Periodic Reporting for period 2 - CausT (Monte-Carlo Determination of Causation in Turbulence)
Reporting period: 2023-02-01 to 2024-07-31
Description
Removing restrictions in the search for causes of turbulence
Modelling system behaviours based on its previous history has been extremely useful to our understanding of processes from climate change and environmental pollution to pharmaceutical activities or a nanomaterial’s toxic effects. However, these algorithms, much like human beings themselves, can converge towards solutions and ‘suggestions’ that have been influenced by prior knowledge and assumptions. The EU-funded CausT project is taking advantage of today’s state-of-the-art computing power and Monte Carlo simulation methods to turn this process upside down to identify novel turbulent flow structures. Rather than defining or restricting the properties important to turbulent flow structures, scientists will look for flow configurations most sensitive to perturbations and unveil their properties.
Objectives
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.
Removing restrictions in the search for causes of turbulence
Modelling system behaviours based on its previous history has been extremely useful to our understanding of processes from climate change and environmental pollution to pharmaceutical activities or a nanomaterial’s toxic effects. However, these algorithms, much like human beings themselves, can converge towards solutions and ‘suggestions’ that have been influenced by prior knowledge and assumptions. The EU-funded CausT project is taking advantage of today’s state-of-the-art computing power and Monte Carlo simulation methods to turn this process upside down to identify novel turbulent flow structures. Rather than defining or restricting the properties important to turbulent flow structures, scientists will look for flow configurations most sensitive to perturbations and unveil their properties.
Objectives
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.
After half of the project has elapsed, many of the anticipated results have been achieved. While the flows that had been examined three years ago were almost in the category of ‘toys’ (mainly two-dimensional turbulence), we have now analysed at least two realistic cases: three-dimensional isotropic turbulence, a model for most small-scale mixing, and a turbulent channel, essentially an idealised pipe. In both cases, the results were (as initially suspected), fairly unexpected. While the accepted theories in both cases were not ‘wrong’, they turned out to emphasize the wrong flow structures. We can now begin to reconsider some of the old models in terms of the new information.
In addition, besides what we are learning from randomised experiments, it turns out that a lot can be obtained from reconsidering classical flow histories, which can now be done much longer than was possible before, and can be analysed in more detail. Again, the results suggest new experiments on new variables, both in the channel and in isotropic turbulence.
In addition, besides what we are learning from randomised experiments, it turns out that a lot can be obtained from reconsidering classical flow histories, which can now be done much longer than was possible before, and can be analysed in more detail. Again, the results suggest new experiments on new variables, both in the channel and in isotropic turbulence.
An intriguing possibility, deriving from the analyses of the flow histories mentioned above, is that ‘physics-free’ data-driven models can be created for turbulence, much in the way of Large Language Models based in conversation without much attention to grammar. Because the new models are applied to something much simpler that human language, they can be analysed much more thoroughly, including their mathematical underpinning. Although still in its infancy, this line of work may one day be generalised to fields beyond turbulence.