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MUREITHI EUNICE W.; DENIER JAMES P.; STOTT JILLIAN A. K. 《IMA Journal of Applied Mathematics》1997,58(1):19-50
We investigate the effect of buoyancy on the upper-branch linearstability characteristics of an accelerating boundary-layerflow. The presence of a large thermal buoyancy force significantlyalters the stability structure. As the factor G (which is relatedto the Grashof number of the flow, and defined in Section 2)becomes large and positive, the flow structure becomes two layeredand disturbances are governed by the Taylor-Goldstein equation.The resulting inviscid modes are unstable for a large componentof the wavenumber spectrum, with the result that buoyancy isstrongly destabilizing. Restabilization is encountered at sufficientlylarge wavenumbers. For G large and negative the flow structureis again two layered Disturbances to the basic flow are nowgoverned by the steady TaylorGoldstein equation in themajority of the boundary layer, coupled with a viscous walllayer. The resulting eigenvalue problem is identical to thatfound for the corresponding case of lower-branch TollmienSchlichtingwaves, thus suggesting that the neutral curve eventually becomesclosed in this limit. 相似文献
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The structure of nonlinear short-wavelength Taylor vorticesin the flow between rotating concentric cylinders is considered.In the short-wavelength limit, the nonlinear vortex motion isgoverned by a mean-flow-first-harmonic interaction problem.The initial structure of the nonlinear vortex state is shownto be governed by a multilayer structure in which the vortexis constrained to lie between the inner cylinder and a positioninternal to the flow regime. This position is dependent uponthe Taylor number and it is found that there is a critical valueof the Taylor number at which the vortex first impinges on theouter boundary. The vortex field then develops a double boundarylayer structure at both the inner and outer boundary as theTaylor number is increased past this critical Taylor number. 相似文献
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