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Dissertations / Theses on the topic 'Wave interactions'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Zhu, Qiang 1970. "Features of nonlinear wave-wave and wave-body interactions." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/8853.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2000.<br>Includes bibliographical references (leaves 295-302).<br>Although nonlinear water waves have been the subject of decades of research, there are many problems that remain unsolved, especially in the cases when one or more of the following factors are involved: high-order nonlinear effects, moving boundaries, wavestructure interactions and complicated geometries. In this dissertation, a high-order spectral-element (HOSE) method is developed to investigate problems about nonlinear waves. An exponentially c

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2

Ferdousi, Mariya. "Nonlinear Wave-Wave Interactions in the Brain." Thesis, The University of Sydney, 2019. https://hdl.handle.net/2123/21410.

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Neural field theory of the corticothalamic system is used to analyze nonlinear wave-wave interactions in sleep and wake states and steady state visual evoked potential responses. The nonlinear power spectrum is analytically calculated by convolving the linear power spectrum with itself and other factors. Analysis shows that strong spectral peaks generate a harmonic at twice the original frequency with peak power proportional to the square of that of the original peak. Periodic sine and square wave stimuli are used to generate steady state visual evoked potential responses and to study stimulus

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3

Sun, Haili. "Ray-tracing internal wave/wave interactions and spectral energy transfer /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/10973.

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4

Kalkavage, Jean Hogan. "Nonlinear wave-wave interactions in ionospheric plasmas caused by injected VLF and HF waves." Thesis, Boston University, 2014. https://hdl.handle.net/2144/21184.

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Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>The study of wave-wave interactions in the ionosphere is important for designing communication systems, satellite systems, and spacecraft. Ionospheric research also informs laser and magnetic fusion plasma physics. This thesis

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5

Gibson, Richard Stewart. "Wave interactions and wave statistics in directional seas." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413426.

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6

Naciri, Mamoun. "On wave-wave interactions on the ocean surface." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/47312.

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7

Bird, Charlotte C. "Nonlinear interactions of water waves, wave groups and beaches." Thesis, University of Bristol, 1999. http://hdl.handle.net/1983/c8fedc4e-9c73-4791-b1d8-b4ff14646025.

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8

Bourne, Neil Kenneth. "Shock wave interactions with cavities." Thesis, University of Cambridge, 1990. https://www.repository.cam.ac.uk/handle/1810/250963.

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9

Andreae, Sigrid Barbara Margrid. "Wave interactions with material interfaces /." Aachen : Shaker, 2008. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=016487715&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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10

Jones, David Caradoc. "Wave interactions in photorefractive materials." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257934.

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11

Smith, Sean Paul. "Laboratory Experiments on Colliding Nonresonant Internal Wave Beams." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3300.

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Internal waves are prominent fluid phenomena in both the atmosphere and ocean. Because internal waves have the ability to transfer a large amount of energy, they contribute to the global distribution of energy. This causes internal waves to influence global climate patterns and critical ocean mixing. Therefore, studying internal waves provides additional insight in how to model geophysical phenomena that directly impact our lives. There is a myriad of fluid phenomena with which internal waves can interact, including other internal waves. Equipment and processes are developed to perform laborat

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12

Longley, Kaitlyn E. "WAVE CURRENT INTERACTIONS AND WAVE-BLOCKING PREDICTIONS USING NHWAVE MODEL." Monterey, California. Naval Postgraduate School, 2013. http://hdl.handle.net/10945/32857.

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Wave blocking in river inlets is examined using the NHWAVE (Non-Hydrostatic Wave) model under development. Blocking flows at river inlets are a significant hazard to navigation. Refractive and shoaling effects contribute to the enhancement of wave field energy, causing instabilities and breaking, resulting in energy dissipation and transfer at the blocking point. The non-linearity of wave-current interactions and wave breaking makes the dynamics of blocking flows difficult to model. Current efforts to use wave-averaged models are insufficient to describe the complex dynamics that occur within

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13

Semedo, Alvaro. "Atmosphere-ocean Interactions in Swell Dominated Wave Fields." Doctoral thesis, Uppsala universitet, Geovetenskapliga sektionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-130650.

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Ocean wind waves represent the atmosphere-ocean boundary, playing a central role in the air-sea exchanging processes. Heat, mass and momentum are transferred across this boundary, with waves mediating the exchange of principally the momentum between the winds and the ocean surface. During the generation process waves are called wind sea. When they leave their generation area or outrun their generating wind they are called swell. The wave field can be said to be dominated either by wind sea or swell. Depending on the wave regime the momentum and energy exchanging processes and the degree of cou

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14

Xue, Ming 1967. "Three-dimensional fully-nonlinear simulations of waves and wave body interactions." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10216.

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15

Chapman, John Richard. "Ultrasonic wave interactions with magnetic colloids." Thesis, University of Nottingham, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366409.

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16

Weaver, P. M. "Shock wave interactions with aqueous foams." Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292434.

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17

Frank, Donya P. "Wave-Current Bottom Boundary Layer Interactions." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1229087949.

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18

Ooi, Eng Seng. "Rayleigh wave interactions with tribological contacts." Thesis, University of Sheffield, 2015. http://etheses.whiterose.ac.uk/9963/.

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The use of ultrasonic reflectometry is a proven method of condition monitoring machine systems. The working principles are simple. A burst of ultrasonic signal is sent to the interface of interest where reflection of the signal takes place. The manner in which reflection takes place depends on the properties of the interface. As such, the reflected signal carries information regarding the interface that can be extracted with proper techniques. However, the use of ultrasonic reflectometry in condition monitoring is not without its limitations. Conventional ultrasound techniques make use of ultr

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19

Wu, Cheng Y. (Cheng Yi) 1938. "Wave-wave interactions and the infrasonic pressure field in the ocean." Thesis, University of Auckland, 1988. http://hdl.handle.net/2292/2469.

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Building on Kibblewhite's long term investigations of the nonlinear wave-wave interactions and the infrasonic ocean noise and the microseisms these induce, this thesis further explores the physical nature of these processes. The classical description of this interaction, which takes into account only the homogeneous component of the induced field, has been extended to include the inhomogeneous component. A complete expression for the wave induced noise spectrum is established following a geometrical analysis of the dispersion relations among interacting waves. The relative importance of these

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20

Blackhurst, Tyler D. "Numerical Investigation of Internal Wave-Vortex Dipole Interactions." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3133.

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Three-dimensional linear ray theory is used to investigate internal waves interacting with a Lamb-Chaplygin pancake vortex dipole. These interactions involve waves propagating in the same (co-propagating) and opposite (counter-propagating) horizontal directions as the dipole translation. Co-propagating internal waves in the vertical symmetry plane between the vortices of the dipole can approach critical levels where the wave energy is absorbed by the dipole or where the waves are overturned and possibly break. As wave breaking cannot be simulated with this linear model, changes in wave steepne

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21

Barker, Adrian John. "Tidal interactions between planets and stars." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240581.

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Since the first discovery of an extrasolar planet around a solar-type star, observers have detected over 500 planets outside the solar system. Many of these planets have Jovian masses and orbit their host stars in orbits of only a few days, the so-called 'Hot Jupiters'. At such close proximity to their parent stars, strong tidal interactions between the two bodies are expected to cause significant secular spin-orbit evolution. This thesis tackles two problems regarding the tidal evolution of short-period extrasolar planets. In the first part, we adopt a simple model of the orbit-averaged effec

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22

Ellin, Hannah Catherine. "Aspects of wave interactions in photorefractive materials." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296992.

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23

Fashanu, Udofe Peter Taiwo. "Simulation and analysis of wave-structure interactions." Thesis, University of Newcastle Upon Tyne, 2011. http://hdl.handle.net/10443/1310.

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Today, it is widely recognized that Computational Fluid Dynamics (CFD) methodologies should be used for the analysis of Engineering systems and that design and method of simulation must be practical and realistic to provide cost effective solutions. The recent development in CFD of Engineering Structures has led to the adoption of the Eulerian and Lagrangian concepts of numerical analysis. Although the importance of these concepts cannot be overemphasised in offshore structures hydrodynamics, thus the choice of a concept to define the flow field surrounding a structure is one of the fundamenta

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24

Ye, Jianhong. "Numerical analysis of Wave-Seabed-Breakwater interactions." Thesis, University of Dundee, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604579.

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25

King, Daniel Martin. "Wind/wave interactions in the surf zone." Thesis, University of Nottingham, 1994. http://eprints.nottingham.ac.uk/12802/.

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Wind/wave interactions in the surf zone are studied using a wave tank and environmental wind tunnel. The wind simulation is achieved over a relatively short fetch using accelerated growth techniques at a scale of roughly 1:100. Waves are scaled at approximately 1:50, and consequently there is some scaling mis-match between the wind and wave simulations. Results show that wind has a significant effect on the breaking of the waves. Both breaker location and breaker type are shown to be affected by the wind. Results are in agreement with those of Douglass (1989 & 1990), who used a wind/wave flume

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26

Baddeley, Lisa. "Wave-particle interactions in the terrestrial magnetosphere." Thesis, University of Leicester, 2003. http://hdl.handle.net/2381/30668.

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This thesis examines small scale poloidal mode magnetohydrodynamic waves which have an energy generation mechanism internal to the magnetosphere in the form of unstable particle populations. The energy from these particles is fed into a resonant wave mode and, ultimately, dissipated in the terrestrial ionosphere. By analysing Ion Distribution Functions (IDFs) the statistical occurrence of the driving magnetospheric particle populations is presented. Results indicate that the dominant driving particle populations are those of ~10 - 40 keV protons. The free energy of the particles has been quant

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27

Touber, Emile. "Unsteadiness in shock-wave/boundary layer interactions." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/161073/.

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The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. This work investigates the interaction between an impinging oblique shock and a supersonic turbulent boundary layer via large-eddy simulations. Special care is taken at the inlet in order to avoid introducing artificial low-frequency modes that could affect the interaction. All simulations cover extensive integration times to allow for a spectral analysis at the low frequencies of interest. The simulations b

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28

Nové-Josserand, Clotilde. "Converting wave energy from fluid-elasticity interactions." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC124/document.

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Le développement des systèmes houlomoteurs ainsi que la gestion du littoral reposent sur une bonne compréhension des mécanismes liés aux interactions houle-structure. Dans cette thèse, nous nous intéressons à l'étude d'un champ de structures flexibles soumises à des ondes de surface, en vue de développer un système qui puisse à la fois atténuer les vagues et absorber l'énergie qui leur est associée de manière efficace. Les résultats présentés se basent autour d'expériences réalisées dans des installations de petite échelle, dans lesquelles la disposition spatiale des objets flexibles est le pr

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29

Koo, Weoncheol. "Fully nonlinear wave-body interactions by a 2D potential numerical wave tank." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/1118.

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A 2D fully nonlinear Numerical Wave Tank (NWT) is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Nonlinear Wave deformation and wave forces on stationary and freely floating bodies are calculated using the NWT. For verification, the computed mean, 1st, 2nd, and 3rd order wave forces on a single submerged cylinder are compared with those of Chaplin's experiment, Ogilvie's 2nd-order theory, and other nonlinear computation called high-order spectral method. Similar calculations for dual submerged cylinders are also

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30

McLandress, Charles. "A study of wave-wave interactions in a steady-state stratospheric model /." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75839.

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Interactions among stationary planetary waves in the winter stratosphere are studied using steady-state quasi-geostrophic models from both a theoretical and numerical point of view.<br>A triad of small amplitude waves is examined analytically using a constant zonal wind $ beta$-plane model in which dissipation is required for the waves to interact. The nature of the modifications to the linear solutions is found to depend both on the propagation characteristics and the zonal wavenumber of the modes.<br>Numerical solutions are determined using a climatological basic state and boundary forcing.

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31

Xie, Jinhan. "Wave-mean flow interactions : from nanometre to megametre scales." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10475.

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Waves, which arise when restoring forces act on small perturbations, are ubiquitous in fluids. Their counterpart, mean flows, capture the remainder of the motion and are often characterised by a slower evolution and larger scale patterns. Waves and mean flows, which are typically separated by time- or space-averaging, interact, and this interaction is central to many fluid-dynamical phenomena. Wave-mean flow interactions can be classified into dissipative interactions and non-dissipative interactions. The former is important for small-scale flows, the latter for large-scale flows. In this thes

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32

Wheadon, Andrew John. "Wave-turbulence interaction in shallow water numerical models : asymptotic limits, and subgrid interactions." Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/34333.

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The ability to directly simulate all atmospheric motion is currently well beyond the limits of the computers available to us. As such techniques must be developed that accurately model important processes in an affordable manner. Large-scale balanced motion is well understood, but as affordable resolution increases, models are able to resolve scales where large-scale turbulence and small-scale waves are important. This requires a new set of techniques that respect the interactions between these different kinds of motion. In this thesis we look at two ways of assessing the accuracy of models ca

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33

Threadgill, James. "Unsteadiness of shock wave boundary layer interactions across multiple interaction configurations and strengths." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/48475.

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Shock Wave Boundary Layer Interactions (SWBLIs) represent complex flow phenomena that remain poorly understood despite their prevalence on high-speed vehicles, in part due to their complicated underlying physics. In particular, the mechanisms that drive the high-amplitude, low-frequency unsteadiness within the interaction have perplexed researchers for many years while remaining a limitation to vehicle performance and a potential danger to airframe integrity. This investigation has specifically examined the influence of interaction strength and configuration type on the characteristic unsteady

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34

Alves, Jose Henrique Gomes de Mattos Mathematics UNSW. "A Saturation-Dependent Dissipation Source Function for Wind-Wave Modelling Applications." Awarded by:University of New South Wales. Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17786.

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This study reports on a new formulation of the spectral dissipation source term Sds for wind-wave modelling applications. This new form of Sds features a nonlinear dependence on the local wave spectrum, expressed in terms of the azimuthally integrated saturation parameter B(k)=k^4 F(k). The basic form of this saturation-dependent Sds is based on a new framework for the onset of deep-water wave breaking due to the nonlinear modulation of wave groups. The new form of Sds is succesfully validated through numerical experiments that include exact nonlinear computations of fetch-limited wind-wave ev

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35

Gately, Bernard M. Colson William B. "A theory for whistler wave amplification and wave particle interactions in the magnetosphere /." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from the National Technical Information Service, 1992. http://handle.dtic.mil/100.2/ADA257782.

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36

Gately, Bernard M. "A theory for whistler wave amplification and wave particle interactions in the magnetosphere." Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/38526.

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Approved for public release; distribution is unlimited.<br>Whistler waves are a type of very low frequency (VLF) radiation which propagate through the earth's magnetosphere. This phenomenon can occur as a result of a lightning discharge and can be produced using ground-based VLF transmitters. It is theorized that these signals travel through ducts centered on geomagnetic field lines. While passing through these ducts the waves are amplified through resonant interaction with electrons in the radiation belts which are following helical paths around magnetic field lines. A description of whistler

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37

Li, Zhaobin. "Two-phase spectral wave explicit Navier-Stokes equations method for wave-structure interactions." Thesis, Ecole centrale de Nantes, 2018. http://www.theses.fr/2018ECDN0041/document.

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Cette thèse propose un algorithme efficace pour la simulation numérique des interactions houle-structure avec des solveurs CFD bi-phasiques. L'algorithme est basé sur le couplage de la théorie potentielle et des équations bi-phasiques de Navier-Stokes. C'est une extension de la méthode Spectral Wave Explicit Navier-Stokes Equations (SWENSE) pour les solveurs CFD bi-phasiques avec une technique de capture d'interface. Dans cet algorithme, la solution totale est décomposée en une composante incidente et une composante complémentaire. La partie incidente est explicitement obtenue avec des méthode

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38

Tan, Loh Teng Young. "Assessments of wave-structure interactions for an oscillating wave surge converter using CFD." Thesis, University of Plymouth, 2018. http://hdl.handle.net/10026.1/12230.

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This thesis is concerned with the use of the open source computational fluid dynamics (CFD) software package, OpenFOAM® for predicting and analysing the behaviour of a near-shore oscillating wave surge converter (OWSC), when subject to various types of ocean wave conditions in a numerical wave tank (NWT). OpenFOAM® which utilises a Finite Volume Method (FVM) is used to solve the incompressible, Reynolds Averaged Navier-Stokes (RANS) equations for a two-phase fluid, based on a Volume of Fluid (VOF) phase-fraction approach to capture the interface between the air and water phases. Preliminary st

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39

Spentza, Eirini. "Nonlinear wave interactions with fixed and floating bodies leading to unexpected wave impacts." Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/8987.

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This thesis deals with the nonlinear interaction of water waves with fixed and floating bodies. The case of a two-dimensional fixed surface body is first investigated using a newly developed linear and second-order boundary element model, the fully nonlinear model of Hague & Swan (2009) and new experimental observations. In this case, second-order freely propagating harmonics arising due to the wave-structure interaction are identified and quantified. Subsequently, a two- dimensional floating body is investigated, undergoing one or two motion modes, and comparisons with the fixed body case are

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40

Haase, Heiko. "Full-wave field interactions of nonuniform transmission lines." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975448641.

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41

Andreae, Sigrid B. [Verfasser]. "Wave Interactions with Material Interfaces / Sigrid B Andreae." Aachen : Shaker, 2008. http://d-nb.info/1164342029/34.

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42

Hanasoge, Shravan M. "Theoretical studies of wave interactions in the sun /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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43

Renaud, Antoine. "On wave-mean flow interactions in stratified fluid." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEN059/document.

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La dynamique des écoulements géophysiques planétaires est fortement influencée par des processus physiques souvent non résolus par les modèles numériques de circulation générale. Il est essentiel de comprendre les mécanismes physiques sous-jacents pour paramétrer l’effet des petites échelles sur les grandes. Dans cette thèse, nous étudions un problème emblématique d’interactions entre ondes et écoulements moyens : la dynamique des écoulements zonaux forces par des ondes internes de gravite. Une manifestation remarquable de ces interactions est l’oscillation quasi-biennale (QBO) des vents équat

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44

Weller, Samuel David. "Wave energy extraction from device arrays : experimental investigation in a large wave facility." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/wave-energy-extraction-from-device-arrays-experimental-investigation-in-a-large-wave-facility(5e43e3e5-4776-42c1-9d4e-22160de8abbe).html.

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Multiple wave energy devices supported by a common structure represent one possible method of efficiently converting ocean wave energy into electricity. In this study, experimental measurements of multiple small-scale wave energy devices are reported to assist the development and validation of numerical models. Through observation and measurement, the response of two float geometries subjected to a range of wave conditions and device settings were determined. A range of regular wave conditions were identified that caused a linear relationship to occur between the heave displacement amplitude o

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45

Gras, Slawomir M. "Opto-acoustic interactions in high power interferometric gravitational wave detectors." University of Western Australia. School of Physics, 2009. http://theses.library.uwa.edu.au/adt-WU2010.0093.

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[Truncated abstract] Advanced laser interferometer gravitational wave detectors require an extremely high optical power in order to improve the coupling between the gravitational wave signal and the optical field. This high power requirement leads to new physical phenomena arising from nonlinear interactions associated with radiation pressure. In particular, detectors with multi-kilometer-long arm cavities containing high density optical fields suffer the possibility of 3-mode opto-acoustic interactions. This involves the process where ultrasonic vibrations of the test mass cause the steady st

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46

Saputo, Roberto. "Two dimensional P-wave superconductors with long range interactions." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16315/.

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L' interesse crescente che circonda lo studio delle proprietà topologiche della materia è profondamente collegato all' effettiva possibilità di verifica in laboratorio. Negli ultimi decenni infatti la fisica sperimentale degli atomi ultrafreddi ha raggiunto livelli di precisione prima inimmaginabili. Attraverso reticoli ottici si possono riprodurre sistemi multicorpo fortemente interagenti di cui si possono controllare in maniera quasi esatta i parametri fisici, come i potenziali. In questo contesto si inserisce il modello bidimensionale P-wave con interazioni a lungo raggio. Le interazio

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47

Levinsen, Jesper F. "Paired fermionic superfluids with s- and p-wave interactions." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3284444.

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48

Risch, Stephan Hermann. "Large-scale wave interactions in baroclinic flow with topography." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312449.

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49

Mahoney, Daniel J. (Daniel John). "On wave interactions--explosive resonant traids and critical layers." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/12055.

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50

Yan, Hongmei. "Computations of fully nonlinear three-dimensional wave-body interactions." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/61616.

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Thesis (Ph. D. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references.<br>Nonlinear effects in hydrodynamics of wave-body interaction problems become critically important when large-amplitude body motions and/or extreme surface waves are involved. Accurate prediction and understanding of these fully nonlinear effects are still challenges in the design of surface ships and marine structures, owing to the complexity of the hydrodynamic problem itself and limited computati

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