Density Viscosity Kinematic Viscosity

Abstract

Table 2. Neutral eigenvalues with decreasing step-size: m = 1, = 1 and R e = 800. 27 Figure captions Figure 1(a). Basic ow of air over water: velocity prooles with wall blowing and water depth D = 0:5; 1:2; 3; 4. Figure 1(b). Basic ow of air over water: velocity prooles with wall suction and water depth D = 0:5; 1:2; 3; 4.. Figure 2(a). Basic ow of air over water: water depth D and corresponding blow-ing/suction. Figure 2(b). Basic ow of air over water: streamlines with wall blowing. Figure 2(c). Basic ow of air over water: streamlines with wall suction. Figure 3. Neutral curves with equal viscosities and densities: Impermeable plate = 0, blowing with = 0:137 and = 0:4, and suction with = ?0:1. Figure 5(a). Neutral curves: solid line corresponds to the ow of air over water with increasing wall blowing; dotted line shows the neutral curve for a single uid with no wall blowing. Figure 5(b). Neutral curves: the stability of air ow over water with suction at the wall. Figure 6. Eigenvalues 0 as a function of viscosity ratio m. Figure 7. Eigenvalue 0 for similar uids: a comparison of asymptotic and numerical results when the viscosity ratio m is close to unity. 26 19] Malik, M. (1986) The neutral curve for stationary disturbances in rotating-disk ow. On the stability of three-dimensional boundary layers with application to the ow due to a rotating disk. On the instability of a three dimensional attachment-line boundary layer; weakly nonlinear theory and a numerical approach. Shear-ow instability due to a wall and a viscosity discontinuity at the interface. Experimental investigations of the stability of channel ows. Part 2. Two-layered co-current ow in a rectangular region. J. Fluid Mech. 52 pp. 401-423. 24 For matched uid properties the eeective wavenumber and wave angle given above correspond to the single uid case. As viscosity stratiication is introduced, we obtain the above corrections to these quantities and these in turn are in agreement with our numerical results for general viscosity and density ratios. These calculations are based on an innnite Reynolds number assumption. This work could be extended to include viscous eeects in an analogous manner to the method used by Hall 10] for the ow over a rotating disk. Viscous eeects enter at O R ?1=16 e , the corresponding momentum equations must then be solved to determine U j1 …