Meccanica

, Volume 26, Issue 2–3, pp 135–141 | Cite as

On flow and stability of a Newtonian fluid past a rotating plane

  • Maria Cristina Patria
Article
  • 32 Downloads

Abstract

An exact solution is given for the steady flow of a Newtonian fluid occupying the halfspace past the plane z=0 uniformly rotating about a fixed normal axis (≡Oz). This solution is obtained in a velocity field of the form considered by Berker [2] and can be deduced as a limiting case, as h→+∞, of the solution to the problem relative to the strip 0≤zh imposing at z=h either the adherence boundary conditions or the free surface conditions. Furthermore, the stability of this flow, subject to periodic disturbances of finite amplitude, is studied using the energy method and the result is compared with those corresponding to stability of flows in the strip 0≤zh.

Key words

Flow Stability Newtonian fluids 

Sommario

In questa nota si mostra che-oltre alla calssica soluzione di von Karman [1] — esiste, per opportuni valori del gradiente di pressione all'infinito, una soluzione esatta per il moto stazionario di un fluido Newtoniano posto nel semispazio limitato dal piano z=0 uniformemente rotante attorno ad un asse ad esso perpendicolare (≡Oz). Tale soluzione, ottenuta sulla scia del lavoro di Berker [2], si può dedurre anche come limite, per h→+∞, della soluzione del problema relativo alla striscia 0≤zh quando sul piano z=h si assegnano o le condizioni di aderenza o le condizioni di frontiera libera. Si studia poi la stabilità di tale moto rispetto a perturbazioni spazialmente periodiche di ampiezza finita col metodo dell'energia e si confronta il risultato ottenuto con quelli relativi alla stabilità dei moti nella striscia 0≤zh.

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Maria Cristina Patria
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di FerraraFerraraItaly

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