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Title: Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field

Here, 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.
Authors:
ORCiD logo [1] ;  [1]
  1. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
Publication Date:
Grant/Contract Number:
NA0002382
Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 826; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Research Org:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; baroclinic flows; instability
OSTI Identifier:
1434324

Prathama, Aditya Heru, and Pantano, Carlos. Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field. United States: N. p., Web. doi:10.1017/jfm.2017.511.
Prathama, Aditya Heru, & Pantano, Carlos. Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field. United States. doi:10.1017/jfm.2017.511.
Prathama, Aditya Heru, and Pantano, Carlos. 2017. "Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field". United States. doi:10.1017/jfm.2017.511. https://www.osti.gov/servlets/purl/1434324.
@article{osti_1434324,
title = {Inviscid linear stability analysis of two vertical columns of different densities in a gravitational acceleration field},
author = {Prathama, Aditya Heru and Pantano, Carlos},
abstractNote = {Here, 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.},
doi = {10.1017/jfm.2017.511},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 826,
place = {United States},
year = {2017},
month = {8}
}