Turbulent flow: deciphering fluid dynamics

5 December 2016

In her career as a theoretical physicist, Dr Emily Ching (2007 Croucher Senior Research Fellow) has explored fundamental questions in physics that have garnered her international recognition and accolade. She received an Achievement in Asia Award from the Overseas Chinese Physics Association in 1999 for her research on complex fluctuations in fluid turbulence, and in 2004 and 2005, was inducted as a Fellow of the UK Institute of Physics and the American Physical Society respectively.

Ching’s current research interests lie in polymer effects and boundary layer profiles in turbulent Rayleigh-Bénard convection as well as the reconstruction of networks from dynamics. She traces her interest in science back to her childhood love for puzzles, stating that though these research focuses may not be interrelated, they fall under a category she refers to as complex systems. They are all challenging problems, she says, and thus prove to be interesting puzzles for her mind to solve.

“I joke with my students that we are using a so-called ‘brain assisted method’ when carrying out research. We are really inventing our own techniques and methods, anything we can think up and use in order to help solve the problems that lie in front of us,” says Ching.

Fluid turbulence and the addition of polymers

Fluid turbulence refers to the state of fluid motion when the speed of the fluid is large. In this state, there are fluctuations in the velocity and pressure fields. Despite extensive research, turbulence is still considered to be one of the most important unsolved problems in classical physics. A core component contributing to the difficulty in deciphering all the nuances of turbulence lies in the mathematical equations involved being non-linear partial differential equations, for which there is no proof yet of the existence of solutions, or if they are unique.

Past experiments have proven that the addition of polymers can reduce the drag of turbulent fluid flow drastically, but the reasons for this effect have yet to be uncovered.

Says Ching, “The reduction of drag by polymers has already been made use of in application. For example, polymers are injected into the oil within the Trans Alaska Pipeline System to reduce the drag, and thus reduce the energy expended in the oil transfer process. So, it is common knowledge that polymers reduce the drag or increase the mass transport. It is likely that they can also affect other transport properties of turbulent fluid flow.”

Her research, using turbulent Rayleigh-Bénard convection, has been focused on understanding the effects of polymers on the transfer of heat.

Polymer effect on heat transfer in turbulent convection

If the temperature difference between the top and the bottom of a container of fluid is large enough, the fluid within would be set into motion and cause a transfer of heat by convection. Ching and her team sought to understand the effect of polymers on such a Rayleigh-Bénard system and how heat transfer would be modified. By carrying out an analysis of laminar boundary layer flow with polymers, which in this case are modelled by two masses joined by a nonlinear spring, the team was able to and narrow down the effect of polymers to an effective viscosity in the equation. This effective viscosity is position dependent, and is a result of the stretching of the polymers, which takes place when the two masses of a polymer chain experience different velocity at the two points.

I don’t think about a problem as a physics problem or a math problem or a biology problem. Rather, I more think of it as an interesting problem for which I can use whatever tools I have to get the answer.

Serving as the basis for the next step in her research, Ching took this line of mathematical analysis and the viscosity profiles derived from computer simulations to study the polymers’ effect on heat transfer when the convective motion is turbulent. In this scenario, polymers undergo a larger degree of stretching compared to the laminar state, and stretch beyond the region close to the plate boundaries, which is additionally enabled by the turbulent flow in the environment. Computer simulations reveal that there is an enhancement in heat transfer when the stretching of the polymers takes place further away from the boundary plate.

“Although we were unable to directly calculate the effective viscosity profile, we were able to get it from the computer simulations and use it as an input to insert back into the theoretical framework. Once placed in the framework, we could do the calculations and explain the numerical results, and indeed understand the enhancement of heat transfer within the framework, with the help of the computer data,” says Ching.

Applying expertise to a new scientific avenue

Several years ago, Ching began to apply her expertise in extracting information from complicated data sets to an entirely new field of science. She found parallels between physics and biology in that many systems of interest consist of many interacting parts and are networks of many nodes with links among each other. She says that to understand the overall behaviour of such systems, it is not enough to know detailed information of each individual component, one must also be aware of the interactions that take place amongst them.

“In the language of networks, we do not know the graphs, or how the nodes, which are the individual components, connect to one another, but we do know the dynamics and activity of each node. These things can all be measured. The challenge arises when we are meant to use these measurements to gain information about the connectivity of the network. Mathematically, this is known as an inverse problem – I give you the end result and ask for the structure,” she says.

Network reconstruction

While her first foray into biological research was analysing data on heartbeat dynamics to determine state of health, Ching’s true curiosity lies in decoding the brain. More and more connections or synapses are formed as a neuronal network grows in time. This is believed to lead to an increase in neuronal activity causing a bursting event, which is when different neurons start to spike at the same time, even without a particular stimulus. These events are believed to be essential in different functions of the brain, i.e. memory, learning process. The question of interest is how to identify these links or connections that are being formed from the recorded dynamics of the neurons.

Ching says, “My collaborators have already started working on this line of questioning and had released a paper using the method of correlation to decipher the data that they had measured. Correlation is a common method used in the field to infer links but it is known to have shortcomings because correlation does not automatically mean you have causation.”

Another strategy used in this research in the past was to study the presence of noise within the system, which in fact induces a relation between the dynamics of the nodes and the network structure. Systems with no noise can be synchronised perfectly, and the information of the network structure would be lost as one cannot record any unusual information emerging from the activity, and thus cannot determine any connections. The presence of noise leads to fluctuations in the system’s dynamics, which will be the source of information from which to interpret the network structure.

While Ching and her collaborators pursued the essential theory of the latter method, which is that information can be derived from the mathematical relation between connectivity and quantities measured, this particular method is only applicable to bidirectional networks with unweighted couplings, where the interactions are mutual and the strength of couplings is always equal. However, in many biological systems, and in the case of neurons, networks are more commonly directed, or uni-directional and the strength of the couplings may differ from node to node.

With her team, she has devised a method that can reconstruct directed networks. The method is based on a mathematical relation between the network structure and the correlation of the measurements at different times. Using computer simulations to generate dynamics for different networks, they show that their method can reach a fairly accurate reconstruction of the networks.

“We are developing this method to apply to experimental data of the neuronal networks taken by our collaborators. The constraint is that we need time series measurements, as that serves as a key basis for the method. So while I am looking for other possible biological systems to use the method, we are limited by the time series measurements available for such systems,” she says.

Interdisciplinary nature 

While the problem of reconstructing systemic networks is challenging in itself, Ching explains that this is further intensified by the interdisciplinary nature of the research. Getting accustomed to a new set of terminology and languages, in addition to the vast amounts of knowledge that needs to be acquired and understood before pursuing research in a field of science beyond that of your own personal training and expertise, is no small task. According to her, such a leap can be more easily taken when collaborators on both spectrums can fill in the gaps of knowledge and guide each other long.

Ching says, “If I don’t personally understand the details of a problem, I would ask an expert to tell me if I am correct or not, and guide me forward. Usually, I don’t think about a problem as a physics problem or a math problem or a biology problem. Rather, I more think of it as an interesting problem for which I can use whatever tools I have to get the answer. Every advance in fundamental science is useful.”

Professor Emily S. C. Ching is currently a Professor in the Department of Physics at the Chinese University of Hong Kong, which she joined in 1995. She completed her MPhil in the Chinese University of Hong Kong as well, and completed her PhD in the University of Chicago, USA. Her MPhil thesis on light refraction in fluids is considered to a standard work of reference. In her career as a research scientist, her work has garnered significant international recognition, and she was awarded the Achievement in Asia Award from the Overseas Chinese Physics Association in 1999 for her research on fluid turbulence. She was elected Fellow of the UK Institute of Physics and the American Physical Society in 2004 and 2005 respectively. She serves in the Editorial board of various journals including the Journal of Turbulence. Ching was awarded a Croucher Senior Research Fellowship in 2007. 

To view Prof Ching’s personal Croucher profile, please click here