Question: Insert gravity into the analysis of the Kelvin-Helmholtz instability (with the uniform gravitational acceleration g pointing perpendicularly to the fluid interface, from the upper +

Insert gravity into the analysis of the Kelvin-Helmholtz instability (with the uniform gravitational acceleration g pointing perpendicularly to the fluid interface, from the upper “+” fluid to the lower “−” fluid). Thereby derive the dispersion relation (14.86).

k P+V P_P+ - + [* - k P+ +P_ P+ +P_

k P+V P_P+ - + [* - k P+ +P_ P+ +P_ P+P_ (P+ +p_) 1/2 (14.86)

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