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Experiments in Fluids

, Volume 3, Issue 5, pp 261–269 | Cite as

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

  • F. Peters
Originals

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.

Keywords

Attenuation Excellent Agreement Gravity Wave Linear Theory Fringe Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

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

XS

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 y0=0

ξ

fluid displacement in x-direction

ϱ

density

φ

amplitude function

ω

excitation frequency

Subscripts

0

static values

s

salt

w

water

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References

  1. Debler, W. R.; Vest, C. M. 1977: Observation of a stratified flow by means of holographic interferometry. Proc. R. Soc. Lond. A. 358, 1–16Google Scholar
  2. Görtler, H. 1943: Über eine Schwingungserscheinung in Flüsig-keiten mit stabiler Dichteschichtung. ZAMM 23, 2Google Scholar
  3. Hodgman, C. 1977: Handbook of chemistry and physics. Cleveland: Chemical RubberGoogle Scholar
  4. Lighthill, I. 1978: Waves in fluids. London: Cambridge University PressGoogle Scholar
  5. Merzkirch, W. 1974: Flow visualization. New York: Academic PressGoogle Scholar
  6. 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, 1–16Google Scholar
  7. Sernas, V. 1977: The Wollaston prism schlieren interferometer. Von Karman Institute Brussels, Lecture Series 96Google Scholar
  8. Stevenson, T. N.; Woodhead, T. I.; Kanellopulos, D. 1983: Viscous effects in some internal waves. Appl. Sci. Res. 40, 185–197Google Scholar
  9. Thomas, N. H.; Stevenson, T. N. 1972: A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • F. Peters
    • 1
  1. 1.Lehrstuhl für StrömungslehreUniversität ĖssenEssenGermany

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