SUMMARY ~N T R O D U C T I O NA number of investigators have analysed wave records to determine statistical relations between the various parameters describing a particular record. For example Putz (1952) analysed 15 records from underwater pressure recorders in various depths of water between 45 and 90 ft off the California coast, and Seiwell (1948) carried out a series of analyses of similar records from the North Atlantic; more recently Watters (1953) has analysed pressure records made by an Admiralty wave recorder at Greymouth in New Zealand. From a theoretical approach Longuet-Higgins (1952) deduced relations between the root-mean-square wave height, the mean height of the highest one-third of the waves and the most probable height of the largest wave in a given interval of time. His results are in good agreement with those published by the investigators mentioned above.The National Institute of Oceanography has recently developed an instrument (Tucker 1952) which may be fitted to the hull of a ship below the water-line and which continuously records the water-level. A feature of the instrument is the elimination, by an ingenious device, of the ship's own vertical motion. When the ship is stopped the record may be expected to provide wave measurements more detailed and accurate than any obtained by eye estimation, no matter how experienced the observer. Such an automatic record can be made anywhere at sea. The instrument responds to waves with periods between 5 and 25 sec and within this range there is practically no attenuation of short-period waves such as is inherent in bottom pressure recorders. One of the instruments has been installed in a British Ocean Weather Ship, and through the kindness of the Director of the Meteorological Office and the Director of the National Institute of Oceanography a series of records, made three-hourly in February and March 1953, have been made available for analysis. This paper summarizes the results. As far as the writer is aware these are the first instrumental records of deep ocean waves to be analysed. METHOD OF ANALYSISThis was quite straightforward. The height H of each wave from crest to trough was measured to the nearest foot and the period T of each wave taken off the time scale on the record to the nearest second. The records include a few taken while the ship was moving slowly to regain station; parameters for these have been calculated but none of them has been plotted on the diagrams, nor have they been used when calculating ' best-fit' straight lines or correlation coefficients. They are included in the table of results for the sake of completeness. THE RESULTSThe analysed results are shown in Table 1, and plots showing the relation between various 138 records were made while the ship was stopped. The pairs of quantities have been drawn. parameters are defined as follows : G1Y
September 1969This document has been approved for public release e* f^-Vi.' its distribution is unlimited, .^/>Ot-r 71^ This document io nubjeefr-te^pixräi^xprnina)ltl.lOlS , Jlidnationals may rw made-only-with-pcieM-approvaLof -Air Force -Aere-Pfeputeien-JsafeeRttory-(AP.IEa2),»JWtighiPa«eMen=iAF'B»se^Ohiö-45433. ROCKET TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEEWOHER OF U n S" m E02CB mim when U. S. Government drawings specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any way supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.Qualified users may obtain copies of this report from the Defense Documentation Center.References to named commercial products in this report are not to be considered in any sense as an endorsement of the product by the United States Air Force or the Government. AEDCTR-69- ABSTRACTDesign characteristics and performance of a combustor for use as a high energy, ionized gas source in magnetohydrodynamic power generator studies are described. The liquid oxygen (LC»2)/JP-4 combustor was operated over a chamber pressure range from 240 to 300 psia and at a characteristic exhaust velocity efficiency of 91 ± 1 percent for oxidizer/fuel ratios ranging from 2. 0 to 3. 1. Combustor power output was approximately 17.5 to 20.5 megawatts (MW) over its range of operation. Provisions were incorporated into the design for injection of a saturated solution of water and cesium carbonate seeding agent into the thrust chamber to provide a high ion concentration in the exhaust gases.This document is subject to special export controls and each transmittal to foreign governments or foreign nationals may be made only with prior approval of Air Force Aero-Propulsion Laboratory (APIE-2), WrightPatterson AF Base, Ohio 45433.Ill AEDC-TR.69.167 CONTENTS
Both papers were presented together by Dr. M. S. Longuet-Higgins)Mr. D. E. CARTWRIGHT : As a corollary to Dr. Longuet-Higgins's talk, I wish to give an account of the analysis, and application to sea waves, of a probability distribution derived by S. 0. Rice in 1944 for the peak values of random noise. This distribution has the advantage over the Rayleigh distribution that it is valid not only for a narrow wave spectrum but for spectra of any width or shape; the appropriate probability curve for a given wave-record is one of a family of curves whose parameter is determined by the shape of the spectrum. It degenerates to the Rayleigh curve only if the spectrum is narrow, but it can also approach the Gaussian curve, and in general is intermediate in shape.To use this distribution it is necessary to re-define a ' wave-height ' as the height of a crest above, or the depth of a trough below, the mean level. The usual definition, as the vertical distance between a crest and the trough which precedes it, does not lend itself easily to mathematical treatment and, as yet, the distribution of wave heights so defined has been justified only for a narrow spectrum. As re-defined, a wave-height can of course be negative, if a crest occurs below the mean level, or a trough above, and Rice's distribution allows for this.The assumption made to justify the application of Rice's distribution is very general, namely that the form of the water surface is the linear resultant of a large number of sinusoidal components of different period in random phase relation. It follows that the ordinates and derivatives of the wave surface are distributed normally, and it is then a simple step to derive the distribution of heights of crests and troughs.It is clear from the slides shown that the theoretical curves give a very good fit to wave heights recently measured in the R.R.S. Discovery II and also to some amplitudes of ship motion.It would probably apply equally well to the distributions of slopes, velocities, and accelerations involved, and I would suggest that this probability distribution, being based on very general assumptions, might fit other fluctuating quantities of meteorological interest. A fuller account will be published in due course. 630
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