VARIANCE MAINTAINED BY STOCHASTIC FORCING OF NONNORMAL DYNAMICAL-SYSTEMS ASSOCIATED WITH LINEARLY STABLE SHEAR FLOWS

The level of variance maintained in a stochastically forced asymptotically stable linear dynamical system with a non-normal dynamical operator cannot be fully characterized by the decay rate of its normal modes, unlike normal dynamical systems. The nonorthogonality of modes may lead to transient growth which supports variance far in excess of that anticipated from the decay rate given by the eigenvalues of the operator. As an example, the variance maintained by stochastic forcing in a canonical shear Flow is found to increase with a power of the Reynolds number between 1.5 and 3. This great amplification of variance suggests a fundamentally linear mechanism underlying shear how turbulence.