Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Doostmohammadi, A. and Ardekani, A. M. 2014. Reorientation of elongated particles at density interfaces. Physical Review E, Vol. 90, Issue. 3,


    ×
  • Journal of Fluid Mechanics, Volume 690
  • January 2012, pp. 571-606

Stratified flows with vertical layering of density: experimental and theoretical study of flow configurations and their stability

  • Roberto Camassa (a1), Richard M. McLaughlin (a1), Matthew N. J. Moore (a2) and Kuai Yu (a3)
  • DOI: http://dx.doi.org/10.1017/jfm.2011.476
  • Published online: 25 November 2011
Abstract
Abstract

A vertically moving boundary in a stratified fluid can create and maintain a horizontal density gradient, or vertical layering of density, through the mechanism of viscous entrainment. Experiments to study the evolution and stability of axisymmetric flows with vertically layered density are performed by towing a narrow fibre upwards through a stably stratified viscous fluid. The fibre forms a closed loop and thus its effective length is infinite. A layer of denser fluid is entrained and its thickness is measured by implementing tracking analysis of dyed fluid images. Thickness values of up to 70 times that of the fibre are routinely obtained. A lubrication model is developed for both a two-dimensional geometry and the axisymmetric geometry of the experiment, and shown to be in excellent agreement with dynamic experimental measurements once subtleties of the optical tracking are addressed. Linear stability analysis is performed on a family of exact shear solutions, using both asymptotic and numerical methods in both two dimensions and the axisymmetric geometry of the experiment. It is found analytically that the stability properties of the flow depend strongly on the size of the layer of heavy fluid surrounding the moving boundary, and that the flow is neutrally stable to perturbations in the large-wavelength limit. At the first correction of this limit, a critical layer size is identified that separates stable from unstable flow configurations. Surprisingly, in all of the experiments the size of the entrained layer exceeds the threshold for instability, yet no unstable behaviour is observed. This is a reflection of the small amplification rate of the instability, which leads to growth times much longer than the duration of the experiment. This observation illustrates that for finite times the hydrodynamic stability of a flow does not necessarily correspond to whether or not that flow can be realised from an initial-value problem. Similar instabilities that are neutral to leading order with respect to long waves can arise under the different physical mechanism of viscous stratification, as studied by Yih (J. Fluid Mech., vol. 27, 1967, pp. 337–352), and we draw a comparison to that scenario.

Copyright
Corresponding author
Email address for correspondence: moore@cims.nyu.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.N. Abaid , D. Adalsteinsson , A. Agyapong & R. M. McLaughlin 2004 An internal splash: falling spheres in stratified fluids. Phys. Fluids 16 (5), 15671580.


4.R. Camassa , C. Falcon , J. Lin , R. M. McLaughlin & N. Mykins 2010 A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number. J. Fluid Mech..

5.R. Camassa , C. Falcon , J. Lin , R. M. McLaughlin & R. Parker 2009 Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime. Phys. Fluids 21, 031702.

6.R. Camassa , R. M. McLaughlin , M. N. J. Moore & A. Vaidya 2008 Brachistochrones in potential flow and the connection to Darwin’s theorem. Phys. Lett. A 372, 67426749.

9.K. R. Helfrich & J. A. Whitehead 1990 Solitary waves on conduits of buoyant fluid in a more viscous fluid. Geophys. Astrophys. Fluid Dyn. 51, 3552.

10.H. E. Huppert 1982 Flow and instability of a viscous current down a slope. Nature 300, 427429.

11.H. E. Huppert , R. S. J. Sparks , J. A. Whitehead & M. A. Hallworth 1986 Replenishment of magma chambers by light inputs. J. Geophys. Res. 91 (B6), 61136122.


15.T. W. Kao 1965b Role of the interface in the stability of stratified flow down an inclined plane. Phys. Fluids 8, 21902194.


18.S. MacIntyre , A. L. Alldredge & C. C. Gottschalk 1995 Accumulation of marine snow at density discontinuities in the water column. Limnol. Oceanogr. 40 (3), 449468.


23.D. R. Scott , D. J. Stevenson & J. A. Whitehead 1986 Observations of solitary waves in a viscously deformable pipe. Nature 319 (27), 759761.




27.J. S. Turner 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17, 1144.

29.C. S. Yih 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321334.


Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Type Description Title
UNKNOWN
Supplementary Materials

Camassa et al. supplementary material
Supplementary data

 Unknown (216 KB)
216 KB