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Hydrodynamic Instability and Turbulence in Quantum Fluids

Superfluid turbulence consisting of quantized vortices is called quantum turbulence (QT). Quantum turbulence and quantized vortices were discovered in superfluid $^4$He about 50 years ago, but innovation has occurred recently in this field. One is in the field of superfluid helium. Statistical quantities such as energy spectra and probability distribution function of the velocity field have been accessible both experimentally and numerically. Visualization technique has developed and succeeded in the direct visualization of quantized vortices. The other innovation is in the field of atomic Bose-Einstein condensation. The modern optical technique has enabled us to control and visualize directly the condensate and quantized vortices. Various kinds of hydrodynamic instability have been revealed. Even QT is realized experimentally. This article describes such recent developments as well as the motivation of studying QT.