TY - JOUR

T1 - Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

AU - Prathama, Aditya Heru

AU - Pantano, Carlos

N1 - Publisher Copyright:
© 2017 Cambridge University Press.

PY - 2017/9/10

Y1 - 2017/9/10

N2 - We study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin-Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

AB - We study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin-Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

KW - baroclinic flows

KW - instability

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U2 - 10.1017/jfm.2017.511

DO - 10.1017/jfm.2017.511

M3 - Article

AN - SCOPUS:85029501592

SN - 0022-1120

VL - 826

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - R4

ER -