Stability Of Time-periodic Flows Research Articles

Stability of time-periodic flow with laminar boundary-layer separation

The influence of the low-frequency modulation of flow behind a rectangular backward-facing step on the amplitude characteristics of disturbances in the separated laminar boundary layer has been studied. The experimental data were obtained by the method of hot-wire anemometry in a wind tunnel at a low subsonic velocity. Response of the separated flow to the long-wave oscillations generated by a local source of disturbances on the surface of the experimental model was clarified. The low-frequency nonstationarity of the separation region leads to a growth of velocity fluctuations in the separated boundary layer, which dominate the laminar-turbulent transition and the state of the flow in the near-wall region.

Stability of time-periodic flows in a circular pipe

The stability of time-periodic flows in a circular pipe is investigated. The disturbance is assumed to be axially symmetric and to have a small amplitude, so that the governing differential equation is linear. Calculations are carried out for the first ten modes for a range of values of the frequency of the primary motion, of the wavenumber of the disturbance, and of the Reynolds number of the primary flow. In the ranges of the parameters for which the calculations have been carried out, the flows are found to be stable and, as for Stokes flows (von Kerczek & Davis 1974), it is conjectured that the flows under study here are stable for all frequencies and all Reynolds numbers.

The Stability of Time-Periodic Flows

The stability of periodic states of mechanical systems has long been an object of study. Dynamic stabilization and destabilization can lead to dramatic modifications of behavior depending on the proper tuning of the amplitude and frequency of the modulation. It has only been in the recent past that attention has been focused on such possibilities in hydrodynamics. The interest lies not only with the mechanics of this new class of problems but with the possibilities for applications. If an imposed modulation can destabilize an otherwise stable state, then there can be a major enhancement of heat/mass/momentum transport. If an imposed modulation can stabilize an otherwise unstable state, then higher efficiencies can be attained in various processing techniques. The aim here is to give reviews of three prototypal problems having sinusoidal time variation: parallel shear flows, convective instabilities, and centrifugal insta­ bilities.1 These will be used as vehicles for a discussion of scale analysis, a procedure which is crucial to the understanding of these as well as more general flows. Before proceeding with the examination of periodic basic states, a word must be said in reference to the definition of stability. Since the basic state is unsteady, it seems natural to compare the disturbance growth rate with the rate of change of the basic state (Shen 1961). However, in periodic states the repeating sequence of basic-state acceleration followed by basic-state deceleration leads to ambiguities in interpretation. As a result, there is fairly common agreement to follow Rosenblat (1968) and term a basic periodic state unstable if there exists a disturbance that experiences net growth over each modulation cycle. A state on which every disturbance decays at every instant is called stable. namely, monotonically stable. It may happen that a state is neither unstable nor stable, i.e. the basic state is subject