Wave function analysis critical points

Now, following the assumption of Taylor that the principle of exchange of stabilities is satisfied, so that a = 0 at the neutral stability point, the objective of the stability analysis is to obtain nontrivial solutions of (12-147) and (12-148) with a = 0 for various values of a and then determine the minimum value of T as a function of a. This minimum of T is the critical value of the Taylor number for transition to instability. The corresponding value of a is known as the critical wave number and represents the (dimensionless) wave... 

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