Small-scale Dynamics in Turbulence

Florencia Falkinhoff

In our daily lives we are surrounded by turbulent flows. Think of the smoke that comes out of your morning cup of coffee, the atmosphere (not just the Earth's. Jupiter's red spot is a prime example of a turbulent atmosphere), water flowing down a river or waterfall, winds, ocean currents, etc., etc... These flows are unstable, irregular, and seemingly random/chaotic. Their velocity varies irregularly in time and space, and they promote the transport and mixing of matter, heat, and momentum.

 

Turbulent flows are multi-scale. That is, they follow a scale hierarchy bounded by the larger scales on the one hand and the smallest - or dissipative - scales on the other. This is illustrated by the famous Richardson cascade, which qualitatively states that there is an energy transfer from the largest to the smallest scales in three-dimensional turbulent flows. This transfer is stopped until the dissipation range is reached and other mechanisms come into play. These flows can typically be described by their energy dissipation rate and their viscosity (e.g., honey is more viscous than water), and we say that a flow is turbulent if its Reynolds number, which is defined in terms of the flow's characteristic velocity, length, and viscosity, is high.

 

The equations that describe fluid dynamics, the Navier-Stokes equations, have been around for 200 years. This means that we know a lot about turbulence. For example, we know that at intermediate scales the energy dissipation rate is constant and that there are several scaling laws that are valid (this comes from the phenomenological theory proposed by A. Kolmogorov in 1941). Nevertheless, little is known about the smallest scales. This is because technology hasn't caught up with theory: our computational power is not sufficient to model turbulent flows down to the smallest scales while maintaining a reasonably high Reynolds number; and experimentally, we have an instrumental resolution that is simply not high enough.

 

With the Göttingen Variable Density Turbulence Tunnel, we are at the forefront of science, and we are able to achieve spatial resolutions that have not yet been achieved experimentally. Having these measurements at the smallest scales can have a big impact for fluid dynamists, as it will provide the first direct evidence of what really happens in the dissipation regime. This also has implications for modeling techniques actively used in fluid dynamics (LES, RANS), and it provides a further understanding of fluid-particle interactions (e.g., cloud droplets typically interact in the dissipation range).