Nonlinear Wave Seminar
Brown University, Division of Applied Mathematics | |
Center for Fluid Mechanics Seminar
Abstract: For the best part of last century mathematical convenience has confined the bulk of theoretical investigation of the phenomenon of laminar-turbulent flow transition into the realm of assumptions which severely hamper our ability to address every-day life flow instability applications. In the days of modern global flow-field measurement techniques and teraflop-petabyte computing a rethink of our approach to the problem of amplified 'small-amplitude' disturbances and the associated decomposition of a flow-field into steady mean plus unsteady disturbance quantities is warranted.
Starting from exposure of the first principles of laminar-turbulent flow transition prediction based on the theory of small-disturbances (Tollmien 1928) the main part of the talk will be devoted to the much more recent theoretical developments in global linear instability theory. The potential of the theory will be illustrated through discussion of global instability of four prototype essentially two-dimensional steady laminar flows, the pressure-gradient driven rectangular duct, the lid-driven cavity, a boundary layer encompassing a separation bubble and the swept attachment-line boundary layer.
Theoretical knowledge of both local and global eigendisturbances is instrumental to devising measurement techniques appropriate for their experimental recovery and ultimate control of laminar-turbulent flow transition mechanisms. Raising the awareness of the global linear flow eigenmodes contributes to redefining the boundaries between experimental observations which may be attributed to linear global as opposed to nonlinear mechanisms. The implications regarding further theoretical developments, numerical simulations and, not least, experimental verification of the results of the newly-proposed theory will be discussed.
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