About the proper choice of the characteristic length in the convection theory

It is known that convection sets in rather abruptly for stars with T/sub eff/<T/sub b/, where T/sub b/ depends on the luminosity. The boundary line T/sub b/(L) goes through the H-R diagram from late A or early F main-sequence stars to late F or early G supergiants. In the mixing length approach to the theory of convection the exact theoretical position of this boundary temperature depends on the assumptions about the size of the mixing length l. We make the assumption that the red boundary of the Cepheid instability strip agrees with the line T/sub b/(L). If we also assume l=n pressure scale height H, with n being the same constant for all stars, we find lapprox. =H to give the correct T/sub b/(L). If we assume the region of large instability to determine l, the relation lproportionalR2 also gives approximately the correct T/sub b/(L). We do not think, however, that the latter relation has any physical significance