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In a recent letter, Carpenter and Guha (2019) compared the neutral modes of asmooth two dimensional shear profile without an inflection point to the modesof its corresponding piecewise-linear profile. The regular mode in the smoothprofile was identified as the one least sensitive to the numerical resolution,while the singular modes displayed high sensitivity. Here we provide a physicalinterpretation using a wave interaction approach for understanding thestructure and behavior of both the regular and singular modes. The regularmodes are the interfacial Rossby waves located at the concentrated meanvorticity gradient of the shear profile. In contrast, the singular modes resultfrom a one way phase-locking interaction between singular vorticitydisturbances, passively advected by the mean flow at different levels of theprofile, and the interfacial Rossby waves. We show that this one wayinteraction can also lead to a sustained non-modal growth of the interfacialRossby waves that cannot be captured by standard eigenvalue analysis.

Wave interactions in neutrally stable shear layers: regular and singular modes, and non-modal growth