The hydrodynamic stability of flows over Kramer-type compliant surfaces is studied. Two main types of instability are considered. First, there are those which could not exist without viscosity, termed Tollmien–Schlichting Type Instabilities (TSI). Secondly, there are Flow-Induced Surface Instabilities (FISI), that depend fundamentally on surface flexibility and could exist with an inviscid fluid flow. Part 1, the present paper, deals mainly with the first type. The original Kramer experiments and the various subsequent attempts to confirm his results are reviewed, together with experimental studies of transition in flows over compliant surfaces and theoretical work concerned with the hydrodynamic stability of such flows.The Kramer-type compliant surface is assumed to be an elastic plate supported by springs which are modelled by an elastic foundation. It is also assumed that the plate is backed by a viscous fluid substrate having, in general, a density and viscosity different from the mainstream fluid. The motion of the substrate fluid is assumed to be unaffected by the presence of the springs and is determined by solving the linearized Navier–Stokes equations. The visco-elastic properties of the plate and springs are taken into account approximately by using a complex elastic modulus which leads to complex flexural rigidity and spring stiffness. Values for the various parameters characterizing the surface properties are estimated for the actual Kramer coatings.The boundary-layer stability problem for a flexible surface is formulated in a similar way to that of Landahl (1962) whereby the boundary condition at the surface is expressed in terms of an equality between the surface and boundary-layer admittances. This form of the boundary condition is exploited to develop an approximate theory which determines whether a particular change to the mechanical properties of the surface will be stabilizing or destabilizing with respect to the TSI. It is shown that a reduction in flexural rigidity and spring stiffness, an increase in plate mass, and the presence of an inviscid fluid substrate are all stabilizing, whereas viscous and visco-elastic damping are destabilizing.Numerical solutions to the Orr–Sommerfeld equation are also obtained. Apart from Kramer-type compliant surfaces, solutions are also presented for the rigid wall, for the spring-backed tensioned membrane with damping, previously considered by Landahl & Kaplan (1965), and for some of the compliant surfaces investigated experimentally by Babenko and his colleagues. The results for the Kramer-type compliant surfaces on the whole confirm the predictions of the simple theory. For a free-stream speed of 18 m/s the introduction of a viscous substrate leads to a complex modal interaction between the TSI and FISI. A single combined unstable mode is formed in the case of highly viscous substrate fluids and in this case increased damping has a stabilizing effect. When the free-stream speed is reduced to 15 m/s the modal interaction no longer occurs. In this case the eff...

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

No abstract

This paper considers the early experiences of the development of wind turbines and the wind energy industry in order to try and identify lessons learned that could now be applied to the developing marine renewables technology and industry. It considers both political and commercial incentives and engineering development.

No abstract

No abstract

No abstract

No abstract