Renardy, Yuriko; Olagunju, David O. Inertial effect on stability of cone-and-plate flow. II: Non-axisymmetric modes. (English) Zbl 0972.76030 J. Non-Newtonian Fluid Mech. 78, No. 1, 27-45 (1998). [For part I, see the second author, J. Fluid Mech. 343, 317-330 (1997; Zbl 0898.76030).]From the summary: We consider torsional flow of a viscoelastic fluid in a cone-and-plate device. This flow is known to undergo a purely elastic instability when the Deborah number reaches a critical value. Beyond this critical value, a Hopf bifurcation to spiral vortices occurs. In this paper we consider the stability of the flow to non-axisymmetric disturbances when the Reynolds number is non-zero. We examine the effect of inertia on the critical value of the Deborah number at the onset of instability, the winding number of the spiral waves as well as the wave number of the vortices. MSC: 76E05 Parallel shear flows in hydrodynamic stability 76E09 Stability and instability of nonparallel flows in hydrodynamic stability 76A10 Viscoelastic fluids Keywords:critical Deborah numbers; Oldroyd-\(B\) model; torsional flow; viscoelastic fluid; cone-and-plate device; non-axisymmetric disturbances; effect of inertia; winding number; spiral waves; vortices Citations:Zbl 0898.76030 PDFBibTeX XMLCite \textit{Y. Renardy} and \textit{D. O. Olagunju}, J. Non-Newton. Fluid Mech. 78, No. 1, 27--45 (1998; Zbl 0972.76030) Full Text: DOI