New approach to reynolds similitude in superfluids could reveal quantum viscosity

Fluids, ubiquitous in nature, exhibit a fascinating characteristic known as viscosity, defining their response to external forces. Whether it’s the gentle flow of Earth’s atmosphere or the coursing of blood through veins, viscosity dictates how a fluid deforms upon encountering another substance. In a tranquil state known as laminar flow, higher viscosity ensures smooth movement. Conversely, a decrease in viscosity triggers a shift towards turbulent flow, characterized by chaotic motion.

Central to understanding fluid behavior is the Reynolds number, a measure of the degree of laminar or turbulent flow, inversely linked to viscosity. The Reynolds law of dynamic similarity, or Reynolds similitude, posits that fluids flowing around similar structures with different length scales are hydrodynamically identical if they share the same Reynolds number.

Traditionally, quantum superfluids have stood as an exception to Reynolds similitude due to their presumed lack of viscosity. However, a novel theory by Dr. Hiromitsu Takeuchi from the Nambu Yoichiro Institute of Theoretical and Experimental Physics challenges this notion. Dr. Takeuchi proposes a method to explore Reynolds similitude in superfluids, potentially unveiling the existence of quantum viscosity.

“Superfluids have long defied Reynolds similitude,” Dr. Takeuchi remarked. “Establishing similitude in superfluids marks a pivotal step towards unifying classical and quantum hydrodynamics.”

Quantum superfluids, despite lacking viscosity, exhibit turbulence, presenting a paradox: How can turbulence occur without viscosity-induced dissipation? Dr. Takeuchi’s proposed solution lies in examining how a solid sphere descends into a superfluid. By correlating the sphere’s terminal velocity with the resistance encountered from the fluid, an analog for Reynolds similitude emerges, revealing the presence of quantum viscosity.

“This study delves into the theoretical intricacies of quantum turbulence in superfluids, demonstrating the potential verification of Reynolds similitude through the terminal velocity of a falling object,” Dr. Takeuchi explained. “If confirmed, this suggests the existence of quantum viscosity even in pure superfluids at absolute zero. Experimental verification holds great promise for advancing our understanding of these phenomena.”

Source: Osaka Metropolitan University

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