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Schlieren interferometry applied to a gravity wave in a density-stratified liquid

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Abstract

A stably density-stratified liquid is produced in a rectangular glass tank by variation of the concentration of salt in water as a function of height. The glass tank is placed into the parallel beam of a schlieren interferometer with Wollaston prism adjusted to produce straight vertical fringes. A gravity wave of the cross wave type is excited and the resulting periodically deforming fringes are recorded by taking photographs. A method is developed to obtain from the fringe patterns results about propagation of the wave in space and time and about amplitude attenuation. The results are compared with the linear theory of Thomas and Stevenson (1972) and excellent agreement is found within the limits of the linear approach.

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Abbreviations

a :

amplitude factor

A :

amplitude of body

b :

image distance

C, S :

functions of η

d :

distance of interfering rays

E :

envelope of fringes

f :

focallength

g :

gravitational constant

g :

object distance

k :

integration variable K constant

l :

tank width

L :

characteristic length, Eq. (6)

M :

magnification factor

n :

refractive index

Re :

Reynolds number

s :

fringe width

Δs :

fringe displacement

t :

time

V :

volume flux

w :

distance between Wollaston prism and focal point

X S :

distance between x=0 and body

x, y, z :

coordinates

β:

prism constant

ε:

small parameter, Eq. (4)

η:

similarity coordinate

θ:

angle

λ:

wavelength of lightsource

ν* :

kinematic viscosity at y 0=0

ξ:

fluid displacement in x-direction

ϱ:

density

φ:

amplitude function

ω:

excitation frequency

0:

static values

s :

salt

w :

water

References

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  • Merzkirch, W. 1974: Flow visualization. New York: Academic Press

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  • Mowbray, D. E. 1967: A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1–16

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  • Sernas, V. 1977: The Wollaston prism schlieren interferometer. Von Karman Institute Brussels, Lecture Series 96

  • Stevenson, T. N.; Woodhead, T. I.; Kanellopulos, D. 1983: Viscous effects in some internal waves. Appl. Sci. Res. 40, 185–197

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Authors and Affiliations

  1. Lehrstuhl für Strömungslehre, Universität Ėssen, D-4300, Essen, Germany

    F. Peters

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  1. F. Peters
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Peters, F. Schlieren interferometry applied to a gravity wave in a density-stratified liquid. Experiments in Fluids 3, 261–269 (1985). https://doi.org/10.1007/BF00281771

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  • DOI: https://doi.org/10.1007/BF00281771

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