**PLEASE SCROLL TO THE BOTTOM OF THE PAGE FOR SERVICE INFORMATION AND DIRECTIONS**
Professor Marshall Peter Tulin died peacefully in his sleep at home in Santa Barbara, California, by his daughter's side, on Saturday, August 31, at 9:45 a.m. He was 93 years old.
Marshall was born in Hartford, Connecticut, on March 14, 1926, to William Wilbur Tulin
and Rose Cantarow Tulin. He grew up in Hartford where he was very close to his maternal grandmother Helenya Karp Cantarow who encouraged Marshall in his passion for airplanes & plane models as a young boy and for aerodynamics later on. Marshall entered Massachusetts Institute of Technology (M.I.T.) at 17. He eventually changed his major from aerodynamics to hydrodynamics, graduating at 20 in February 1946. He also did graduate studies at Brown University.
Marshall had a long and distinguished career. He started working for the National Advisory Committee for Aeronautics (N.A.C.A.) in Langley, Virginia; then for the David Taylor Model Basin (Washington, D.C.); while at the Office of Naval Research (O.N.R.), after having served as the scientific attaché in London, he developed a basic research program in Naval Hydrodynamics and also shared major responsibility for creating in 1956 the famous series of Symposia on Naval Hydrodynamics. In 1959, Marshall co-founded Hydronautics, Inc., a highly successful hydrodynamics research company with 100 employees where he served as Technical Director and Chief Scientist until 1982. He opened a branch of Hydronautics, Inc. in Israel that was mainly involved in developing advanced desalination techniques in order to provide Israel with more usable water.
Marshall is best known for his work on supercavitation ranging from the mathematical theory to the engineering design of highly powered propellers, his contributions in the field of non-linear bow wave effects including breaking, and his research on polymer flow additives for drag reduction. He holds half a dozen patents on various subjects. Marshall made many more contributions to the world through his work in eliminating pollution from water; in providing more usable water; in saving submarines in distress; in detecting submarines underwater from the air; and much more. He trained and taught ocean engineering students and scientists all over the world, in Italy, China, Russia, Eastern Europe, Japan, France, Israel, Scandinavia, Iceland, etc.
Marshall was a member or chairman of several important boards and committees (including the Rieger Foundation). Marshall was elected to membership of the National Academy of Engineering in 1979. A recipient of the prestigious University of California President Chair (1982-1987), Marshall was professor of Mechanical and Environmental Engineering at the University of California Santa Barbara and the founder and director of the Ocean Engineering Laboratory. One of the highest awards the Navy gives, the prestigious Distinguished Public Service Award was presented to Professor Marshall P. Tulin in 1994 by the Navy for his distinguished career and achievements. Marshall received an honorary doctorate from Tel Aviv University in Engineering in the year 2000 for his achievements/contributions worldwide.
Marshall was a much loved, admired, and respected son, grandson, father, brother, uncle, cousin, nephew, professor, scientist, colleague, ocean engineer. He was an independent thinker with a brilliant mind who used his gifts generously as a mentor, loyal friend, colleague, scientist, father, uncle to many, many people throughout the world. His passing is an irreplaceable loss to us all---he will be missed enormously by so many.
Marshall was pre-deceased by his beloved son Michael Alex, by his beloved sister Joan, his former wife Ella, his parents Bill & Rose, his Aunts Eleanore & Phyllis, his Uncles Max & Leon, his nephew Michael, his Uncle Pete & Aunt Freddie, his cousin Walter, & his two Uncles Abraham; and he is survived by his beloved daughter Leah and his beloved nieces & nephews Louise, Patricia, Pamela, Robert, Peter, and all their children, and his cousins Ellen, Jan, and Mary Tim.
There will be a Memorial Gathering at his home: 4356 Via Glorieta, Santa Barbara, California 93110, On Sunday, November 3rd, 2019 from 1:00pm to 8:00pm. Please bring your loving thoughts, stories, and memories to share of our beloved Marshall Peter Tulin and something he loved to eat. The Burial and Graveside Service, by Rabbi Steve Cohen, will be the next day, on Monday, November 4th, 2019, at 1:30pm at the Santa Barbara Cemetery, 901 Channel Drive, Santa Barbara, California 93108. Marshall will be buried beside his beloved son, Michael Alex Tulin.
Mathematical Approaches in Hydrodynamics
Edited by Touvia Miloh
Society for Industrial and Applied Mathematics, Philidelphia
To honor Professor Marshall P. Tulin on his sixty-fifth birthday. March 14, 1991, fluid mechanicians and applied mathematicians from nine countries have contributed the articles collected in this anniversary volume. Marshall has indeed had a remarkable scientific and engineering career, in governmental service, industry, private enterprise, and as a university professor. His many engineering accomplishments and scientific works are characterized by a unique and rare capability to combine deep physical understanding with a keen analytical ability aimed at solving practical problems. During the last four decades his main interest has been focused on the fascinating field of naval hydrodynamics. It is rather unfortunate that his many important, contributions to this subject have not been widely disseminated due to their appearance in classified reports or internal company reports.
One of Marshall’s greatest achievements for which he has established a world reputation, is his research on supercavitating flows and its application to propellers. He was elected to the National Academy of Engineering for this pioneering work in 1979. Other areas in which Marshall has made significant contributions are cavity flows, turbulent boundary layers, drag reduction, non-acoustic remote sensing of submarines, ship wave resistance, non-linear waves. breaking waves and internal waves. The title of this book, “Mathematical Approaches in Hydrodynamics,” and the diversity of the topics dealt with here reflect the spirit with which Marshall approaches the intriguing problems in naval hydrodynamics.
The idea of publishing this anniversary volume, instead of organizing a symposium to honor Marshall’s 65th birthday, was first conceived by Julian Cole, Jin Wu, and myself in September, 1989. Many of Marshall’s colleagues and friends from all over the world were invited to contribute a paper. The various papers are research, expository or survey oriented and have been arranged in thirteen parts in alphabetical order by author. Due to the space limitation, only scientists who have had close association and collaborated with Marshall during his career were invited to submit a paper. On behalf of the Editorial Committee, I apologize to those who were forgotten and whose names do not appear among the authors. The invited contributors have all responded with great enthusiasm to the idea of publishing this volume to honor Marshall. We thought, that the appropriate publisher for this book is the Society for Industrial and Applied Mathematics (SIAM) for whom Marshall has been actively involved for many years. We have again received a very favorable response from the Managing Director …
As the fourth American generation of Jewish family who had emigrated to New England from Russia circa 1890, Marshall Tulin was born on March 14, 1926 in Hartford, Connecticut. His family on either side was committed to higher education and included prominent professors of medicine and law, and an architect of international reputation. Highly encouraged by parents and teachers, he entered MIT in July 1943.
At MIT he profited from contact with a very fine faculty, including Dirk Struik, Philip Franklin, and Francis Sears. The heavy design orientation of the aeronautical engineering program gave him a lifelong taste and feel for design connections and implementation of advanced results.
After graduation in February 1946, he chose employment as a research engineer in the Langley Laboratory of the National Advisory Committee for Aeronautics (NACA). Assigned to the 8 foot (diameter) high speed tunnel, the work horse of the Compressibility Division, he took part in demanding, round the clock testing of the X-1 and DD558 transonic aircraft and novel transonic propellers; these aircraft piloted by Chuck Yeager, were slated to break the sound barrier as part of an aggressive NACA program led by John Stack. At night, he pursued graduate studies at the University of Virginia extension school run by Langley, where he later taught a course in compressible aerodynamics together with Dick Whitcomb, who was later to achieve fame for his invention and implementation of the area rule for the design of transonic aircraft. He served on many report review committees as part of the rigorous review process at Langley, and was fortunate to be influenced by renowned Langley aerodynamicists, including Antonio Ferri, Carl Kaplan, l.E. Garrick, Clinton E. Brown, Albert von Doenhoff, Adolf Rusemann, Sam Katzoff, and others.
Assigned to a small team, he was asked by John Stack to design insertable circular nozzles for the 8 foot tunnel so that the X-1 could be tested at low supersonic speeds before flight. These nozzles were considered very risky by some experts and represented a significant advance over past technology. He was asked to familiarize himself with the boundary layers, to devise methods of calculating their behavior in the throat and elsewhere, and to integrate these calculations with inviscid design calculations, which were based on characteristics in the supersonic region. The methods he devised involved obtaining experimental data on boundary layer parameters in the existing tunnel at high subsonic speeds. He took part in the installation and testing of nozzles for Mach numbers 1.1 and 1.2. These were highly successful, performing as designed, and they eventually supplied a wealth of valuable stability and control data on the low supersonic performance of the X-1 and other aircraft. These experiences led to a lifelong pursuit of goal -oriented research, based on both testing and theoretical analysis. In his propeller research, he became acquainted with the Goldstein factors, which were based on Sydney Goldstein’s brilliant mathematical analysis of the flow induced at the screw by the vortex wake. This, together with Garrick and Kaplan’s classic analysis of flutter aerodynamics, convinced him of the great power of mathematics as a tool for solving urgent engineering problems.
In 1947, he took leave from Langley for two months to attend a special session at the Graduate Division of Applied Mathematics (GDAM) at Brown University, to take courses given by Sydney Goldstein and C.C. Lin. In 1948, he returned to MIT on leave. While there, he took courses in applied mathematics and aerodynamics, served as a research assistant on a flutter project under Holt Ashley, and wrote a short thesis on unsteady laminar boundary layers including the case of a long flat plate under an impulsive start. His interesting result, that the starting point of the motion closely separates the steady Prandtl solution in front from the unsteady Rayleigh solution to the rear, led the way to later detailed studies by Keith Stewartson. In publishing this thesis work in the proceedings of an engineering meeting, he began a lifelong habit which made much of his work relatively inaccessible. Offered a Rockefeller Fellowship in Applied Mathematics at Brown University, in 1949 he left MIT with his master’s degree, and pursued courses at GDAM-Brown with Wally Hayes, Dan Drucker, Joe Diaz, and Ras Lee. After the outbreak of the Korean War, he left Brown to return to active Civil Service.
Instead of returning to Brown, he chose to work for the Navy, at the David Taylor Model Basin (DTMB) in Washington, D.C., where he was assigned to the Hydrodynamics Division and put in charge of a small group working on turbulence and frictional resistance research. His colleagues and the work environment in his division were excellent for long term goal-oriented research and provided him with an education in new subjects such as waves, acoustics, naval hydrodynamics and cavitation. As part of his group’s work, he designed and put into operation a low turbulence research wind tunnel containing a very long test section with deformable walls, and he supervised boundary layer and wake research. He took part in projects involving the first streamlined submarine designed for low drag, called the Albacore, which forever changed the design philosophy for the exterior lines and propulsion of naval submarines. Following a conversation with Paul Garabedian of Stanford University, he became interested in cavitating flows with long trailing cavities, which he eventually called supercavitating flows. After acquainting himself with the status of the theory in Garrett Birkhoff’s book on “Hydrodynamics”, he began his own developments.
Three of his accomplishments at DTMB have had a lasting worldwide influence. The first was to recognize that the viscous resistance of a ship model, both frictional and form drag, could be determined experimentally in a towing tank by a wake survey of the static and total pressures behind the ship, together with appropriate formulae. This method, already used in aerodynamics for wings, was believed unsuitable for ships because of wave generation, and it was his accomplishment to prove through mathematical analysis that the method was indeed applicable and to present appropriate formulae. This result, and its application has proved very useful. The second accomplishment was to recognize that supercavitating flows past thin bodies, especially lifting foils, were of importance for high speeds, and that they could be analyzed by linearized methods similar to those already used for thin airfoils. He developed his linearized theory of cavitating flows, showed that linearization itself was sufficient to guarantee the existence of solutions without further modeling, and applied the theory extensively tor both struts and foils, providing a wealth of information useful for performance. This linearized theory has been widely used. His third accomplishment was to discover, by entirely theoretical analysis, the special design of supercavitating hydrofoils of much higher efficiency (ratio of lift to drag) than had previously been thought possible, and to adapt these foils for the design of supercavitating propellers. The first such propeller, a research model, was designed by the DTMB staff with his foils, and tested about 1956. He later designed the first large scale supercavitating propeller for the hydrofoil ship, Dension, which was propelled at 50 knots, absorbing 'about 10,000 horsepower. Subsequently, these kinds of propellers have been adapted throughout the world for propulsion of small craft at high speeds. At the present time, Japanese shipbuilders are intensively studying supercavitating propellers for application to high speed cargo ships.
In 1955, he was recruited from DTMB to work in the Mechanics Branch of the Mathematical Sciences Division of the Office of Naval Research (ONR), where he was responsible for research programs, mostly in universities, for both hydrodynamics and aerodynamics. The latter were devoted to shock tube phenomena and applications which were, about to be of great importance for nose cone testing of ballistic reentry vehicles. Tulin had a lasting impact on the ONR hydrodynamics program, stressing fundamental research related to naval needs, with such subjects as high speed flows, hydrodynamic, noise generation, and water exit. As part of an attempt to familiarize scientists with Navy needs, he proposed and planned the first ONR Symposium on Naval Hydrodynamics in 1956. The 19th Symposia in the series, held every two years, now organized by the National Research Council, will take place in Korea in 1992. At ONR, he also took part in the manned hydrofoil project, a prime influence on later naval hydrofoil developments. He also took a very active part in classified naval projects especially regarding mine counter measures and non-acoustic remote sensing of submarines, a subject which he was later to work on intensively. He continued his own research during this time. In an important accomplishment, he attacked theoretically the problem of the efficiency of low aspect ratio planing surfaces and showed how to shape the bottom surface to reduce spray drag and improve efficiency, a technique later adopted for high speed planing boats by Eugene Clement at the Taylor Model Basin. In the same paper he successfully analyzed non-linear effects near the spray edge of the surface and their effects on performance; his predictions were later confirmed experimentally by Alan Acosta at Cal Tech.
In 1957 he requested a transfer to ONR London, where he was responsible for liaison with and surveys of European research in fluid dynamics. He was able to establish close contact with many European scientists in both aerodynamics and hydrodynamics, and he acquired a strong feeling of the importance of overseas research. He happened to overlap the birth of the British hovercraft project under Sir Christopher Cockerell’s initiative, and acted as a scientific liaison between British and US naval interests in that field. He continued research on supercavitating flows, including studies of supercavitating struts where the detachment point was not specified in advance, and of the flow past slender supercavitating wings. He found considerable interest in Europe concerning supercavitating propellers and particularly with British and Swedish patrol craft builders. As his tour of duty was ending in early 1959, he determined to become more actively and closely involved in research and engineering.
During his post-WWII decade, the beginning of a virtual revolution in naval technology was underway, spearheaded by but not limited to modern submarine developments and Polaris, new and faster ships, and a growing emphasis on detection and quieting. This revolution put great pressure on scientific resources and capability relevant to those technologies, and Tulin had observed in the mid-1950s while at ONR that new and high spirited capabilities for advanced hydrodynamic research were needed, especially those offering a quick response to naval needs. With this in mind, he established a small private company for that purpose. He chose the name Hydronautics, in analogy with Aeronautics, and found a partner in Philip Eisenberg, a former supervisor and colleague at DTMB and ONR.
In July 1959, Hydronautics, Incorporated began its two man operation in Rockville, Md. It would eventually combine ship research, testing, and engineering under one roof and carry out broad research in hydrodynamics. It acquired a proud reputation for the quality of its work and a steady and significant impact on naval hydrodynamics. It eventually employed 100 people, the majority highly skilled engineers and scientists. Hydronautics eventually designed and built its own modern facilities on a beautiful 20 acre rural site near Columbia, Md. These included a free surface water cavitation tunnel specifically designed by Tulin for high speed studies, and a large (300 foot long) towing tank. These provided the means for conducting sophisticated testing of ships, submarines, propulsion devices, and hydrofoils.
Hydronautics became very prominent technically in naval fields involving supercavitating propellers and hydrofoil systems; submarine hydrodynamics; waterjet propulsion; hydrodynamics of air cushion vehicles; cavitation, especially damage; towing tank equipment and techniques; 'non-acoustic" detection; submarine rescue vehicle systems; drag reduction; planing craft, amphibious and swath ship hydrodynamics; and ship model testing. Substantial research was carried out in non-naval areas, too, including: water jet technology; rocket pump cavitating inducers; desalination, especially reverse osmosis; ocean energy, especially OTEO; oil-water separation; sub- micron waste filtration; membrane technology and applications; trace gas detection; and aircraft wake safety. Hydronautics was distinguished by its fine and versatile technical leadership, of which the core, chosen early by Tulin, were aeronautical research scientists from NACA Langley, namely Clinton E. Brown, Alex Goodman, and Virgil Johnson, Jr. With these leaders, Tulin was largely responsible for the scientific and technical vigor and enterprise of Hydronautics, while constantly engaged in research and engineering projects himself. He published a large number of Hydronautics Technical Reports, this being the normal mode of information dissemination for both private and public laboratories (over 2000 reports have been published by all personnel since 1959; the majority are substantial).
In the 1960s, he produced four major technical accomplishments of naval importance: i.) the development and application of advanced technology for supercavitating propellers. This involved foil section development for improved efficiency and strength and the exploration and alleviation of severe off-design performance effects due to blade-cavity interference; ii) major advances in the theory of cavity flows, particularly the invention of new closure models allowing the modeling of the trailing viscous wake (the so-called spiral vortex models), which have been much used since that time; iii) the development of understanding and quantification of highly complex physical phenomena occurring in the water column and involved in the non-acoustic, remote detection of submarines; iv) provision of the first appropriate explanation of the physical mechanism of the highly mysterious drag reducing properties of high molecular weight polymers. This involved the explication of molecular unraveling mechanisms at a critical flow strain rate, scaling inversely with the molecular relaxation time; while initially treated with extreme skepticism, this mechanism is widely accepted today.
Other problems in engineering also attracted his attention during this period: i) he carried out the first study of the dynamic stability of an air cushion platform with a peripheral jet seal, in which he introduced the model of overfed and underfed nonequilibrium jets; ii) curious about the mechanism of the Munro micro-jet (a supersonic waterjet ejected into air by the impact of a water shock wave on a curved air-water interface) he carried out the analysis of a model self similar flow, and thereby explained the effect; iii) following visual observations of the breaking region in front of blunt bows, he developed theory (with Gedeon llagan) for both the low speed and high speed limits, including estimates for breaker inception and of the resistance associated with breaking; iv) again with Dagan, he investigated the mechanism of the traction of a wheel in a plastic medium (mud) including inertial effects. He also became interested in why athero-sclerotic plaques form at a variety of distinct locations in arterial vessels. With Clinton E. Brown, he formed a theory which connected plaque formation with separation bubbles and revealed a remarkable enhancement in boundary layer separation effects due to the wall polarization of high molecular weight species following slow filtration of solute through the arterial walls.
As the 1960s merged into the 1970s he gave increasing attention to areas which had become the focus of national concern: pollution, waste treatment, and desalination. After an intensive study of the potential of various desalination processes, Tulin explored membrane desalination (reverse osmosis) which he concluded had an optimum long range potential. For this reason, he formed an Israeli research subsidiary in 1967, Hydronautics-Israel, Inc. During its lifetime,1967-73, this company carried out a wide variety of research on reverse osmosis, membrane separations, and analytical, instrumentation based on ion-specific, membranes. It also successfully developed an instrument for the remote detection of explosives. Some of this work was shared by Hydronautics. The two companies jointly developed a successful micron filtration process carried out with specially formed porous plastic tubes. Tulin became interested in high-power CO2 lasers during this time, and realizing that the power through a gas discharge tube was limited by transport rates across the tube, he carried out analyses with Josef Schwartz to show the effect of turbulent flow rates through the length of the tube; they were awarded patents based on the results of this work.
He maintained and extended his interest in naval hydrodynamics in the 1970s and 1980s. Working with C. C. Hsu on the problem of unsteady hull loading on commercial ships, he developed a non-linear analysis of cavitation propeller blades that allowed accurate predictions both for planar foils and wings. He also extended the analysis to include unsteady motion. He saw the connection between the leading edge cavity problem and separation bubbles on airfoils, and was able to integrate his inviscid theory for the outer flow with very simple, viscous considerations to predict both the bubble pressure and length. He successfully extended this method to trailing wakes, wherein he modeled the outer flow with his earlier spiral vortex model; he thereby provided a simple resolution to a very old classical problem.
He became curious about the mathematical relationship of various non-linear ship wave theories and developed a novel theory for predicting wave flows produced by bodies in two dimensions in which the solution could be framed in exact form, but involved mappings dependent on the solution. He showed that the so-called slow ship approximations which were very successful in application and generally believed to be true perturbation on zero Fronde number, were in fact asymptotic to a range of moderate Fronde numbers, neither too small, nor too large. In the late 1970s he became aware of the Navy’s interest in understanding the hydrodynamics of transom sterns, universally applied to major combat vessels, and as a result he devised a theory asymptotic to very high Fronde numbers, explaining quantitatively the large asymptotic resistant coefficient of transom sterns. Around the same time he became curious about the extent to which free surface flows past bodies could be created without waves, and produced several such general systems in 2 and 3 dimensions.
In one instance of enormous significance for transonic aircraft, he served as a very important catalyst. His colleague, Clinton E. Brown, had convinced him that lilting airfoil shapes existed which for high subsonic speeds possessed large imbedded supersonic regions without shocks, and were therefore very efficient. Recognizing the practical importance of Brown’s insight, Tulin approached both Julian Cole and Paul Garabedian with his arguments, and each of these scientists went on to make numerical calculation of these shock free airfoils.
In 1979 Tulin was elected a member of the National Academy of Engineering (NAE), with specific, reference to his early pioneering work in supercavitating flows and its application to propellers. He had become increasingly involved with the NAE as a participant in the work of the National Research Council. This followed earlier service on Advisory and Planning Committees of the Office of Saline Water (for desalination) and of the Naval Research Laboratory (for non-acoustic detection). He served as a member of the Marine Board and as Chairman of a distinguished panel of applied mathematicians on Applications of Mathematics for the Navy. He has served on the Board of Trustees and the Finance Committee of the Society for Industrial and Applied Mathematics (SIAM) since 1984.
As Hydronautics approached its 20th anniversary, the environment around it had changed remarkably since 1959. High technology, science, and research had become a dominant, factor in naval warfare; naval engineering was being carried out on a much more sophisticated level. Concurrently, both the engineering establishment in Washington, and private capabilities had multiplied greatly. For Hydronautics it had meant, a change in emphasis toward testing and engineering development associated with large programs. The partners elected to accept an offer by Tracer, Incorporated to purchase their prosperous and widely known firm.
In 1982 he received and accepted an offer to assume the Presidential Chair at the University of California at Santa Barbara specifically to organize a graduate program in ocean engineering. He was no stranger to universities and teaching, having taught graduate courses in three University extension programs, as well as during visits to UCLA, University of California. Berkeley and University of Washington. At this time in 1991, he serves as Director of the Ocean Engineering Laboratory (OEL), an Engineering Research Center at the University of California, Santa Barbara, which contains fine research facilities built under his direction, including a versatile flume, and a 175 foot wave-towing tank, fitted with a directional wavemaker of his own invention. He is very much dedicated to the appropriate training of graduate students for effective careers in engineering research, and tries to devote most of his time toward that end.
His interest in problems in naval hydrodynamics has continued unabated. In 1984 he presented the Weinblum Memorial Lecture in Hamburg, a singular international honor among hydrodynamicists. He lectured on ship waves from the ray point of view, in which he derived asymptotic ray theory in a new way, including formulae for the wave amplitudes, thereby extending the pioneering theory of Joseph Keller. In the same paper he provided a full theory for the modification of the classical Kelvin wave pattern in the presence of a wedge shaped semi-infinite bow. With his first graduate student, Raymond Cointe of Paris, he developed a theory of steady breaking waves and their stability, that, agreed with the classic experimental study carried out by Duncan at Hydronautics, thus providing the first detailed physical-mathematical model of breaking waves to be verified experimentally.
In the mid 1980s, Walter Munk drew his attention to the long (10--20 km), narrow (about 5° half angle) V wakes observed behind ships by space radars. Subsequently, he became interested in the “dead-water” effect experienced by ships in strongly stratified waters, wherein strong ship internal waves cause both marked disturbances on the ocean surface and greatly enhanced resistance. Tulin interested Touvia Miloh in the mathematical problems involved and they have shed new light on both “dead- water” and hypersonic observations. Miloh and Tulin have also conducted a series of original mathematical investigations on internal solitons; among other things they have proved thorough application of residue theory, that the summation of isolated solitons produces new solutions, just as with KDV solitons.
Having gained a good understanding of steady breaking waves with Raymond Cointe, he determined to better understand breaking waves at sea, which for energetic waves, remain mysterious in their inception, and for which a data base, on their dynamics is lacking. He partially redressed the latter lack in an experimental investigation carried out in 1989-90 with Ali Kolaini, a former graduate student, who measured and quantified the inception and dynamics of spiller breakers on short crested waves. They found these breakers highly transient in relation to steady breakers. At the present time, in addition to theoretical and experimental work on ship internal waves, he is supervising graduate research on stochastic directional waves; the stability of fiber optic cables during their deployment and on a theoretical study of the role of gravity wave resonant perturbations such as sidebands, as an intermediary in waveform deformation leading to breaking. He is also assisting Hajime Mauro in the development of theory and computational means for the prediction of spray formation and the deck wetness of fast naval ships. In the future, he hopes to create a simulation of wind driven ocean spectra, adequate in detail to allow reliable research on real ocean processes within the laboratory.
Tulin has often expressed his good fortune at having discovered hydrodynamics with its wealth of engineering applicability, and with the great variety and complexity of the physical phenomena which occur within it. How many other subjects, he has asked, possess such beautiful patterns, easily visualized within or on the surface of water tanks and tunnels, while at the same time providing applied mathematics, beginning with Euler, such a magnificent scope for the highly varied exercise of its poise and