Link to this article: http://journals.cambridge.org/abstract_S0022112075001425How to cite this article: P. M. Eagles and M. A. Weissman (1975). On the stability of slowly varying flow: the divergent The linear stability of a slowly varying flow, the flow in a diverging straightwalled channel, is studied using a modification of the 'WKB' or 'ray' method.It is shown that 'quasi-parallel' theory, the usual method for handling such flows, gives the formally correct lowest-order growth rate; however, this growth rate can be substantially in error if its magnitude is comparable to that of the rate of change of the basic state. The method used clearly demonstrates the dependence of the growth rate, wavenumber, neutral curves, etc., on the crossstream variable and on the flow quantity under consideration. When applied to the divergent channel, the method yields a much wider 'unstable' region and a much lower 'critical ' Reynolds number (depending on the flow quantity used) than those predicted by quasi-parallel theory. The determination of the downstream development of waves of constant frequency shows that waves of all frequencies eventually decay.
A series of experiments was conducted in a wind‐wave tank to determine the dynamic response of thin‐wire wave gauges as a function of probe diameter in terms of their spatial resolution and frequency response. Two resistance thin‐wire gauges with probe diameters of 0.13 and 0.4 mm were used in the experiments. They were calibrated against a nonintrusive, optical device (the laser displacement gauge, or LDG). The two thin wires were mounted side by side in close proximity to the laser beam at a fetch of 4 m. The outputs from the LDG and thin‐wire gauges were recorded alternately as well as simultaneously by using two separate recording systems. The spectral density measured with the LDG proves to be consistently higher than that measured with either thin wire, especially for frequencies higher than the dominant frequency. Only a slight difference is observed between the two spectra of the thin‐wire data. From the experimental results, an empirical correction for the meniscus‐induced bias in the variance spectrum of capillary waves is derived.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.