Flow-Induced Waves on Compliant Surfaces Subject to a Turbulent Boundary Layer

Abstract

In this paper, we are concerned with waves that form on a compliant surface when it is subjected to a turbulent flow. Two types of waves have been observed so far in the experiments: a fast travelling wave on nearly elastic surfaces, and a nearly stationary or slowly moving wave on surfaces with significant damping. In their incipient state, the fast waves have small amplitude and propagate at speeds ranging from 0.3–0.5 times the freestream speed U∞, whereas the slow waves (also termed static divergence waves) have large amplitude and move forward at speeds of less than 0.05U∞ . Details of these waves were recorded in experimental studies by Gad-el-Hak et al. (1984), Gad-el-Hak (1986) and Hansen et al. (1980). This paper discusses the progress that has been made in the theoretical modelling of these waves. Emphasis is given to the recent works and the new insight that they offer about unstable interaction between turbulent flow and compliant surface. Quasipotential flow approximations have been fairly successful in predicting some of the qualitative and quantitative aspects of the observed waves. However, the quasipotential models are reliant on the availability of accurate parameter inputs from other experiments or additional modelling for them to work well. In this regard, they are not self-sufficient for general application. The effects of viscosity and turbulence are needed to produce a complete and self-consistent model for the accurate prediction of onset wave conditions. While linear stability models are generally adequate for predicting onset flow velocities for the waves, nonlinear wave effects are necessary to explain the detailed features of the observed waves.