Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Improving productivity - Opening the black box

Hourly productivity levels in the UK still remain behind those in some competitor countries. The government devotes much policy attention to enhancing productivity and continues to emphasise its five drivers - investment, innovation, skills, enterprise, and competition. This article argues that it is investment broadly defined that is the key to sustained productivity improvement. The emphasis should be on improving productivity simultaneously with improving the quality of production. Only thus will the gains be widely shared. In achieving these aims there are two prerequisites for policy-makers. The first is to ensure better coordination of policy than appears to be currently achieved by the present departmental structures in Whitehall. The second is to recognize fully the long and complex chain of causation that can be triggered by pulling on one policy lever. Such complexity can only be fully understood by more research on what actually goes on inside the black box of the organization. © 2006 Oxford University Press.