The geometric similarity of the laminar sections of boundary layer-type flows

Experimental observations of the shape of the laminar and transition sections of a confined coaxial jet show that the laminar length (L) is always approximately ten times greater than the wavelength of the first sinusoidal deformation of the flow (λ). This discovery coincides with the L∼ 10λ proportionality noted in an earlier study of the laminar sections of air plumes rising above concentrated heat sources. A search of the literature shows that the L∼ 10λ proportionality characterizes other boundary layer-type flows, for example the flow over a flat plate and the plane mixing layer. Using the confined jet and the round plume as examples, it is shown also that the L∼ 10λ proportionality can be derived theoretically.