Research Article

Weakly Nonlinear Hydrodynamic Stability of the Thin Newtonian Fluid Flowing on a Rotating Circular Disk

Table 1

Various states of Landau equation.

Linearly stable (subcritical region) 𝑑 𝑖 < 0 Subcritical instability 𝐸 1 < 0 𝜀 𝑎 0 𝑑 < ( 𝑖 𝐸 1 ) 1 / 2 𝑎 0 0 Conditional stability
𝜀 𝑎 0 𝑑 > ( 𝑖 𝐸 1 ) 1 / 2 𝑎 0 Subcritical explosive state
Subcritical (absolute) stability 𝐸 1 > 0 𝑎 0 0

Linearly unstable (supercritical region) 𝑑 𝑖 > 0 Supercritical explosive state 𝐸 1 < 0 𝑎 0
Supercritical stability 𝐸 1 > 0 𝜀 𝑎 0 𝑑 ( 𝑖 𝐸 1 ) 1 / 2
𝑁 𝑐 𝑟 𝑑 𝑟 + 𝑑 𝑖 ( 𝐹 1 𝐸 1 )