The virtual mass and lift force on a sphere in rotating and straining inviscid flow.

*(English)*Zbl 0627.76014The central issue of this paper is some “principle of objectivity”, stating that constitutive equations should not depend in a substantial way on the coordinate system used to express them. It has been argued [G. Ryskin and J. M. Rallison, J. Fluid Mech. 99, 513-519 (1980; Zbl 0447.76085)] that cases exist where this plausible assumption is not appropriate. The authors aim to meet criticism along such lines against an earlier paper [the authors, Int. J. Multiphase Flow 5, 243-264 (1979; Zbl 0434.76077)]; they find that at least in the limiting case of a single particle dispersed the principle applies, though this has been questioned [O. V. Voinow, Zh. prikl. Mekh. tekh. 14(4), 592-594 (1978)]. The authors use the tensor notation as invented to coordinate free representation.

Reviewer feels that their result, expressing the force in terms of Kelvin impulse and Reynolds tensor, was essentially derived for general body forms by [W. Tollmien, Ing. Arch. 9, 308-326 (1938)], who called attention to ambiguities when the Kelvin impulse is defined via control surfaces extended to infinity [W. Tollmien, Z. Angew. Math. Mech. 18, 151-154 (1938)].

Reviewer feels that for flows with linear variation in the far field (hence tending to infinity finally) as considered by the authors, similar ambiguities may occur and may possibly resolve the controversy.

Reviewer feels that their result, expressing the force in terms of Kelvin impulse and Reynolds tensor, was essentially derived for general body forms by [W. Tollmien, Ing. Arch. 9, 308-326 (1938)], who called attention to ambiguities when the Kelvin impulse is defined via control surfaces extended to infinity [W. Tollmien, Z. Angew. Math. Mech. 18, 151-154 (1938)].

Reviewer feels that for flows with linear variation in the far field (hence tending to infinity finally) as considered by the authors, similar ambiguities may occur and may possibly resolve the controversy.

Reviewer: K.Eggers

##### MSC:

76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |

76U05 | General theory of rotating fluids |