Advanced multiscale fluid science

Multiscale Fluid Science at the Forefront
―Uncovering the Essence of Flow Across Scientific Frontiers―

When I was learning the piano as a child, I often heard the phrase, “The foundation of music is the piano.” I now interpret this to mean that the piano’s wide range, tonal diversity, and clarity of musical structure offer insights into music that transcend any specific instrument. By analogy, fluid dynamics can be regarded as the “piano” of STEAM—Science, Technology, Engineering, Arts, and Mathematics. From the standpoint of mathematical sciences, exploring problems across STEAM often reveals underlying structures and mechanisms that converge on fluid dynamics. In fundamental science, this includes phenomena like superfluid helium near absolute zero; in applied contexts, it encompasses river flow, traffic congestion, air travel, and collective human behavior—all nonlinear phenomena. Fluid dynamics is also crucial in CG art powered by physics engines.

One of the oldest scientific disciplines, fluid dynamics dates back to ancient irrigation and flood control efforts. Archimedes laid the foundation of hydrostatics with his principle of buoyancy. During the Renaissance, Leonard o da Vinci’s vortex sketches foreshadowed modern turbulence studies. In the 18th century, Daniel Bernoulli’s Hydrodynamica aimed to systematize ideal fluid theory and hinted at kinetic concepts by linking gas pressure to particle motion. The 19th century introduction of the Navier–Stokes equations accelerated advances in vortex theory, turbulence, and boundary layers.

Historically, fluid dynamics has balanced two perspectives: an ontological view that treats fluids as atomistic systems, and a phenomenological one based on observable phenomena. The philosophical divide between Ludwig Boltzmann and Ernst Mach exemplifies this tension. Maxwell and Boltzmann advanced kinetic theory into statistical mechanics. In response to Hi lbert’s sixth problem in 1900—"the axiomatization of physics”—Chapman and Enskog derived macroscopic fluid equations from kinetic theory. Knudsen later defined the limits of fluid dynamics with his dimensionless number. Kolmogorov’s K41 theory described turbulence as a multiscale energy cascade, while his K62 theory foreshadowed multifractal analysis.

Hilbert’s sixth problem can be seen as asking how microscopic d ynamics manifest at macroscopic scales—a question still unanswered. This is especially true in exotic fluids like superfluid helium, where quantum effects emerge on macroscopic levels. Multiscale characteristics also appear in functional fluids, such as ferrofluids. Unraveling these mechanisms promises not only fundamental scientific advances but also progress in applications like chemical engineering.

Advanced multiscale fluid science reflects the long legacy of the field while addressing diverse challenges across STEAM. It is an ambitious academic pursuit aimed at tackling the “unfinished homework” posed at the dawn of the 20th century.

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• A free-surface simulation involving fluid-structure interaction with a complex-shaped structure

Member

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• • Lecturer
    Satori TSUZUKI
  Research Area: Fluid dynamics

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