Monte-Carlo Determination of Causation in Turbulence

Simulations have driven many recent scientific advances.

In the case of the physics of fluid turbulence, they have involved some of the most expensive computations at any time, but faster computers now permit meaningful simulations to run in minutes in a modest machine.

This proposal centres on exploring the role of simulations in this limit of ‘zero’ computing cost, and on the analysis of the resulting data.

What ‘free’ simulations allow is ‘Monte-Carlo’ research, in which ideas are ‘randomly’ tested and only evaluated afterwards, in the hope that some of them be fruitful.

Their main advantage is to alleviate ‘paradigm lock’, in which radically new ideas are unlikely to get tested and knowledge gets stuck in a local optimum.

But ensembles of cheap simulations also provide causal information about what the effect of a particular ‘random’ initial condition is.

The main result in turbulence is expected to be the identification of novel flow structures, with definitions grounded in the underlying physics.

Up to now, structures have mostly been described in terms of properties assumed to be important (e.g. intensity), with their effect on the flow being tested a-posteriori, but Monte-Carlo search allows us to reverse the process, identifying structures from their effects.

In particular, we will search for flow configurations that are ‘causally most sensitive’ to perturbations, in the sense that the perturbations are most effective when applied to them. Both the probing perturbations and the receptive flow states constitute ‘causes’.

The implied definition of causality only applies over times of the order of a turnover, and is connected with control: changing the cause modifies the effect, with obvious applications.

The flows examined will mainly be wall-bounded ones, including effects such as rotation and rheology, but we will also examine the general inverse energy and momentum cascades towards larger scales. Some preliminary experiments are described.