  Flow instability and turbulent transition can be well explained using a new
proposed theory--Energy gradient theory [1]. In this theory, the stability of a
flow depends on the relative magnitude of energy gradient in streamwise
direction and that in transverse direction, if there is no work input. In this
note, it is shown based on the energy gradient theory that inviscid non-uniform
flow is unstable if the energy in transverse direction is not constant. This
new finding breaks the classical linear theory from Rayleigh that inviscid flow
is unstable if the velocity profile has an inflection point in parallel flows
and inviscid flow is stable if the velocity profile has no inflection point in
parallel flow. Then, stability of rotating viscous and inviscid flows is
studied, and two examples of rotating flows (rotating rigid body motion and
free vortex motion) are shown, respectively.
