TY - GEN
T1 - Near-planar TS waves and longitudinal vortices in channel flow
T2 - Nonlinear Interaction and Focussing
AU - Hall, P.
AU - Smith, F. T.
PY - 1990/1/1
Y1 - 1990/1/1
N2 - The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, was studied the most here and it usually produced spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This pointed to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 corresponded to still higher amplitudes, with 3 being related to 2, while 4 was connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude. (A)
AB - The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, was studied the most here and it usually produced spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This pointed to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 corresponded to still higher amplitudes, with 3 being related to 2, while 4 was connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude. (A)
UR - http://www.scopus.com/inward/record.url?scp=85041145437&partnerID=8YFLogxK
U2 - 10.1007/978-1-4612-3432-6_2
DO - 10.1007/978-1-4612-3432-6_2
M3 - Conference Paper
AN - SCOPUS:85041145437
SN - 978-0-387-97324-1
T3 - ICASE/ NASA LaRC Series
SP - 5
EP - 39
BT - Instability and Transition
PB - Springer
CY - New York USA
ER -