The purpose of this note is to present a sketch of the inexpensive Moire fringe technique, which provides a quick and easy visualization of concentration gradients and which can be used for quantitative measurements…

Baker, D. James, Jr.

English

Yale University

      P.O. BOX 208118 | NEW HAVEN CT 06520-8118 USA | PEABODY.YALE. EDU   JOURNAL OF MARINE RESEARCH The Journal of Marine Research, one of the oldest journals in American marine science, published important peer-reviewed original research on a broad array of topics in physical, biological, and chemical oceanography vital to the academic oceanographic community in the long and rich tradition of the Sears Foundation for Marine Research at Yale University.  An archive of all issues from 1937 to 2021 (Volume 1–79) are available through EliScholar,  a digital platform for scholarly publishing provided by Yale University Library at  https://elischolar.library.yale.edu/.  Requests for permission to clear rights for use of this content should be directed to the authors, their estates, or other representatives. The Journal of Marine Research has no contact information beyond the affiliations listed in the published articles. We ask that you provide attribution to the Journal of Marine Research.  Yale University provides access to these materials for educational and research purposes only. Copyright or other proprietary rights to content contained in this document may be held by individuals or entities other than, or in addition to, Yale University. You are solely responsible for determining the ownership of the copyright, and for obtaining permission for your intended use. Yale University makes no warranty that your distribution, reproduction, or other use of these materials will not infringe the rights of third parties.  This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. https://creativecommons.org/licenses/by-nc-sa/4.0/   The Use of Moire Fringes tn Laboratory Oceanography' D. James Baker, Jr. Pierce Hall, Harvard University Cambridge, Massacliusetts ozr38 The purpose of this note is to present a sketch of the inexpensive Moire fringe technique, which provides a quick and easy visualization of concentra-tion gradients and which can be used for quantitative measurements. This technique is one of the clear demonstrations of isolated,geophysical phenomena that form an integral part of the educational curriculum, both in lectures and in the laboratory. Although the technique is well known in other contexts (e.g., see Nishijima and Oster 1964) and has been used to some extent i·n various oceanographic applications, it has not been fully exploited either in geophysical laboratory studies or instruction. It deserves a wider use. Details for the use of this technique, bibliographies, and corrections for various types of error are available in the literature (Oster et al. 1964, Van Oss 1964). Here the use of this inherently simple technique is outlined, and photographs from a typical experimental arrangement [similar to the thermo-cline-mixing experiment of Cromwell ( 1960 )] are presented to show the value of the technique as a visualization tool for a variety of experiments relevant to thermocline maintenance and turbulent-mixing processes. The Moire fringes are produced by the illumination of two gratings placed on either side of a tank of fluid in which concentration gradients (of heat, salt, etc.) are to be studied as a function of position and time (Fig. 1 ). The rulings of the gratings (e.g., Ronchi rulings available from Edmund Scientific Company, or enlarged photographs of these rulings)2 are placed at a small angle to one another. The system is illuminated from behind by either a point source or, better, a diffuse source. Since the position of the resultant Moire fringes is sensitive only to changes in the concentration gradient, homogeneous and linearly stratified solutions produce the same pattern. The pattern consists 1. Accepted for publication and submitted to press 19 May 1969. 2.. Useful films for this purpose arc Adlux photographic projection film (E. I. DuPont de Nemours & Co.) or Kodalith ortho type 3 (Eastman Kodak Co.). 361 Journal of Marine Research [ 2 7,3 screen ~"'7"7+--t--300---· observation point Figure I. The experimental arrangement. The Moire pattern• arc photographed at a diotancc of 300 cm, ueing a 300-mm telephoto lens. The gratings actually arc in contact with the tank. All dimeneione in cm. of a series of parallel straight lines whose separation is b/sin fJ, where b is the ruling spacing and (J is the angle between the gratings. Changes in the concen-tration gradients produce deviations from the initial straight lines. Fig. 2 illustrates the fringe pattern as produced in a system consisting of two layers of salt water whose densities are, respectively, 1.02 gm/cm3 and 1.07 gm/cm3. The horizontal deflection at the point z = Zo of a fringe away from its initial position is (Oster et al. 1964) Ax = cotO--- -/Y 2 1 (dn) 2 n (zo) dz z = z.' where Wis the distance between the gratings and n(z) is the index of refrac-tion of the liquid at point z. From tables of index of refraction vs concentra-tion [e.g., salinity (Cox 1965)] or index of refraction vs temperature, density gradients may be inferred from the fringe deflection. If the density is known for a given point, integration in the vertical direction provides the density as a function of vertical position. For example, in a two-layer system, the area under the deflected Moire fringe is proportional to the total-density difference between the layers. Changes in the specific gravity as small as I part in 103 may easily be observed with a vertical resolution of about 0.3 cm. An accuracy of10°/o is readily achieved. It must be emphasized that this technique averages over the thickness of the tank; thus, effects due to variations in density in the direction perpendicular to the two gratings may be ambiguous. Baker: Use of M oire Fringes Figure ' The Moire fringe pattern in a two-layer system. Upper-layer density = 1.03 gm/cm3, lower-layer density= 1.07 gm/ cm3. Gratings of 25 lines/inch used, with 0 = 0 .0 4 rad. Figure 3. 2 3 4 5 6 I 7 8 9 Deepening of the upper mixed layer (in i ti al density= 1.00 gm/cm3) by turbulent entrain-ment of fluid from the lower layer (ini tial density = 1.07 gm/ cm3) by propeller-blade stirrer. Photographs taken 8 sec, 22 sec, r, 2, 3, 4 , 5, 6, and ro minutes after sti rring began. Baker: Use of Moire Fringes The experimental arrangement provides a clear visualization of some oceanic effects-the deepening of the mixed layer by a gale (Francis and Stommel 1953), intensification of the temperature gradient at the bottom of a mixed layer (Cromwell and Reid 1956) by turbulent mixing, and the vari-able depth of the seasonal thermocline (Turner and Kraus 1967). Fig. 3 [an especially good example of "thermocline erosion" (Phillips 1966 )] illustrates the deepening of an upper mixed layer by turbulent entrainment of the fluid below. Early experiments of this type (Cromwell 1960) did not have the present advantage of visualizing the changing density structure in situ. The present experiment has proved successful as an undergraduate-laboratory ex-periment. Other laboratory experiments involving geophysical and turbulent phenom-ena, such as those by Turner (1968), Turner and Stommel (1964), and Rouse and Dodu (1955), are easily visualized and demonstrated with this technique. The reader is referred to those papers for a discussion of the geo-physical relevance of these experiments and the various modeling problems. The actual arrangement and details of a given demonstration or visualization will, of course, depend on the nature of the phenomena to be studied. Nigel Shevchik perf.9rmed the experiments described here. This work has been supported by grant NoNR 14-67-A-0298-0011 from the Office of Naval Research to Harvard University and by a grant from the Faculty Committee on Science Research Support of Harvard University. REFERENCES Cox, R. A. 1965. The physical properties of sea water. In Chemical Oceanography. Ed., J.P. Riley and G. Skirrow. Academic Press, New York. 712 pp. CROMWELL, TOWNSEND 1960. Pycnoclines created by mixing in an aquarium tank. J . mar. Res., I8 : 73-82. CROMWELL, TOWNSEND, and J . L. REID, JR. 1956. A study of oceanic fronts. Tellus, 8: 94-101. FRANCIS, J. R . D., and HENRY STOMMEL . 1953. How much does a gale mix the surface layers of the ocean? Quart. J. r. Meteor. Soc., 79: 534-536. NISHIJIMA, Y . and G . OSTER 1964. Moire patterns: their application to refractive index and refractive-index gradient measurements. J. opt. Soc. Amer., 54: 1-5. OSTER, G., M . WASSERMANN, and C. ZWERLING 1964. Theoretical interpretations of Moire patterns. J . opt. Soc. Amer., 54: 169-17 5· PHILLIPS, 0. M. 1966. The dynamics of the upper ocean. Cambridge University Press. 261 pp. RousE, H., and J. DoDu . . . . . 1955. Turbulent diffusion across a density d1scontmu1ty. La Homlle blanche, IO : 522- 532. Journal of Marine Research [ 2 7,3 TURNER,]. S. 1968. The behavior of a stable salinity gradient heated from below. J. fluid Mech., 33: 183-200. TURNER, J. S., and E. B. KRAUS 1967. A one-dimensional model of the seasonal thermocline I. Tellus, r9: 88-99. TURNER,]. S., and HENRY STOMMEL 1964. A new case of convection in the presence of combined vertical salinity and temper-ature gradients. Proc. nat. Acad. Sci., 52: 49-53. VAN Oss, C. J. 1964. Moire patterns for measuring refractive-index gradients. J. Sci. Inst., 4r : 227-228. 

The use of Moire fringes in laboratory oceanography

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The use of Moire fringes in laboratory oceanography

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