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Pierre Lermusiaux. Humara, Michael Jesus. Joint Program in Applied Ocean Science and Engineering. Massachusetts Institute of Technology. Department of Mechanical Engineering. Woods Hole Oceanographic Institution. Joint Program in Applied Ocean Science and Engineering Massachusetts Institute of Technology. Department of Mechanical Engineering Woods Hole Oceanographic Institution 2020-09-03T17:50:12Z 2020-09-03T17:50:12Z 2020 2020 https://hdl.handle.net/1721.1/127163 1191844374 Thesis: S.M., Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 119-126). Developing accurate and computationally efficient models for ocean acoustics is inherently challenging due to several factors including the complex physical processes and the need to provide results on a large range of scales. Furthermore, the ocean itself is an inherently dynamic environment within the multiple scales. Even if we could measure the exact properties at a specific instant, the ocean will continue to change in the smallest temporal scales, ever increasing the uncertainty in the ocean prediction. In this work, we explore ocean acoustic prediction from the basics of the wave equation and its derivation. We then explain the deterministic implementations of the Parabolic Equation, Ray Theory, and Level Sets methods for ocean acoustic computation. We investigate methods for evolving stochastic fields using direct Monte Carlo, Empirical Orthogonal Functions, and adaptive Dynamically Orthogonal (DO) differential equations. As we evaluate the potential of Reduced-Order Models for stochastic ocean acoustics prediction, for the first time, we derive and implement the stochastic DO differential equations for Ray Tracing (DO-Ray), starting from the differential equations of Ray theory. With a stochastic DO-Ray implementation, we can start from non-Gaussian environmental uncertainties and compute the stochastic acoustic ray fields in a reduced order fashion, all while preserving the complex statistics of the ocean environment and the nonlinear relations with stochastic ray tracing. We outline a deterministic Ray-Tracing model, validate our implementation, and perform Monte Carlo stochastic computation as a basis for comparison. We then present the stochastic DO-Ray methodology with detailed derivations. We develop varied algorithms and discuss implementation challenges and solutions, using again direct Monte Carlo for comparison. We apply the stochastic DO-Ray methodology to three idealized cases of stochastic sound-speed profiles (SSPs): constant-gradients, uncertain deep-sound channel, and a varied sonic layer depth. Through this implementation with non-Gaussian examples, we observe the ability to represent the stochastic ray trace field in a reduced order fashion. by Michael Jesus Humara. S.M. S.M. Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Mechanical Engineering; and the Woods Hole Oceanographic Institution) 126 pages eng Massachusetts Institute of Technology MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 Joint Program in Applied Ocean Science and Engineering. Mechanical Engineering. Woods Hole Oceanographic Institution. Stochastic acoustic ray tracing with dynamically orthogonal equations Thesis application/pdf 2020-09-03T17:50:12Z Publication Master MechE unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="9a00c980-4093-4469-adae-1c364fb59c20"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Stochastic acoustic ray tracing with dynamically orthogonal equations</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2020</PublicationDate> <Authors> <Author> <DisplayName>Humara, Michael Jesus.</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Joint Program in Applied Ocean Science and Engineering.</Keyword> <Keyword>Mechanical Engineering.</Keyword> <Keyword>Woods Hole Oceanographic Institution.</Keyword> <Abstract>Developing accurate and computationally efficient models for ocean acoustics is inherently challenging due to several factors including the complex physical processes and the need to provide results on a large range of scales. Furthermore, the ocean itself is an inherently dynamic environment within the multiple scales. Even if we could measure the exact properties at a specific instant, the ocean will continue to change in the smallest temporal scales, ever increasing the uncertainty in the ocean prediction. In this work, we explore ocean acoustic prediction from the basics of the wave equation and its derivation. We then explain the deterministic implementations of the Parabolic Equation, Ray Theory, and Level Sets methods for ocean acoustic computation. We investigate methods for evolving stochastic fields using direct Monte Carlo, Empirical Orthogonal Functions, and adaptive Dynamically Orthogonal (DO) differential equations.</Abstract> <Abstract>As we evaluate the potential of Reduced-Order Models for stochastic ocean acoustics prediction, for the first time, we derive and implement the stochastic DO differential equations for Ray Tracing (DO-Ray), starting from the differential equations of Ray theory. With a stochastic DO-Ray implementation, we can start from non-Gaussian environmental uncertainties and compute the stochastic acoustic ray fields in a reduced order fashion, all while preserving the complex statistics of the ocean environment and the nonlinear relations with stochastic ray tracing. We outline a deterministic Ray-Tracing model, validate our implementation, and perform Monte Carlo stochastic computation as a basis for comparison. We then present the stochastic DO-Ray methodology with detailed derivations. We develop varied algorithms and discuss implementation challenges and solutions, using again direct Monte Carlo for comparison.</Abstract> <Abstract>We apply the stochastic DO-Ray methodology to three idealized cases of stochastic sound-speed profiles (SSPs): constant-gradients, uncertain deep-sound channel, and a varied sonic layer depth. Through this implementation with non-Gaussian examples, we observe the ability to represent the stochastic ray trace field in a reduced order fashion.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>