Fractal Dissipation of Energy in Turbulent Flows: fluid dynamics underlies wide range of physical ph

The science of modeling and describing the behavior of fluids, referred to as fluid dynamics, is surprisingly pivotal to understanding some of the most elementary constituents and processes underlying physical phenomena. Fluid dynamics can tell you everything from how a plane or bird flies through the air to how quantum vortexes form in superconductors, Bose-Einstein condensates and superfluids. The latter example suggests that fluid dynamics may even be essential to understanding quantum mechanics, and indeed hydrodynamic quantum analogs have demonstrated all the seemingly weird properties of quantum mechanics in purely classical macroscopic systems.

As such, fluid dynamics is developing as a key link in the unification of physics, as we have seen it can describe the ultra-small—codified in de Broglie-Bohm pilot wave theory, or Bohmian mechanics—but it is also essential to describing behavior of the ultra-large, as the substance of spacetime itself is a kind of ætheric superfluid, with torque and Coriolis forces included in Einstein’s geometrization of spacetime explaining not only gravity but the source of spin and modified gravitational interaction. The fluid description of spacetime, and hence gravity—one regime of modified gravitational interaction at the largest scales —in part explains the seemingly anomalous behavior of galaxies’ rotation curves, normally attributed to dark matter; the energy driving the seeming expansion of space; and at the smallest scales explains the nuclear coupling force via a quantum gravitational solution (normally attributed to the so-called Strong Force of quantum chromodynamics).

This list is by no means comprehensive, as we can only touch on a number of the areas where fluid dynamics is essential to explaining physical phenomena. However, the overall picture that begins to emerge is that understanding the fluid behavior is no trivial endeavor.

David Castelvecchi reports for Nature on how a team of aeronautical engineers are working to solve the long-standing challenge of explaining the movement of energy in turbulent fluids:

Mysteries of turbulence unravelled (as reported in Nature)

“When I meet God, I’m going to ask him two questions: why relativity? And why turbulence? I really believe he’ll have an answer for the first.”

This probably apocryphal quote, attributed to physicist Werner Heisenberg, captures the way many scientists feel about turbulence: a phenomenon in which the orderly flow of a fluid (a liquid or a gas) disintegrates into seemingly unpredictable swirls, such as when a river flows round a rock, or when milk mixes with coffee.

But researchers are making progress on understanding the physics of turbulence. In a paper published on 17 August in Science[1], simulations by a Spanish team of aeronautical engineers help to solve a long-standing puzzle over how energy moves around in turbulent fluids. And in the past 12 months, mathematicians have made progress in explaining how turbulence helps to dissipate the energy of fluids, causing them to stop moving.

An improved understanding of turbulence and its implications for energy transfer could have big pay-offs for scientists — from astrophysicists who want to model how gas flows in galaxy clusters to climatologists simulating how ocean currents carry heat.

An issue of scale

In theory, the Navier–Stokes equations, developed almost 200 years ago, describe the physics of fluids well. But these equations are devilishly hard to solve. So engineers and scientists usually come up with simplified theoretical models or resort to numerical simulations when they want to predict fluid flow. This approach has its limits: modelling turbulence bogs down even supercomputers.

Now, aeronautical engineer José Cardesa of the Polytechnic University of Madrid and his collaborators say that they have been able to fully simulate for the first time how turbulence spreads kinetic energy across swirls of smaller and smaller scales. For water held in a large tank, for instance, their computer simulations could track how energy is transferred over about a minute from a 1-metre-diameter swirl into smaller eddies down to the 12-centimetre scale.

Their results validate a theory formulated by Russian mathematical physicist Andrei Kolmogorov in the early 1940s. Among its consequences is that turbulence occurs in a cascade: large eddies break down into smaller ones, which in turn split into even smaller ones, in a fractal fashion. In this model, the transfer of kinetic energy occurs rather like a baton being passed around runners in a relay race, Cardesa says, but one in which the runners get progressively smaller and more numerous.

Kolmogorov’s picture implies that energy spreads from large swirls to smaller eddies nearby, rather than spreading to farther distances. That has some support from mathematical theorems, but Cardesa’s team has confirmed it, says Gregory Eyink, a theoretical physicist at Johns Hopkins University in Baltimore, Maryland. Cardesa says that understanding these dynamics could help to improve predictions of energy flow in phenomena such as aerodynamic drag.


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