The existing linear stability analysis of incipient channellization was limited to the case of self-preserving slope profiles. In this study, the theory is extended to include the channellization on slopes with arbitrary shapes. Since arbitrary base state slope shape is evolving in time, the frozen time approach and the concept of momentary stability are employed. The analysis showed the possibility of channellization in the case of the arbitrary slope profile. It is found that the dominant wavelength decreases with increasing curvature of the slope.
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