High-amplitude Disturbances Research Articles

Simulation techniques for spatially evolving instabilities in compressible flow over a flat plate

In this paper we present numerical techniques suitable for a direct numerical simulation in the spatial setting. We demonstrate the application to the simulation of compressible flat plate flow instabilities. We compare second and fourth order accurate spatial discretization schemes in combination with explicit multistage time stepping for the simulation of the 2D Navier-Stokes equations. We consider Mach numbers 0.5 and 4.5. In the vicinity of the outflow boundary, an efficient buffer domain treatment is introduced, which is suitable in conjunction with an explicit time integration scheme. This treatment requires only a short buffer domain to damp wave reflections at the outflow boundary. Results for the instability of Tollmien-Schlichting (T-S) waves are compared with two instability theories, linear stability theory (LST) and linear parabolized stability equations (PSE). The growth rates of T-S waves for parallel base flow at both Mach numbers compare well with LST results. Moreover, the growth rates of T-S waves for nonparallel base flow compare well with results obtained by solving the PSE at Mach number 0.5. The second order discretization scheme requires, however, considerably higher grid resolution than the fourth order method to achieve accurate results. High amplitude disturbances were also considered to activate nonlinear terms. The nonlinearity strongly affects the form of the T-S waves and the growth rate of the disturbances. The results obtained here support the use of these numerical techniques in flow simulations with increasing complexity such as flat plate flow simulations up to the turbulent regime and with separation regions in 3D. The results also encourage the use of perturbations derived from the compressible PSE as inlet perturbations for nonparallel flow.

A predictive median threshold filter with robust prediction estimation

Measurement signal preprocessing consists of several techniques for data preanalysis and modification. The removal of erroneous samples is one of these tasks. This paper presents a predictive median threshold filter with robust prediction estimation. The filter can be applied to the elimination of impulsive disturbances of short duration. The main demand for this kind of filter is that the elimination of a disturbance must not distort the signal in the time domain outside the erroneous region. The filter structure and some results of tests illustrating the performance of the filter in both the time and the frequency domain are presented. The results show that the new filter structure is less sensitive to changing properties of disturbances than the corresponding former filter structure. This means that the values for the filter parameters are easy to select and that the filter can be applied to suppress high-amplitude disturbances with great reliability.

On nonlinear effects near the wing-tips of an evolving boundary-layer spot

A study is made concerning nonlinear effects arising in the free evolution of three-dimensional disturbances in boundary layers, these disturbances having a spot-like character sufficiently far downstream of the initial disturbance. The theory proposed here takes an inviscid initial-value formulation, typically that involving the three-dimensional unsteady Euler equations; such a formulation is felt to offer hope of considerable analytical progress on the nonlinear side, as well as being suggested by some of the available experimental evidence on turbulent spots and by engineering modelling and previous related theory. As the typical disturbance amplitude is increased, nonlinear effects first enter the reckoning of the large-time large-distance behaviour in edge layers near the spot’s wing-tips which correspond to caustics in linear theory. This behaviour is associated with the major length scales, proportional to (time) 1/2 and to (time), in the evolving spot; within the former scale it is interesting that the three-dimensional Euler flow exhibits a triple-deck-like structure; within the latter scale, in contrast, there are additional time-independent scales in operation. Two possible mechanisms I and II are found for nonlinearity to affect the evolution significantly, near a wing-tip. In I, weakly nonlinear effects make themselves felt in the bulk of the wing-tip flow, accompanied by a near-wall layer where full nonlinearity substantially alters the local vorticity. The analysis then leads to a nonlinear amplitude equation which is the second Painlevé transcendent, whose solution properties are well known. In contrast, mechanism II, which is believed to be the more likely case, has its nonlinearity being mostly due to a three-dimensional mean-flow correction that varies relatively slowly. The resulting nonlinear amplitude equation then has a novel form, solutions for which are obtained computationally and analytically. The further repercussions from the two mechanisms are somewhat different, although each one points to a subsequent flooding of nonlinear effects into the middle of the spot. Mechanism I suggests that strong nonlinearity is produced next by relatively high-amplitude disturbances, whereas the favoured mechanism II indicates instead a strongly nonlinear influence on the mean flow next occurring at input amplitudes that are still relatively low. The additional significance of viscous sublayer bursts is also noted, along with comments on comparisons with experiments and direct numerical simulations. Firm comparisons are felt likely to arise for the next stage implied above, where the middle of a typical spot is affected substantially.

The control of transient disturbances in a flat plate boundary layer through active wall motion

Experimental results are presented demonstrating the evolution and control of a large amplitude and highly three-dimensional disturbance in a laminar boundary layer. A localized disturbance was introduced into a laminar boundary layer at Reδ* =1095 by means of a flexible membrane mounted on a flat plate. For low amplitudes, the disturbance initially decayed, leaving a slowly growing wave packet comprised of linearly unstable Orr–Sommerfeld modes. At higher amplitudes, the disturbance grew rapidly, leading to a turbulent spot. The high-amplitude disturbance was acted upon by an active wall counterdisturbance consisting of a traveling bump at the wall. The counterdisturbance was generated by an array of eight small flexible membranes mounted next to one another, flush with the wall and activated in rapid succession. The breakdown of the disturbance to a turbulent spot is shown to be delayed by the active wall motion by approximately 50δ*. The active wall motion is shown to inhibit the development of the initial disturbance and to decrease the amplification rate of spanwise vorticity by reducing the level of cross-stream stretching ∂w/∂z.

The solar causes of geomagnetic disturbances

Geomagnetic disturbances have been identified with respect to their sources for 1977–1983. The disturbance level was found using the daily planetary index Ap. High-amplitude (∼ 50), mean-amplitude (∼24) and low-amplitude (∼ 12) disturbances are caused by solar flares of importance ≥ 1, coronal holes, and filament cavities, respectively. The ranges of probable amplitudes of disturbances of different nature and their relative number are found from Poisson random distributions of amplitudes.