Abstract:

The problem of growth of small perturbations in fluid flow and the related problem of maintenance of perturbation variance has traditionally been studies by appeal to exponential modal instability of the flow. in the event that a flow supports and exponentially growing modal solution, the initially unbounded growth of the mode is taken as more of less compelling evidence for eventual flow breakdown. However, atmospheric flows are characterized by large thermally forced background rates of strain and are subject to perturbations that are not infinitesimal in amplitude. Under these circumstances there is an alternative mechanism for growth and maintenance of perturbation variance: amplification is straining flow of stochastically forced perturbations in the absence of exponential instabilities. From this viewpoint the flow is regarded as a driven amplifier rather than as an unstable oscillator. We explore this mechanism using as examples unbounded constant shear and pure deformation flow for which closed-form solutions are available and neither of which supports a nonsingular mode. With diffusive dissipation we find that amplification of isotropic band-limited stochastic driving is unlinear velocity profile. A phenomenological model of the contribution of linear and nonlinear damped modes to the maintenance of variance results in variance levels increasing linearly with shear. We conclude that amplification of stochastic forcing in straining field can maintain a variance field substantially more energetic than that resulting from the same forcing in the absence of a background straining flow. our results further indicate that existence of linear and non linear damped modes is important in maintaining high levels of variance byt he mechanism of stochastic excitation.