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January 14, 2019

Turbulence Topography

How to visualize the surface of turbulence?

Turbulence Topography

Hill-shading ideas can be applied to turbulence too - but what's the point? In geophysical fluid dynamics flows are usually very close to being in geostrophic balance. Geostrophic balance means the pressure gradient force and the Coriolis force perfectly oppose each other. Furthermore, this means that the flow field can be obtained from the sea surface only. That's also the reason why, if you look at a weather map with high and low pressure systems you can say where the wind comes from! On the northern hemisphere: Wind circulates clockwise around high pressure and anti-clockwise around low pressure.

In a similar sense, if you only look at one component of the velocity (say zonal velocity) and map positive (westward) to light-grey/white and negative (eastward) to dark-grey/black your eyes can infer the high/low pressure structure from it! In the ocean the analogy of pressure is the sea surface height. An ocean high pressure system is a whirl, where in the centre the sea surface is slightly higher (a meter or so) than elsewhere. And vice versa for low pressure. 

Instead of plotting simply the sea surface height with hill-shading, which gives our eyes a 3D-impression of the actual surface, we can also enhance the hill-shading structure by including the ageostrophic flows: The colour indicates the sea surface height, but the shading is derived from the zonal velocity, which is slightly different as a turbulent ocean is not in perfect geostrophic balance. Many small scale features are less evident in sea surface height, but involve quite strong flow speeds. Hill-shading the topography therefore based on zonal velocity enhances turbulent structures and our eyes construct a beautiful surface with little hills and valleys.

A little example: