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Effect of depth discontinuity on interfacial stability of tangential-velocity discontinuity in shallow-water flow

  • It is well known as the Kelvin-Helmholtz instability (KHI) that an interface of tangential velocity discontinuity is necessarily unstable, regardless of the velocity difference's strength. However, the KHI is suppressed for shallow water flows if the Froude number, defined by the ratio of the velocity difference to the gravity wave's speed, is sufficiently large. In this investigation, we examine the effect of the depth difference of two fluid layers on the KHI. The depth difference enhances instability. Given the Froude number in the instability range, the growth rate sensitively depends on the depth ratio and increases monotonically with the depth ratio difference from unity. The critical value of the Froude number for stabilization varies with the depth ratio and attains the minimum value √8 for equal depth. This behavior is verified by asymptotic analysis.
Author:Thi Thai LeORCiD, Yasuhide FukumotoORCiD
Document Type:Article
Parent Title (English):Physics Letters A
First Page:128073
Year of first publication:2022
Published in:Physics Letters A
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