Vinen's latest thoughts on the "bump'' puzzle in decaying He II counterflow turbulence

The pioneering work of William F. Vinen (also known as Joe Vinen) on thermal counterflow turbulence in superfluid helium-4 largely inaugurated the research on quantum turbulence. But despite decades of research on this topic, there are still open questions remaining to be solved. One such question is related to the anomalous increase of the vortex-line density $L(t)$ during the decay of counterflow turbulence, which is often termed as the ``bump’’ on the $L(t)$ curve. In 2016, Vinen and colleagues developed a theoretical model to explain this puzzling phenomenon (JETP Letters, $\mathbf{\text{103}}$, 648-652 (2016)). However, he realized in the last a few years of his life that this theory must be at least inadequate. In remembrance of Joe, we discuss in this paper his latest thoughts on counterflow turbulence and its decay. We also briefly outline our recent experimental and numerical work on this topic.