Studies on Quantum Turbulence with Vinen

In my research career in the field of quantum turbulence, I have been encouraged by Vinen. In this article, I review my works motivated by him and my joint collaborations with him. Vinen encouraged me in studies on quantum turbulence at zero temperature, Kolmogorov spectrum of a vortex tangle without mutual friction, and fully coupled dynamics of quantized vortices and normal fluid. Joint works include studies on diffusion of a vortex tangle, Kelvin wave cascade, quantum turbulence created by an oscillating object, and coupled dynamics of tracer particles and quantized vortices.