Abstract
This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Coleman, B. D., W. Noll, Rev. Modern Phys.33, 239 (1961).
Becker, E., Adv. Appl. Mech.20, 177 (1980).
Markovitz, H., B. D. Coleman, Adv. Appl. Mech.8, 69 (1964).
Serrin, J., Arch. Rational Mech. Anal.3, 1 (1959).
Akbay, U., S. Sponagel, Rheol. Acta20, 579 (1981).
Joseph, D. D., Arch. Rational Mech. Anal.75, 251 (1981).
Gleissle, W., Rheol. Acta21, 484 (1982); H. Giesekus, K. Kirschke, J. Schurz, Progress and Trends in Rheology, Steinkopff Verlag (Darmstadt 1982), pp. 130.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ramkissoon, H., Becker, E. & Akbay, U. Three-dimensional disturbances of planar viscometric flow. Rheol Acta 22, 284–290 (1983). https://doi.org/10.1007/BF01359128
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01359128