, Volume 9, Issue 1, pp 3-19

On the use of spherical means in hydrodynamics. Application to the study of the inception of turbulence

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Abstract

In Part I Continuous Medium is defined and the A gular Momentum Theorem is applied to a spherical volume of the medium. Applied to perfect fuids this yields classical results. Applied to solids and to viscous fluids it yields maximum radii of stability.

In Part II a number of physical assumptions are made about the inception and the nature of turbulent flow and various formulas are obtained.

In Part III spherical means, considered as functions of the radius of the sphere, are expanded into power series. These expansions are used to analyse the limitations of the use of spherical means in hydrodynamics.