The role of the convective modes and sheared variables in the Hamiltonian dynamics of uniform-shear-flow perturbations

The convective modes in shear flows are associated with the algebraic time evolution of perturbations. The sheared variables, corresponding to the amplitudes of the convective modes, are shown to diagonalize the quadratic Hamiltonian. In other words, the sheared variables are the normal variables of the Hamilton equations, and the convective modes are the normal modes in the Hamiltonian dynamics.