Published online by Cambridge University Press: 07 October 2011
The Background of the Problem
This chapter will be devoted to the analysis of one of the fundamental problems of hydrodynamics: ascertaining the limiting state for the steady flow behind a body of finite size as the Reynolds number Re → ∞ in cases where unseparated flow over the body is impossible, for example, behind a blunt body such as a circular cylinder or a plate placed normal to the oncoming flow. Although in reality such flows already become unsteady at Reynolds numbers of the order of 101–102, and undergo transition to a turbulent state with further increase in Reynolds number, the solution of this problem is of great interest in principle. Moreover, one might anticipate that such a solution would allow the study of fluid flows at moderate Reynolds numbers when a steady flow regime is still maintained but the methods of the theory of slow motion (Re < 1) are no longer applicable.
There are several points of view about possible ways of solving this problem. According to the first of these, already stated by Prandtl (1931) and then developed by Squire (1934) and Imai (1953, 1957b), the limiting flow configuration as Re → ∞ is the classical Kirchhoff (1869) flow with free streamlines and a stagnation zone that extends to infinity and expands asymptotically according to a parabolic law (Figure 6.1). This picture has been severely criticized both because of poor quantitative agreement with experimental results (for measurements of body drag) and also for some fundamental reasons.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.