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

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

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

Switchable filtering in vivaldi antenna

Presented is a new frequency switchable Vivaldi antenna that has a capability to operate in a wideband mode (1-3 GHz) and reconfigure to six different subbands of operations. The reconfiguration is realised by coupling and changing the effective electrical length of ring slots inserted in the structure by means of pin diode switches. To examine antenna performances, simulated and measured results are presented. Good impedance matches and radiation patterns have been achieved. The proposed antenna is suitable for wideband and multimode radio applications

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

E6SSM vs MSSM gluino phenomenology

The E6SSM is a promising model based on the group E6, assumed to be broken at the GUT scale, leading to the group SU(3)\times SU(2)\times U(1)\times U(1)' at the TeV scale. It gives a solution to the MSSM {\mu}-problem without introducing massless axions, gauge anomalies or cosmological domain walls. The model contains three families of complete 27s of E6, giving a richer phenomenology than the MSSM. The E6SSM generically predicts gluino cascade decay chains which are about 2 steps longer than the MSSM's due to the presence of several light neutralino states. This implies less missing (and more visible) transverse momentum in collider experiments and kinematical distributions such as M_eff are different. Scans of parameter space and MC analysis suggest that current SUSY search strategies and exclusion limits have to be reconsidered.Comment: Presented at the 2011 Hadron Collider Physics symposium (HCP-2011), Paris, France, November 14-18 2011, 3 pages, 7 figure

Investigation of plane-strain flaw growth in thick-walled tanks Final report, 26 Jun. 1964 - 26 Oct. 1965

Flaw growth rates and fracture toughness data for materials used in thick walled cylindrical tank