Neutral curve (2)

Figure 4 shows neutral curves evaluated by (11) at P=1 for several different values of h.

When the rotation rate is sufficiently large, a neutral curve has a local minimum at non-zero k. Note that the horizontal wave number k_c' of the local minimum increases as the rotation rate increases. Let us evaluate the asymptotic behavior of the local minimum point. By differentiating (11) with k², and assuming that k and h are large enough, we obtain the expressions of horizontal wavenumber k_c', frequency w_c' and the Rayleigh number R_c' at the local minimum.

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The asymptotic expressions of the horizontal wavenumber and the Rayleigh number of the local minimum coincide with those for the case of the fixed temperature condition obtained by Busse and Or (1986), although there is a difference in the coefficients in the equation of the Rayleigh number. The coefficient of our expression is 3p²/8 ~3.70, while that of Busse and Or (1986) is 3.

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Fig.4 Neutral curves of convection in rotating cylindrical annulus under the fixed heat flux condition at P=1 for several values of h.