Taylor–Couette flow of helium II

• Published in: International journal of engineering science 1998-09, Vol.36 (12), p.1481-1492
• Main Author: Swanson, Chris J.
• Format: Article
• Language: English
• Subjects: Boson degeneracy and superfluidity of 4he; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Hydrodynamics in specific geometries, flow in narrow channels; Instability of shear flows; Physics; Quantum fluids and solids; liquid and solid helium
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/S0020-7225(98)00044-5

The wealth of experience and information available about the classical Taylor–Couette system makes it an ideal candidate for studies of the flow of helium II. In particular, the stability of Couette flow of helium II has proven to be an excellent test bed for the equations of motion. As early as 1957 Chandrasekhar and Donnelly began examining the stability of flowing helium II. Progress, however, has been slow due to the quantum ‘two-fluid’ nature of helium II. In helium II the Navier–Stokes equation is transformed into a pair of coupled non-linear equations significantly complicating any analysis. Furthermore, there has been some debate over which terms are to be included in the equations. Recent efforts by Barenghi and Jones have produced a computational linear stability program which is based upon the modern ‘HVBK’ equations. For rotation of the inner cylinder only, they have made predictions of the critical Taylor number as a function of temperature. Data from experiments performed by two different groups corroborate the computed temperature dependence putting the modern equations of motion on a firm footing. In addition to the determination of the onset of instability, studies have been made of flow beyond the instability, of flow between counter-rotating cylinders, and of high Reynolds number flow. With the inner cylinder rotating at a Reynolds number just above the instability, the flow exhibits Taylor rolls. In counter-rotating flow, the appearance of instability has been correctly computed by linear stability analysis. Finally, at high Reynolds number, flow visualization shows Taylor rolls very similar in size to classical rolls.