@article{2982108,
    title = "Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow",
    author = "Farrell, B.F. and Ioannou, P.J.",
    journal = "Physics of Fluids",
    year = "2000",
    volume = "12",
    number = "11",
    pages = "3021-3028",
    publisher = "American Inst of Physics, Woodbury",
    issn = "1070-6631, 1089-7666",
    doi = "10.1063/1.1313549",
    keywords = "Compressible flow;  Incompressible flow;  Mathematical models;  Perturbation techniques;  Reynolds number, Couette problem;  Mach number;  Perturbation growth, Shear flow, Couette flow;  Mach number;  Shear flow;  Viscous flow",
    abstract = "A comprehensive assessment is made of transient and asymptotic two-dimensional perturbation growth in compressible shear flow using unbounded constant shear and the Couette problem as examples. The unbounded shear flow example captures the essential dynamics of the rapid transient growth processes at high Mach numbers, while excitation by nonmodal mechanisms of nearly neutral modes supported by boundaries in the Couette problem is found to be important in sustaining high perturbation amplitude at long times. The optimal growth of two-dimensional perturbations in viscous high Mach number flows in both unbounded shear flow and the Couette problem is shown to greatly exceed the optimal growth obtained in incompressible flows at the same Reynolds number. (C) 2000 American Institute of Physics.
The stability of compressible shear flow was studied by evaluating the perturbation growth due to both modal and nonmodal processes. Using the unbounded constant shear flow and the Couette problem as examples, the transient and asymptotic two-dimensional perturbation growth was assessed. Initial perturbations producing optimal energy growth over specified time intervals were determined using singular value decomposition to identify the potential for perturbation growth in compressible shear flow. Perturbation growth in incompressible flows were exceeded by that of the two dimensional perturbations in viscous high Mach number flows in both unbounded shear flow and the Couette problem at the same Reynolds number."
}