Fluid Dynamics in the 21st Century

"Fluid dynamics" is the field of study that deals with the motion of "fluids," a general term for things that flow, such as gases and liquids. The partial differential equations that describe the motion of fluids, known as the "Navier-Stokes equations," were established in the first half of the 19th century. However, these equations cannot be solved analytically except in very limited cases, such as those covered in the second-year "Fundamentals of Fluid Dynamics" lecture in the Department of Mechanical Engineering. The mathematical proposition of whether a smooth solution even exists is one of the Millennium Prize Problems (with a one-million-dollar prize).

Although the Navier-Stokes equations generally cannot be solved analytically, numerical simulations using computers (i.e., approximate calculations of the Navier-Stokes equations) have become quite feasible over the past half-century. However, performing numerical simulations is not straightforward. This is due to a property of the Navier-Stokes equations called "nonlinearity." Nonlinearity refers to interactions determined by some form of multiplication. For example, when waves of a certain wavelength interact through multiplication, a wave with half the wavelength is generated. When this half-wavelength wave interacts with the original wave, a wave with one-third the wavelength is generated, and so on. This nonlinearity continuously creates higher harmonics. Fluid motion is the same; nonlinearity results in motion with an extremely broad spectrum, ranging from the scale of the system at the large end down to a scale where it would be considered molecular motion at the small end. When performing fluid simulations, to capture this broad spectrum, the space is divided into a fine mesh to perform approximate calculations of the Navier-Stokes equations, and the fineness of this mesh greatly affects the prediction accuracy. The dramatic improvement in weather forecasting accuracy compared to several decades ago is largely due to the development of supercomputers, which has made it possible to perform fluid simulations using finer meshes.

In 21st-century fluid dynamics, I hope we can contribute to society by increasing the reliability of fluid simulations for predicting natural phenomena and designing industrial equipment, as well as by freely controlling flow. Figure 1 shows an example of a numerical simulation conducted in joint research with the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). This research suggests the possibility of suppressing heavy rainfall from linear precipitation bands through dehumidification equivalent to the full operation of all household air conditioners in the region. While we cannot immediately undertake large-scale projects within the budget and time scales of university laboratories, I believe that presenting such innovative flow control ideas using numerical simulation results is crucial as a seed for driving societal change. Furthermore, influenced by the recent third AI boom, the application of machine learning technologies to fluid dynamics is flourishing globally. Our group has also been actively working on this theme since fiscal year 2018 with support from Grants-in-Aid for Scientific Research (KAKENHI). In addition, 21st-century fluid dynamics holds great potential, including the utilization of quantum computing. Please look forward to the future progress of "fluid dynamics," an old yet new field of study.