Experiments on the stability of two types of spiral flow

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

“…In early experiments by Snyder [21,22] or Takeuchi and Jankowski [20] the distinction between absolute and convective instability was not yet established. PV patterns were observed with wavelengths below the critical one for Reynolds numbers Re < 10 [21,22].…”

“…PV patterns were observed with wavelengths below the critical one for Reynolds numbers Re < 10 [21,22].…”

“…Only for higher through-flow rates, which are not investigated here, there is a bifurcation [19,20] to spirals [20][21][22][23][24][25][26]. We have performed numerical simulations of the full, rotationally symmetric, two dimensional (2D) Navier-Stokes equations (NSE).…”

“…We have performed numerical simulations of the full, rotationally symmetric, two dimensional (2D) Navier-Stokes equations (NSE). They are compared with our numerical and analytical results obtained from the appropriate [27] 1D Ginzburg-Landau amplitude equation (GLE) approximation to the problem of PV flow and with experimental results [20][21][22]25,28,29] The eigenvalue problem of the pattern selection by the imposed flow can best be analyzed and explained within the GLE framework. Therein, the complex amplitude A(z, t) of the PV flow depends in the absolutely unstable regime on the streamwise position z and on time t in a multiplicative way only, A(z, t) = a(z)e −iΩt , (1.1)…”

“…Linear stability analyses of the basic state to traveling axisymmetric vortices were performed using various approximations, e. g. , for the narrow-gap limit, or simplified azimuthal velocity, or axial through-flow profiles [40], and later on for various aspect ratios fixed by the diameters of both cylinders [19,20,41,42]. Also, many experiments and comparisons with the theoretical predictions were done [21][22][23][24][25]28,29,[31][32][33][34][35]43,44].…”