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The flow field of two stratified liquids in the presence of interfacial waves

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Abstract

Generated interfacial waves are under investigation in this paper. The flow field and the movement of the interface between two stratified newtonian fluids will be considered. Cylindrical geometry is examined. All results are given in an analytical form. With the help of an algebraic computation programm it is possible to reduce computation time for parameter studies. The dependence of the wavenumber of several dimensionless groups are studied intensively.

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Abbreviations

a( j), b( j):

integration constants

 :

wave amplitude at the origin

g :

acceleration due to gravity

h :

interface distortion

i :

imaginary unit

J 0, J 1 :

zero/first order Bessel function

k 1, k 1(j), k 2(j):

complex wave numbers

p(j):

pressure

t :

time

v jr , v jz :

velocity component in r and z direction

Re(j), Bo, We :

Reynolds, Bond and Weber number

R ρ :

density ratio

λ :

wavelength

µj, v j :

dynamic/kinematic fluid viscosity

ρj :

fluid density

σ :

interfacial tension

τ :

non dimensional time

Φj :

potential function

ψj :

stream function

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Author information

Authors and Affiliations

  1. University of Bremen, FB 4, P.O. Box 33 04 40, D-28334, Bremen, Germany

    U. Nordbrock

  2. Technische Universität München, D-85 350, Freising, Germany

    A. Delgado (Chair for fluid mechanics and process automation)

  3. Center of applied space technology and microgravity (ZARM), Hochschulring/Am Fallturm, D-28359, Bremen, Germany

    H. J. Rath

Authors
  1. U. Nordbrock
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  2. A. Delgado
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  3. H. J. Rath
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Additional information

Communicated by S. N. Atluri, 27 March 1996

J=1, 2, where the index 1 refers to the upper fluid and the index 2 refers to the lower fluid. In the text the asterisk indicates non dimensional quantities.

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Nordbrock, U., Delgado, A. & Rath, H.J. The flow field of two stratified liquids in the presence of interfacial waves. Computational Mechanics 18, 279–289 (1996). https://doi.org/10.1007/BF00364143

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