Stability of the parallel flow of a fluid over a slightly heavier fluid

摘要: The incompressible, inviscid, parallel flow of a layer fluid over slightly denser fluid, in the presence gravity, is investigated for stability. Two idealized piece-wise-linear steady velocity profiles are examined analytically, and comparison with related experimental results made.The dimensionless parameter U/(gh)½, where U velocity, g acceleration h thickness upper layer, appears to have critical value between 0.2 0.7, below which stable flows can persist. At onset instability disturbances wavelength about or 2h predicted, more violent longer occurring at higher values U/(gh)½ For continuous this phenomenon found be relatively insensitive ratio densities two fluids.