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# Case when surface tension and difference of density are absent

In this case,where , there is continuity of pressure by crossing the interface:
With Bernoulli equation, we can write for each fluid:
With these two equations, we obtain for terms of first order:
We look for solutions with the following form:
with  which is the rate of development of perturbation and k the wave length.

By injecting these solutions in last equations we obtain a linear homogeneous system with the unknown variables A, and . The condition of compatibility is obtain by saying the determinant of the matrix of the system equal to zero so :

which is the relation of dispersion for wave. Like  can be positive,we can say that there's always an instable state for this king of flow, and amplification of perturbation is more important when wave lengths are little.

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