We investigate the effect of buoyancy on the upper-branch linear stability characteristics of an accelerating boundary-layer how. The presence of a large thermal buoyancy force significantly alters the stability struc...
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We investigate the effect of buoyancy on the upper-branch linear stability characteristics of an accelerating boundary-layer how. The presence of a large thermal buoyancy force significantly alters the stability structure. As the factor G (which is related to the Grashof number of the flow, and defined in Section 2) becomes large and positive, the flow structure becomes two layered and disturbances are governed by the Taylor-Goldstein equation. The resulting inviscid modes are unstable for a large component of the wavenumber spectrum, with the result that buoyancy is strongly destabilizing. Restabilization is encountered at sufficiently large wavenumbers. For G large and negative the flow structure is again two layered. Disturbances to the basic flow are now governed by the steady Taylor-Goldstein equation in the majority of the boundary layer, coupled with a viscous wall layer. The resulting eigenvalue problem is identical to that found for the corresponding case of lower-branch Tollmien-Schlichting waves, thus suggesting that the neutral curve eventually becomes closed in this limit.
The coupled wave dynamics of a compressible fluid and an elastic solid are studied when the motion is forced by a nonuniform line source lying in their common interface. The nonuniformity arises as a result of a distr...
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The coupled wave dynamics of a compressible fluid and an elastic solid are studied when the motion is forced by a nonuniform line source lying in their common interface. The nonuniformity arises as a result of a distribution in phase along the forcing site, and this is taken as being representative of the effects of the scattering of an acoustic plane wave which is obliquely incident upon a shallow, surface-breaking inhomogeneity in the solid. An appropriate boundary-value problem is posed and solved exactly using an integral transform. This solution is then decomposed into its constituent asymptotic wave contributions, and the structure of each of these contributions is examined in the far field for all values of the phasing parameter.
The conformal mapping of a curvilinear quadrangle to a half-plane is a classical problem in analysis;it occurs during the analytical solution of free-boundaryproblems involving groundwater flows. Apart from degenerat...
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The conformal mapping of a curvilinear quadrangle to a half-plane is a classical problem in analysis;it occurs during the analytical solution of free-boundaryproblems involving groundwater flows. Apart from degenerate cases, in general, it is not known how to perform such mappings;the difficulty arises because the mapping functions are given by the solutions of a Fuchsian differential equation. For a quadrangle this Fuchsian equation involves both accessory parameters and free points that are unknown a priori;the analysis of such equations is therefore difficult, and there are usually no obvious solutions. In this paper conformal mappings involving a special class of curvilinear quadrangles are constructed, and a general approach is devised in the special cases when one (or more) vertex angle is equal to 2 pi. By implication this suggests that there are degenerate classes of Fuchsian equations involving accessory parameters and free points;these classes are discussed.
Fast two-dimensional stratified flow over several obstacles is considered, in particular over thin wings. The problem is reduced to a linear boundary-value problem by a nonlinear substitution. The linear problem is st...
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Fast two-dimensional stratified flow over several obstacles is considered, in particular over thin wings. The problem is reduced to a linear boundary-value problem by a nonlinear substitution. The linear problem is studied by potential theory. The solution of the nonlinear problem is obtained.
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