The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

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, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is 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

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response

The strong nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flow

Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states

Report of an excursion to the St. Austell district, Cornwall

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The use of computer-generated color graphic images for transient thermal analysis

Color computer graphics techniques were investigated as a means of rapidly scanning and interpreting large sets of transient heating data. The data presented were generated to support the conceptual design of a heat-sink thermal protection system (TPS) for a hypersonic research airplane. Color-coded vector and raster displays of the numerical geometry used in the heating calculations were employed to analyze skin thicknesses and surface temperatures of the heat-sink TPS under a variety of trajectory flight profiles. Both vector and raster displays proved to be effective means for rapidly identifying heat-sink mass concentrations, regions of high heating, and potentially adverse thermal gradients. The color-coded (raster) surface displays are a very efficient means for displaying surface-temperature and heating histories, and thereby the more stringent design requirements can quickly be identified. The related hardware and software developments required to implement both the vector and the raster displays for this application are also discussed

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Pure Gravity Mediation with m_{3/2} = 10-100TeV

Recently, the ATLAS and CMS collaborations reported exciting hints of a Standard Model-like Higgs boson with a mass around 125GeV. Such a Higgs boson mass can be easily obtained in the minimal supersymmetric Standard Model based on the "pure gravity mediation model" where the sfermion masses and the Higgs mass parameters are in tens to hundreds TeV range while the gauginos are in the hundreds GeV to TeV range. In this paper, we discuss detalis of the gaugino mass spectrum in the pure gravity mediation model. We also discuss the signals of the model at the current and future experiments such as cosmic ray observations and the LHC experiments. In particular, we show that the parameter space which is consistent with the thermal leptogenesis can be fully surveyed experimentally in the foreseeable future.Comment: 21 pages, 7 figure

Feasibility study of silicon nitride protection of plastic encapsulated semiconductors

The application of low temperature silicon nitride protective layers on wire bonded integrated circuits mounted on lead frame assemblies is reported. An evaluation of the mechanical and electrical compatibility of both plasma nitride and photochemical silicon nitride (photonitride) passivations (parallel evaluations) of integrated circuits which were then encapsulated in plastic is described. Photonitride passivation is compatible with all wire bonded lead frame assemblies, with or without initial chip passivation. Plasma nitride passivation of lead frame assemblies is possible only if the chip is passivated before lead frame assembly. The survival rate after the environmental test sequence of devices with a coating of plasma nitride on the chip and a coating of either plasma nitride or photonitride over the assembled device is significantly greater than that of devices assembled with no nitride protective coating over either chip or lead frame

Effect of inversion asymmetry on the intrinsic anomalous Hall effect in ferromagnetic (Ga,Mn)As

The relativistic nature of the electron motion underlies the intrinsic part of the anomalous Hall effect, believed to dominate in ferromagnetic (Ga,Mn)As. In this paper, we concentrate on the crystal band structure as an important facet to the description of this phenomenon. Using different k.p and tight-binding computational schemes, we capture the strong effect of the bulk inversion asymmetry on the Berry curvature and the anomalous Hall conductivity. At the same time, we find it not to affect other important characteristics of (Ga,Mn)As, namely the Curie temperature and uniaxial anisotropy fields. Our results extend the established theories of the anomalous Hall effect in ferromagnetic semiconductors and shed new light on its puzzling nature