condition.

We have done a series of direct numerical simulations in which we generate artificial land-water patterns from noise created from a Gaussian spectrum centered around a dominant wave number. This method creates realistic random patterns, but we are still in control of the length scales.

We show that the system can manifest itself in three regimes: micro-, meso- and macro-scale. In the micro-scale, we find perfect mixing of the near-surface atmosphere that results in identical air properties over water and land. In the meso-scale, secondary circulations alter the heat exchange considerably by advecting air between land and water. In addition, they bring the surface temperature of the land closer to that of the air, thereby modulating the energy loss due to outgoing longwave radiation. In the macro-scale regime, the flow over land and water become independent of each other and only the large scale forcings determine the energy balance.