Abstract
By revisiting the linear dynamics of plane channel flow between compliant walls it is shown that the instability is mainly dominated by perturbations of varicose symmetry. The prevailing modes are of traveling-wave-flutter type and governed by the reduced velocity, a nondimensional control parameter measuring the response of the flexible wall to hydrodynamic loading. Analysis of the energy transfer mechanisms reveals that a stabilizing effect for one class of modes is often accompanied by a destabilizing effect for another class. Thus it seems impossible to significantly delay instability onset by wall compliance.
Highlights
The constant scientific interest to extend the laminar regime for industrial applications has led to the development of compliant walls since the beginning of the 20th century
Since the base state is symmetric in y, the entire spectrum consists of the same number of modes of either varicose or sinuous symmetry
The inset in the figure shows that for small values of d, flexural rigidity has a moderately stabilizing effect on traveling-wave flutter (TWF) modes: VRc increases as B is increased for fixed d
Summary
The constant scientific interest to extend the laminar regime for industrial applications has led to the development of compliant walls since the beginning of the 20th century. Deformability plays a prominent role in blood flow as well as peristaltic transport, for example through the intestines and the urogenital tract (see for a review). Such interest arose from the Gray’s paradox. Gray showed that to overcome the friction drag of a swimming dolphin subjected to a turbulent flow around its body, the muscles have to be capable of generating a power at least seven times greater than that of other kinds of mammalian muscle. Gray has suggested that the dolphin skin is able to delay the laminar–turbulent transition. The power developed by muscles would still conform to that of other types of mammalian muscle
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