Patterns and transport in axisymmetric compressible taylor-couette flow via direct numerical simulations

Abstract

The story of flow between two concentric differentially rotating cylinders started its journey during the twilight years of seventeenth century when Sir Isaac Newton hypothesized the definition of modern day Newtonian fluid. In the Book 2, Section 9, Proposition 51, Corollary 2 of Principia Mathematica, Newton states - “If a fluid be contained in a cylindric vessel of an infinite length, and contain another cylinder within, and both the cylinders revolve about one common axis, and the times of their revolutions be as their semidiameters, and every part of the fluid continues in its motion, the periodic times of the several parts will be as the distances from the axis of the cylinders”. After a period of one hundred sixty one years, George Gabriel Stokes (1848) solved for the fluid flow velocity between two rotating coaxial cylinders but expressed his concerns about the boundary conditions of the flow (no-slip condition at the wall and free surface). In the 1880s, Henry Reginald Arnulph Mallock and Maurice Marie Alfred Couette independently determined the viscosity of water in an apparatus consisting of two rotating concentric cylinders. In the year of 1890, the thesis written by Couette illustrated a detailed study of measurement of viscosity of water using a pair of cylinders with the stationary inner cylinder and a rotating outer cylinder. The design of viscometer by Couette (1890) was inspired from the works of Austrian theoretical meteorologist, Max Margules and only the outer cylinder could be rotated. However the apparatus designed by Mallock (1889) operated with more than two different arrangements of the cylinders. This work of Mallock (1889) was communicated by Lord Rayleigh on 30th of November 1888, in response to which Lord Kelvin wrote a letter to Lord Rayleigh, dated 10th July 1895 -