The Temperature Dependent Drag Crisis on a Sphere in Flowing Helium II

Abstract

In a previous paper, we reported observing a drag crisis on a sphere in flowing He I and He II. Data in He II suggested a possible temperature dependence to the critical Reynolds number, as well as the magnitude of the crisis. In this paper, we explore temperature dependence more completely. Dynamical similarity arguments, which lead to Reynolds number scaling in the case of the Navier-Stokes equations, are applied to the two-fluid equations. The result is a modified Reynolds number involving the factor 1-β, where β ≡ ρs/ρ. The ramifications of this argument, together with other possible scaling relationships, are discussed. Data and critical Reynolds numbers are plotted for several temperatures between 1.6 K and 2.0 K. Results appear to agree well with the proposed scaling for He II.