Use of Matched Pressure Initial Conditions for Predicting Low-Altitude Rocket Plume Radiation

Abstract

tanhkH Now this is equivalently 0(0) = R ~' ' (0) where R measures an effective rigidity. In the rigid wall limit we find that 0(0) = 0 and hence (/> vanishes identically; the basic flow, therefore, has no eigensolution s of the discrete c-spectrum. Thus we conclude here that it is the allowance of wall flexibility that gives rise to wavelike perturbations. Discussion and Concluding Remarks The foregoing results for the inviscid shear flow stability over compliant surfaces were obtained to supplement the more detailed viscous studies of Benjamin 1 and Landahl2 using the Orr-Sommerfeld equation. Our work focuses essentially on explicitly obtainable eigenvalue bounds, sufficiency conditions, and dispersion relations for the Benjamin-Landahl membrane model, although, for somewhat restrictive parameter ranges. While the results reported here are not directly applicable to the analysis of finite length plates (panel flutter) per se as contrasted with infinite length membranes, the general methods may be used in conjunction with alternative structural models and with only minor modification. The basic problem, of course, is one for fluid and solid interaction, and a substantial body of more general work appears in the aeroelastic literature. Noteworthy among these are some significant theoretical models for shear flows over flexible boundaries, for example, those pursued by Dowell and his collaborators.4'6 These studies allow for both finite plate dimensions as well as fluid compressibility; their numerical results, moreover, compare favorably with the experiments of Muhlstein et al. 7>8 The analytical approaches adopted here and in Refs. 4-6 are more or less equivalent. The simpler interaction model examined here, though, leads to simple closed-form results, and these may be useful in various applications. Acknowledgments