a multiple purpose optical instrument for studies of short steep water waves
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A Multiple Purpose Optical Instrument for Studies of Short Steep Water WavesJin Wu, J. M. Lawrence, E. S. Tebay, and M. P. Tulin Citation: Review of Scientific Instruments 40, 1209 (1969); doi: 10.1063/1.1684201 View online: http://dx.doi.org/10.1063/1.1684201 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/40/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Instabilities of steep short-crested surface waves in deep water Phys. Fluids 11, 1679 (1999); 10.1063/1.870029 Deepwater gravity wave instabilities at large steepness Phys. Fluids 31, 1286 (1988); 10.1063/1.866757 Numerical computation of steep gravity waves in shallow water Phys. Fluids 22, 1868 (1979); 10.1063/1.862492 Optical Depth Gauge for Laboratory Studies of Water Waves Rev. Sci. Instrum. 37, 1460 (1966); 10.1063/1.1720019 Instrument for Measuring Water Waves Rev. Sci. Instrum. 30, 674 (1959); 10.1063/1.1716720
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AGING OF G-M TUBES 1209
during the Geiger discharge. The stability W", of the molecular ion of the best known quench gas C2H 50H against fragmentation is very low (W m=0.070); also H 20 and CO2 are formed during operation of the counterY By ionization and fragmentation, they form to a great extent the. electronegative radical 0.24 On the basis of these results, it can be concluded that from the different vapors described in the literature1Q-15.27-31 and investigated for
27 W. D. Spatz, Phys. Rev. 64,236 (1943). 28 K. H. Morganstern, C. L. Cowan, and A. L. Hughes, Phys. Rev.
74, 499 (1948). 211 D. Blanc, J. CaM, and C. Lasalle, J. Phys. Radium 20, 43A
(1959). 30 R. Seidl, Czech. J. Phys. 9, 517 (1959). 31 0. Riedl, Nature 186, 876 (1960).
THE REVIEW OF SCIE:-.rTIFIC INSTRUMENTS
their quenching capacity, C2H 5CN gives the best results. This is shown in Table III.
All the aging phenomena mentioned in the first paragraph, except for the large increase of the plateau slope, are present after registration of 2 X 108 counts. These phenomena are neutralized by glowing the anode wire. After each operation we received with this simple method a new counter! A registration possibility of 109 counts seems, nevertheless, to be a maximum because after five glowings the counter indeed shows abnormalities which are probably caused by an increased photosensitivity of the cathode.
The authors wish to thank Professor Dr. P. Mortier for his helpful discussions about the discharge mechanism.
VOLUME 40. NUMBER 9 SEPTEMBER 1969
A Multiple Purpose Optical Instrument for Studies of Short Steep Water Waves
JIN Wu, J. M. LAWRENCE,* E. S. TEBAY, AND M. P. TULIN
Hydronautics, Incorporated, Laurel, Maryland 20810
(Received 10 April 1969; and in final form, 16 May 1969)
An optical instrument, utilizing a light reflection principle, has been designed which is capable of determining not only surface slope, but also surface curvature distribution. This instrument has been successfully tested in laboratory studies of wind generated waves. Some sample results are included to illustrate the applicability of the hstrument.
INTRODUCTION
RIPPLES riding on the top of gravity waves are typical of wind generated waves and make detailed
wave measurement extremely difficult. Since the height of the ripples is only a fraction of that of the gravity waves, a conventional capacitance or conductivity type wave gauge is not sensitive enough to provide a quantitative measurement of the superimposed wavelet. In addition, the capillary effect which produces a meniscus around the sensor, and the viscous effect which maintains a water film along the unsubmerged portion of the sensor make the measurement even more inaccurate. Recently, extensive work has been performed to determine the statistical properties of the microstructure of the air-sea interface (pattern of wavelets) under various wind conditions. In addition to the fundamental interest of the problem, the practical aspect of the study is that this microstructure governs the reflection and the scattering of acoustic, light, and other electromagnetic waves impinging on the interface.
A few optical methods have been adopted in the past for determining the microstructure of the wind disturbed
* Present address: Instrumentation Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
water surface; these include the photographic method of Schooley! and of Cox and Munk2 and the light refraction method of Cox.3 However, the photographic method so far developed involves rather tedious data analysis and, moreover, is not completely apt for laboratory application. Owing to the limited fetch, the water surface structure in the laboratory wind wave tank lacks spatial homogeneity, which is required for the photographic method. In the light refraction method, the apparatus consists of submerged parts which offer obstruction to waves and are rather difficult to construct; in addition, the under tank illumination required is especially inconvenient for a deep wind wave tank which is appropriate to simulate the air-sea interface for more advanced studies. Finally, both the photographic and light refraction methods are seriously hampered by the occurrence of transverse slopes (slopes in a direction normal to the one being measured).
The present instrument, utilizing a light reflection principle, is capable of determining not only the surface
1 A. H. Schooley, J. Opt. Soc. Amer. 44, 37 (1956). 2 C. S. Cox and W. H. Munk, "Slopes of the Sea Surface Deduced
from Photographs of Sun Glitter," Vol. 6, No.9, Bull. of the Scripps Institute of Oceanography, University of California Press, 1956.
a C. S. Cox, J. Marine Res. 16, No.3, 199 (1958).
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1210 WU ET AL.
FIG. 1. General view of optical instrument and support. A-light-signal receiver and adjustment assembly; B-light source and adjustment assembly; Ccross beam and arm unit; D-hinge-join t support; E-angle indicator; and F-water surface.
slope distribution, but offers higher resolution, freedom from transverse slope effect, and also, more importantly, is capable of determining the surface curvature distribution (distribution of facet size); the latter may be essential for an adequate description of the interface microstructure. Further, its application is not limited to the study of wind waves; a wide variety of uses involving the determination of the roughness of either a liqui4 or a solid surface can be foreseen.
DESCRIPTION
The optical instrument consists essentially of a light source (B) and a photomultiplier tube (A). They are supported by a cross beam and arm unit (C) which can be set at any desired angle by swinging the arm around the hinge joints (D) (see Fig. 1). One on either side of the wave tank, the hinge joints (D) are located at the elevation of the water surface (F). The light focused on the water surface at the imaginary axis passing through the center of the hinge joints is reflected into a telescope, which focuses an image of the water surface in front of the photomultiplier tube. Consequently, the photomultiplier tube receives light signals only when the angle of the sloping water surface from the horizontal is the same as the angle of the plane containing the light source and the telescope from the vertical.
The light, a cylindrical lamp, is focused by a rectangular shaped, plano-convex, cylindrical lens to produce a long narrow beam on the water surface. The maximum angle of inclination which produces an output is determined by the length of the light beam in the direction of measurement. To meet the experimental objective, the light box is so arranged that the shorter side of the beam is aligned in the direction of interest. The bandwidth of the instrument can be preset as desired and can also be checked by calibrating it over the calm water surface (tilting the swing arm from the vertical plane). A satisfactory sharp "cutoff" is shown in Fig. 2 on both margins of the calibration curve obtained with our present instrument for the determination of longitudinal slopes.
It is readily seen that, for example, when the instrument is set in the vertical plane, the light signal is continuous and saturated as long as the angular change of the wavy
water surface from one face (downwind) to the other (upwind) is less than the bandwidth of the instrument. If the angular change is greater than the bandwidth, the signal becomes discontinuous and the period of the signal is the time required for the detectable slope to make its complete pass under the instrument. As the angular change further increases or the surface curvature further increases, the signal becomes more and more like a short pulse.
For the present instrument, the focal spot of the telescope on the water surface is 0.7 mm in diameter. The image of this finite size spot is completely bright only when the water surface curvature is smaller than a certain value. Otherwise, the curved surface reflects part of the impinging light away from the telescope and leaves the image partially dark with its bright parts elongated (nearly oval shaped). Since the light is uniformly bright within the spot, the intensity of the light signal or the height of the previously mentioned pulse should be proportional to the ratio between the bright portion and the total area of the image. Consequently, the surface curvature can be detected from the pulse height.
Simple calculations have been made along with a calibration test consisting of passing cylinders, with the same kind of reflecting surface but with various radii, under the instrument. The longitudinal axis of the cylinder is always parallel with the same axis of the lamp. From the geometry in Fig. 3, the following relationships can be
1.0
0.'
0,6 •
~ 0.2
\ t,
\ -1.0 -0.5 0.5 1.0
ANGlfOf INCUNATION, l<kg'.,,,)
FIG. 2. Angular response of optical instrument.
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WAVE STUDIES 1211
obtained for a curved surface with radius of curvature R:
[ Ll-R COSa ] [Lt-R COSa ]
2a=cot-1 -cot-1
w/2+Rsina d/2+Rsina (1)
for a convex surface, and
[ Ll+R COSa ] [Lt+R COSa ]
2a=cot-1 +COC1
w/2+R sina d/2+R sina (2)
for a concave surface, where d is the diameter of the pinhole located in front of the photomultiplier, w is the effective width of the plano-convex cylindrical lens for focusing the light, and L t and L! are the distances from the telescope and the light box lens to the mean water surface, respectively. Only single reflections are considered.
By choosing the size of the pinhole to be much smaller than the beamwidth of the light and by putting the instrument away from the surface (for the present setup, W/d9400 and L t/W9L1/W950), we can show that the second term on the right of Eqs. (1) and (2) is much smaller than the first term in each respective equation. In other words, by the proper setting of the distance between the instrument and the water surface (L1»R) , both Eqs. (1) and (2) can be approximated by
a=i cot-1[L1/(w/2)]. (3)
Hence, the response of the instrument to surface curvature is essentially the same for both concave and convex surfaces.
If we designate r as the radius of the focal spot of the telescope on the water surface, the degree of saturation of the light signal (s= 1 for saturated signal) can be shown as
where h=R sina
CONVEX SURFACf CONCAVE SURfACE.
FIG. 3. Principles for determining surface curvature.
I.e
o 0 0 0-1 o
o o
o o
RAD1US OF CURVA.TURE - <om
FIG. 4. Response of optical instrument to water surface curvature. o--experiments, ---theory.
I
is the half-width of the bright portion of the water surface image (see Fig. 3). Of course, the radius of the focal spot of the telescope on the water surface, r, depends upon the diameter of the pinhole, d, as well as on the characteristics of the telescope lens. The calibrated response for the present setup, as well as those obtained directly from Eqs. (3) and (4), is plotted in Fig. 4. The scattering of the calibration points is believed to be the result of local deflects on the calibration cylinder.
The ripples on wind waves are relatively long crested in comparison with their wavelengths, as well as with the size of the focal spot of the telescope on the water surface. In a laboratory tank, these ripples move with the wind and have their crests approximately normal to the wind direction. If anyone of the foregoing conditions is not realized, the present setup is not directly applicable for determining the surface curvature accurately. However, this setup can be easily modified by merely replacing the sheet type light source with a column type source.
In summary, surface slope measurements are made with the instrument set at different angles of inclination. The relative frequencies of occurrence of various water surface slopes can thus be determined. As for the determination of the surface curvature, the relative frequency of occurrence of light pulses with their height at various degrees of saturation are determined. The instrument, in this latter case, is set at a fixed desired inclination.
EQUIPMENT
The block diagram of the apparatus is shown in Fig. 5. The light source is a 1500 W incandescent type lamp, with a filament approximately 18 em long. The photomultiplier tube is a nine stage, side-on unit with S-4 spectral response. The high voltage power supply is adjustable so that adequate sensitivity with minimum dark current noise can be obtained. The signal-to-noise ratio is further enhanced by locating the electrometer amplifier near the photomultiplier. The low output impe-
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MIOH vOt.l"Gt: POWf~
sUPPLY
dance of the amplifier makes it suitable for driving the long cable to the instrumentation.
The output of the electrometer is comprised of irregularly shaped pulses. This is due to the nature of the surface waves and of the optical system which was discussed in detail earlier. These pulses vary from 0 to 10 V in amplitude and have durations of a few milliseconds. However, the pulse height analyzer (ND-ll0 128-channel analyzer
SIGNAL 11 ;::::;:::; ~ THRESHOlD
SCHMITT TRIGGER ~
°LJ T'~
T/H AMPlITUDE r!fl "HEIGHT~ ~ __ J L ___ _
---- INPUT TO PULSE ANAl VZER
"TIMEn : T/H AMPlITUDE ~
___ J
FIG. 6. Pulse shape and timing diagram of pulses passing various stages of pulse conditioner.
FIG. 5. Block diagram of optical instrument.
manufactured by Nuclear Data, Inc.) requires pulses of much shorter periods and places very stringent requirements on the risetime. The pulse conditioning circuit shown in Fig. 5 is thus required.
The pulse conditioner is capable of analyzing both pulse height and pulse width (pulse period). In both modes, the signal activates the Schmitt trigger. This in turn sets the binary and opens electronic switch No. 1. In the height mode, the track hold amplifier output is compared with the incoming signal. When the input drops, the amplifier is put in hold. In other words, the amplifier tracks the signal to its maximum value and holds this yalue until it is reset. On the other hand, when the signal drops below the threshold of the Schmitt trigger, monostable 71 is started. This closes electronic switch No.2 for 5 ~sec. During this time the amplitude of the track hold amplifier is gated to the pulse height analyzer as a pulse with a suitable width and risetime. At the end of this time, 72 is started again to reset the binary and to close electronic switch No. 1. By doing so the track hold amplifier is reset until a new pulse is received.
In the time mode, the operation is identical except that the Schmitt trigger controls a ramp generator, which is tracked to convert time to amplitude. Consequently, the amplitude gated to the pulse height analyzer is proportional to the signal pulse duration. The pulses described above, from the signal to the pulse height analyzer, are shown in Fig. 6. The widths of 71 and 72 are exaggerated for clarity.
The pulses are sorted according to either their heights or their periods and are directed to the 128-channel pulse height analyzer, which is a very versatile instrument. It
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WAVE STUDIES 1213
has various modes of operation and of readout. The data are stored digitally and can be read out digitally, displayed on an oscilloscope, or plotted on an X-V plotter. It can also be plotted in linear as well as in semilog coordinates.
DATA
With the aid of the optical instrument, laboratory investigations of the microstructure of the air-water interface have been conducted in the Hydronautics wind-wave tank. The pulse number study was performed before the completion of the pulse analyzing system. During this phase of the study, the number of pulses or the number of occurrences of a particular slope for a given period was counted by a digital counter. At each inclination of the instrument, more than 30 sets of readings are recorded, each set consisting of a count of the number of light pulses occurring during a period of 10 sec. The average value of the pulse number per 10 sec, as well as the standard deviation from the average value, is calculated and plotted vs the angles of inclination in Fig. 7 (a). A short vertical straight line accompanying each data point indicates the value of the standard deviation around that point. The reliability of the data is reflected from the small values of the standard deviations.
Many ways can be adopted to interpret the data. For example, the area under the data points can be integrated by means of Simpson's rule to determine the median value. Around this median value, the data points for each wind velocity can then be normalized. The normal distribution curve, found on the basis of the least squares principle, is drawn as the continuous line shown in Fig. 7 (a). It is now seen that the data points follow essentially the Gaussian distribution and that the nearly normal distributed data are skewed at low wind velocity and peaked at high wind velocity. The skewness of the data points toward the downwind direction at low wind velocities reveals that more capillary waves are riding on the downwind face than those on the upwind face. To substantiate this observation, the light pulses were recorded on a visicorder simultaneously with the output of a resistance wave height gauge placed 3 mm transversely from the telescope focal point at the water surface. The location of the light pulse relative to the wave height profile shown on the records corresponds physically to the relative position of the capillary waves along the basic wave profile.
After completion of the pulse analyzing system, the following studies have been conducted.
(a) Surface slope studies. The pulse is sorted according to its period and is directed to the corresponding channel of the pulse analyzer. The numbers of pulses are then accumulated in various channels for a certain counting interval. A sample result, indicating the pulse period distribution and monitored on the 'scope, is shown in Fig.
WINO -L PlANE CONiAINING / OI'TtCAlINSHUMfN;
V. '\ -/:J I e
\.--'
\' -, 'T
""""WAfER SURfACE ~ DHlNHlON SKETCH
O!Sr~ISlJT10N Of PULSf ~t~IODS OR Of Put,f >lE!GH!S
PULSE pERIODS h~c) OR PULSE HEIGHT (~'Ht)
DHINITlONSKiTCH
-45" ,,' SAMPlfRESUl1S
(a)
-,
- -,
~ , ,-
(b)
FIG. 7. Sample results of surface slope and surface curvature studies. (a) Pulse number studies, U 0 is the wind velocity and f is the relative frequency of occurrence. (b) Surface slope and surface curvature studies.
7 (b). Repeating this operation by setting the optical instrument at various angles of inclination and integrating the area under the pulse period distribution curve, one can determine the relative frequency of occurrence of a particular water surface slope as a fraction of the counting interval. This set of data, a time fraction, replaces the previous data, a number fraction, plotted in Fig. 7 (a). Besides the data analysis suggested previously, the root mean square water surface slope, the most important parameter characterizing the wind disturbed water surface, can also be determined.
(b) Surface curvature studies. Instead of period, the pulse is now sorted according to its height and is directed to the corresponding channel of the pulse analyzer. At present, the numbers of the pulses are accumulated in various channels. For the refined system now under construction, the period of the pulse is compared first with a preset time interval (say 1/1000 sec), and the multiple of the pulse period over the preset time interval is counted in the respective channel. Sample results, monitored on the 'scope, are in the same form as those of surface slope studies. From the distribution curve of surface curvature, various statistical properties can be determined. This study can be performed by setting the optical instrument at the vertical position or at other positions as desired.
ACKNOWLEDGMENTS
The authors wish to thank S. F. Wan, J. Bosque, and v. Iorio for their work in designing, constructing, and calibrating various parts of the instrument. Sponsorship of part of this research by the Office of Naval Research under Contract No. Nom 3688(00) is gratefully acknowledged.
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