DOCSLIB.ORG

Analysis of Wave Force Data

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Analysis of Wave Force Data ., 1 Downloaded from http://onepetro.org/jpt/article-pdf/22/03/347/2228075/spe-2711-pa.pdf by guest on 23 September 2021 Introduction The design of a structure for the marine environment data were obtained for 4 years during Wave Force is primarily dependent on the prediction of the forces Project I (1954 to 1958). Then in 1960, newer instm- generated by waves in most coastal areas. Morison ments were located in 100 ft of water where additional da?~ ~ew fihtai.nrl frm ‘4 mrwe veatw dmino wave et ai.~ reiated these forces to the kineinatk ‘wavepop- 1!, ““WAA.”W .“. “ . ..”.- J -- . ---= ~ ..-. erties, the water particle velocity and acceleration. The Force Project II (1960 to 1963). These projects were equation is composed of two parts — a drag term and supported by the California Research Co., Shell Oil an inertial term — that are related to the total force Co., and Humble OiI and Refining Co. Pure Oil Co. by means of the drag and inertial force coefficient, and the U. S. Navy entered the program at a later CD and Clf, respectively. Two primary limitations date. A complete description of the installation ap- associated with the Monson equation are: (1) the pears in Ref. 3. poorly defined values of these hydrodynamic force The theoretical determination of the wave particle coefficients for large waves and (2) the dependency velocity and acceleration and the fitting of the meas- on wave theory or theories to describe the kinematic ured data by means of the correlation coefficients water particle velocity and local acceleration. A sec- (CD and C.) in Morison’s equation was done inde- Qndarv, comideration.- —.—-.—— is the change of these wave force pendently by the participants. Shell has analyzed coefficients with changes of the kinematic flow field the measured wave force data differently for each and changes of the pile dimensions. The drag coe5- of the two wave force projects. The same wave cient has been shown to be a function of the Reynolds theories were used to determine the velocity and number for steady fluid flow.2 However, correlation acceleration terms from the measured wave profile of CD with the Reynolds number in an oscillating data; however, the force coefficients were analyzed by n-— 1-=-l-. - ---. --.11.. L,.,....-.l...:.,a q-ha _ _.ahl -e t--hnimux aQ deccrihecl in t&.e noW nds rxeu gfam WY UHUMUMVG. ~ 11=* ~Luu&eaA,. d~erent . ---.--.-l--”, -“ --”------ -_ section Wave clearly show the need for prototype field measure- Force Coefficient Analysis. With these calibrated co- ments of these wave properties in the high Reynolds efficients, Morison’s equation was used to predict the number range. individual wave forces from various large hurricane m. ..=.*7fm. *,,..,- m..-+ll. nrl Wn”$l fmw.p dfifa ~ 11= ~Gb&Da, Ly ~ul “~.” ~1 “Auw a,,= .._.” .V._ __ waves. The relative agreement of the predcted and for large waves to establish the desired correlation observed forces is used as a measure of the degree resulted, in 1954, in the instrumentation of an off- of correctness of the Morison equation and as a meas- ure of the confidence for the prediction of wave forces shore oii piatform in Xi ft of ‘Waki. lX’--”-Vv avG ‘-Jtulu “-”lul&c on a structure. The ctilbrated Morison equation is ●Presently with Ocean Science and Engineering, Inc. then used to determine the design forces for a struc- 1 I Wave profile and wave force data acquired in the Gulf of Mexico from several hurricanes have been analyzed to provide the drag and inertial coeflcients of Morison’s wave force equation. These coefficients are required to help determine design loads for o#shore structures. MARCH, 1970 ~—fl~ 347 ture using the kinematic flow field determined for a as a function of time, thus providing the parameters design hurricane. By using the same technique for of wave height H and period T for a given water the prediction of the design force as for the analysis depth d. Assuming the waves are unidirectional and of the observed force, the chances for error are steady, the kinematic flow field cart then be computed greatly reduced. from the appropriate wave theories and this surface =__nrnfile.—_. Wave Force Theory This correlation technique calibrates Morison’s equation only in the range of wave heights and Morison’s Force Equation periods and wave forces that have been measured for The basic wave force theory used in design of off- certain pile diameters. Therefore, it is desirable to shore stmctures by Shell Oil Co. is the Morison equa- extend the calibration of the wave force coefficients, tion, which gives the total force on a structural CDand CM,to the wave conditions and pile size other member as the sum of the drag and the inertial forces. * than the experimental values. There have been many The Morison equation, expressed in terms of force attempts to correlate CD with such parameters as the per unit length (lb/ft) on a cylindrical pile, is Reynolds numbers, the Froude number, the Keulegan- Carpenter modulus and several other dimensionless Downloaded from http://onepetro.org/jpt/article-pdf/22/03/347/2228075/spe-2711-pa.pdf by guest on 23 September 2021 zD’ au F~ = + CDIUIU + pcJf— — . (1) parameters’ for an oscillating flow, but generally with 4 at poor success. Several of these relationships were in- where vestigated as well as other parameters such as wave height and period. ;~ mass density of sea water, lb ft-4 sees diameter of the cylindrical pile, ft Composite Wave Theories u= horizontal component of velocity, ft see-’ a24/at= horizontal component of local accelera- The other problem raised by the use of the Monson tion, ft see-z equation is the method of determining the kinematic CD= hydrodynamic drag coefficient flow field. Early investigators of wave force theory’ CM= hydrodynamic inertial coefficient quickly realized that no single theory available would properly describe the kinematic flow field for the many With this equation the measured wave force data can variations of wave conditions. These wave conditions be correlated with theoretically predicted wave force have been described by two parameters, the -~ave----- data, provided the kinematic flow field is known. steepness parameter (H/gT’) and the water depth Ideally this flow field would be measured simul- parameter (d/gT’). Consequently, Shell Development taneously with the wave force field for the most accu- Co. has developed numerical wave theory computer rate analysis of CD and CM.Practically, this has not programs to cover the ranges of wave steepness and been done successfully for very large waves (nor was wave characteristics in various water depths. A selec- it accomplished in the two wave force projects). How- tion graph (Fig. 1) displays the various regions of ever, the sea surface profile at a point can be measured applicability of the several wave theories used by Shell 0.03 r /+ = o C2732 I .< wiiv E t+l Hr, = \ 000 g=32 20 F1/Sec2 CHAP PE LEAR NUMERICAL 002 - / H/Hm, = O 675 . m . z & STOKES– 5~h c . I (JO, -: 0 W OEPTH SOLUTIONS) I I I H, HT, = 005 1 c 002 c C)4 c 06 0 08 . d/gT~ Fig. l—Wave theory selection graph. 348 JOURNAL OF PETROLEUM TECHNOLOGY I , as dictated by the dimensionless parameters, H/gT2 u = wave frequency (2zT-1), see-l and d/gT2. ~s does not imply that other wave k = wave number (27rL-’), ft’ theories are not applicable to similar regions. Fig. 1 shows that two forms of the Stokes (1847) wave Vj = velocity constants in Stokes’ iifth order theories, the first order (Airy) theory and the more wave theory complex tifth order theory, were applicable to most of the ranges of these parameters. The ChappelearO Aj = acceleration constants in Stokes’ fifth numerical wave theory and the McCowan’ solitary order wave theory wave theory were used for the extreme conditions of d = dep@ ft very steep waves in deep and shallow water, respec- tively. With the exception of the Airy and McCmvan When x = O (at the wave crest), sin (kjx) = O, and wave theones, the computations in determining z the inertial force term is likewise O. The velocity single set of water particle velocities and accelerations (hence, drag force) is then a maximum, since cos from the theories in Fig. 1 for a given location were kj(0) = 1 at the wave crest. At x = L/2 (at the wave .... —— -.. -L) .:- l.:tT 19) h -1 - n .~A th- fn~p ic amin nearly prohiiiitive untii they were cornpuwr pru- Uuugu], 3UI #b](&/ 6) la W&) v, -- w“ . ..- .“ -~— grammed for rapid compilation. purely drag. The velocity is a maximum in the nega- Downloaded from http://onepetro.org/jpt/article-pdf/22/03/347/2228075/spe-2711-pa.pdf by guest on 23 September 2021 We cannot begin to delve here into these wave tive direction at the trough but not so strong as at the theories, All appear in the literature in great detail. crest since -m, ~....,. +La ~a.r.in WI..+ .f th. Aim wgy~ Au w a Lue Uw v “.+-S . “. -“ . ——., .- , theory. The Stokes fifth or&r theory is described by ; Vi cosh ki (d + q) cos kj(0) > Skjelbreia et al.,’ and the numerical wave theory ap- j=l crest pears in Chappelear.6 A more recent stream function wave theory by Dean’” is also available as it has ; VJcoshkj(d–q)coskj ~ . (3) specific application for the analysis of the kinematic Ij=l ( )1 flow field of an irregular sea. The continuing effort Trough Of many WLIV-..w.. thenri.
Load more

Recommended publications
  • Is Hydrology Kinematic?
    HYDROLOGICAL PROCESSES Hydrol. Process. 16, 667–716 (2002) DOI: 10.1002/hyp.306 Is hydrology kinematic? V. P. Singh* Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803-6405, USA Abstract: A wide range of phenomena, natural as well as man-made, in physical, chemical and biological hydrology exhibit characteristics similar to those of kinematic waves. The question we ask is: can these phenomena be described using the theory of kinematic waves? Since the range of phenomena is wide, another question we ask is: how prevalent are kinematic waves? If they are widely pervasive, does that mean hydrology is kinematic or close to it? This paper addresses these issues, which are perceived to be fundamental to advancing the state-of-the-art of water science and engineering. Copyright 2002 John Wiley & Sons, Ltd. KEY WORDS biological hydrology; chemical hydrology; physical hydrology; kinematic wave theory; kinematics; flux laws INTRODUCTION There is a wide range of natural and man-made physical, chemical and biological flow phenomena that exhibit wave characteristics. The term ‘wave’ implies a disturbance travelling upstream, downstream or remaining stationary. We can visualize a water wave propagating where the water itself stays very much where it was before the wave was produced. We witness other waves which travel as well, such as heat waves, pressure waves, sound waves, etc. There is obviously the motion of matter, but there can also be the motion of form and other properties of the matter. The flow phenomena, according to the nature of particles composing them, can be distinguished into two categories: (1) flows of discrete noncoherent particles and (2) flows of continuous coherent particles.
    [Show full text]
  • Engenharias, Ciência E Tecnologia 6
    Luís Fernando Paulista Cotian (Organizador) Engenharias, Ciência e Tecnologia 6 Atena Editora 2019 2019 by Atena Editora Copyright da Atena Editora Editora Chefe: Profª Drª Antonella Carvalho de Oliveira Diagramação e Edição de Arte: Geraldo Alves e Lorena Prestes Revisão: Os autores Conselho Editorial Prof. Dr. Alan Mario Zuffo – Universidade Federal de Mato Grosso do Sul Prof. Dr. Álvaro Augusto de Borba Barreto – Universidade Federal de Pelotas Prof. Dr. Antonio Carlos Frasson – Universidade Tecnológica Federal do Paraná Prof. Dr. Antonio Isidro-Filho – Universidade de Brasília Profª Drª Cristina Gaio – Universidade de Lisboa Prof. Dr. Constantino Ribeiro de Oliveira Junior – Universidade Estadual de Ponta Grossa Profª Drª Daiane Garabeli Trojan – Universidade Norte do Paraná Prof. Dr. Darllan Collins da Cunha e Silva – Universidade Estadual Paulista Profª Drª Deusilene Souza Vieira Dall’Acqua – Universidade Federal de Rondônia Prof. Dr. Eloi Rufato Junior – Universidade Tecnológica Federal do Paraná Prof. Dr. Fábio Steiner – Universidade Estadual de Mato Grosso do Sul Prof. Dr. Gianfábio Pimentel Franco – Universidade Federal de Santa Maria Prof. Dr. Gilmei Fleck – Universidade Estadual do Oeste do Paraná Profª Drª Girlene Santos de Souza – Universidade Federal do Recôncavo da Bahia Profª Drª Ivone Goulart Lopes – Istituto Internazionele delle Figlie de Maria Ausiliatrice Profª Drª Juliane Sant’Ana Bento – Universidade Federal do Rio Grande do Sul Prof. Dr. Julio Candido de Meirelles Junior – Universidade Federal Fluminense Prof. Dr. Jorge González Aguilera – Universidade Federal de Mato Grosso do Sul Profª Drª Lina Maria Gonçalves – Universidade Federal do Tocantins Profª Drª Natiéli Piovesan – Instituto Federal do Rio Grande do Norte Profª Drª Paola Andressa Scortegagna – Universidade Estadual de Ponta Grossa Profª Drª Raissa Rachel Salustriano da Silva Matos – Universidade Federal do Maranhão Prof.
    [Show full text]
  • Variational of Surface Gravity Waves Over Bathymetry BOUSSINESQ
    Gert Klopman Variational BOUSSINESQ modelling of surface gravity waves over bathymetry VARIATIONAL BOUSSINESQ MODELLING OF SURFACE GRAVITY WAVES OVER BATHYMETRY Gert Klopman The research presented in this thesis has been performed within the group of Applied Analysis and Mathematical Physics (AAMP), Department of Applied Mathematics, Uni- versity of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. Copyright c 2010 by Gert Klopman, Zwolle, The Netherlands. Cover design by Esther Ris, www.e-riswerk.nl Printed by W¨ohrmann Print Service, Zutphen, The Netherlands. ISBN 978-90-365-3037-8 DOI 10.3990/1.9789036530378 VARIATIONAL BOUSSINESQ MODELLING OF SURFACE GRAVITY WAVES OVER BATHYMETRY PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. H. Brinksma, volgens besluit van het College voor Promoties in het openbaar te verdedigen op donderdag 27 mei 2010 om 13.15 uur door Gerrit Klopman geboren op 25 februari 1957 te Winschoten Dit proefschrift is goedgekeurd door de promotor prof. dr. ir. E.W.C. van Groesen Aan mijn moeder Contents Samenvatting vii Summary ix Acknowledgements x 1 Introduction 1 1.1 General .................................. 1 1.2 Variational principles for water waves . ... 4 1.3 Presentcontributions........................... 6 1.3.1 Motivation ............................ 6 1.3.2 Variational Boussinesq-type model for one shape function .. 7 1.3.3 Dispersionrelationforlinearwaves . 10 1.3.4 Linearwaveshoaling. 11 1.3.5 Linearwavereflectionbybathymetry . 12 1.3.6 Numerical modelling and verification . 14 1.4 Context .................................. 16 1.4.1 Exactlinearfrequencydispersion . 17 1.4.2 Frequency dispersion approximations . 18 1.5 Outline .................................
    [Show full text]
  • Shallow Water Simulation of Overland Flows in Idealised Catchments
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Shallow Water Simulation of Overland Flows in Idealised Catchments Dr. Dongfang Liang (corresponding author) Tel: +44 1223 764829; E-mail: [email protected] Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK Mr. Ilhan Özgen Tel: +49 30 31472428; E-mail: [email protected] Chair of Water Resources Management and Modeling of Hydrosystems, Technische Universität Berlin, Berlin, Germany Prof. Reinhard Hinkelmann Tel: 49 30 31472307; E-mail: [email protected] Chair of Water Resources Management and Modeling of Hydrosystems, Technische Universität Berlin, Berlin, Germany Prof. Yang Xiao [email protected] State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China Dr. Jack M. Chen [email protected] Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK 1 Abstract This paper investigates the relationship between the rainfall and runoff in idealised catchments, either with or without obstacle arrays, using an extensively-validated fully- dynamic shallow water model. This two-dimensional hydrodynamic model allows a direct transformation of the spatially distributed rainfall into the flow hydrograph at the catchment outlet. The model was first verified by reproducing the analytical and experimental results in both one-dimensional and two-dimensional situations. Then, dimensional analyses were exploited in deriving the dimensionless S-curve, which is able to generically depict the relationship between the rainfall and runoff. For a frictionless plane catchment, with or without an obstacle array, the dimensionless S- curve seems to be insensitive to the rainfall intensity, catchment area and slope, especially in the early steep-rising section of the curve.
    [Show full text]
  • ICHE 2014 | Book of Abstracts | Keynotes
    11th International Conference on Hydroscience & Engineering (ICHE2014) Book of Abstracts Hamburg, Germany, 28 September to 2 October 2014 Table of Contents Keynotes ..................................................................................................................................... 4 Oral Presentations ................................................................................................................... 15 Water Resources Planning and Management ...................................................................... 15 Experimental and Computational Hydraulics ...................................................................... 34 Groundwater Hydrology, Irrigation ..................................................................................... 77 Urban Water Management ................................................................................................... 90 River, Estuarine and Coastal Dynamics ............................................................................... 96 Sediment Transport and Morphodynamics......................................................................... 128 Interaction between Offshore Utilisation and the Environment ......................................... 174 Climate Change, Adaptation and Long-Term Predictions ................................................. 183 Eco-Hydraulics and Eco-Hydrology .................................................................................. 211 Integrated Modeling of Hydro-Systems .............................................................................
    [Show full text]
  • Loop Rating Curve of Tidal River: Flood and Tide Interaction
    International Journal of Engineering and Advanced Technology Studies Vol.4, No.5, pp.13-72, November 2016 Published by European Centre for Research Training and Development UK (www.eajournals.org) LOOP RATING CURVE OF TIDAL RIVER: FLOOD AND TIDE INTERACTION *Edward Ching-Ruey, LUO Faculty of Department of Civil Engineering, National Chi-Nan University, Taiwan ------------------------------------------------------------------------------------------------------------ ABSTRACT: For a steady flow, the rating curve is unique for a non-erodible section where the flow is uniform, but it is a loop for an erodible section when the flow is non-uniform. For an unsteady flow, the rating curve does exist, but it is more complicated, Relationships among water level, flow velocity, and discharge are all affected by flood hydrograph of upstream or tide from downstream. A more general relationship between water level and flow velocity (or discharge) with flood hydrograph from upstream and tide from downstream for time-dependent is derived analytically from diffusion equation and continuity equation. The upstream and downstream boundary conditions are expressed in terms of harmonic functions rather than a step function. The analytical solutions are compared with the numerical results obtained by using finite difference model with implicit scheme based on the complete Sanit-Venant equations for unsteady flow in open channel. It is found from the study that: the peak flow times at different locations are shifted due to the kinematic wave velocity; therefore, the rating curves at different locations are spread, not complete a loop like peacock tail feather. The rating curves for the subcritical flows are below the line of , and the supercritical flow rating curves are above .
    [Show full text]
  • Chapter Seventy Five Current Depth Refraction Of
    CHAPTER SEVENTY FIVE CURRENT DEPTH REFRACTION OF REGULAR WAVES 1 2 Ivar G. Jonsson and John B. Christoffersen ABSTRACT The complete set of equations for the refraction of small surface gravity waves on large-scale currents over a gradually varying sea bed is derived and presented. Wave lengths, direction of propagation and wave heights are all determined along the so-called wave rays as solu- tions to ordinary, first-order differential equations. Dissipation due to bed friction in the combined current wave motion is included. The ray tracing method is used in an example. A method for the calculation of current depth refraction of weakly non-linear waves is proposed. 1 . INTRODUCTION When water waves propagate over an area with a variable water depth and current velocity,the ensuing gradients together with the current wave interaction can cause drastical changes in the direction, length and height of the waves, see e.g. Mallory (1974). In this transformation of the waves, diffraction effects are often negligible, and the phenome- non is termed current depth refraction. This phenomenon is a significant physical process in many coastal and offshore areas, for instance near river mouths and tidal inlets, in the surf zone along a beach, and where wind waves meet major ocean currents. The refraction is of great importance for erosion and deposi- tion in coastal areas, forces on offshore structures, and ship naviga- tion. Current depth refraction is a complex problem of wave propagation in an inhomogeneous, anisotropic, dispersive, dissipative and moving medium . Attempts to solve the general case have therefore been scarce.
    [Show full text]
  • Part VII: ECMWF Wave Model
    Part VII: ECMWF Wave Model IFS DOCUMENTATION – Cy43r1 Operational implementation 22 Nov 2016 PART VII: ECMWF WAVE MODEL Table of contents Chapter 1 Introduction Chapter 2 The kinematic part of the energy balance equation Chapter 3 Parametrization of source terms Chapter 4 Data assimilation in WAM Chapter 5 Numerical scheme Chapter 6 WAM model software package Chapter 7 Wind wave interaction at ECMWF Chapter 8 Extreme wave forecasting Chapter 9 Second-order spectrum Chapter 10 Wave model output parameters References c Copyright 2016 European Centre for Medium-Range Weather Forecasts Shinfield Park, Reading, RG2 9AX, England Literary and scientific copyrights belong to ECMWF and are reserved in all countries. This publication is not to be reprinted or translated in whole or in part without the written permission of the Director. Appropriate non-commercial use will normally be granted under the condition that reference is made to ECMWF. The information within this publication is given in good faith and considered to be true, but ECMWF accepts no liability for error, omission and for loss or damage arising from its use. IFS Documentation – Cy43r1 1 TABLE OF CONTENTS REVISION HISTORY Changes since CY41R2 New subsection on Maximum Spectral Steepness in Chapter 2. • New chapter 10 based on ECMWF Post-processing section in Chapter 6. • 2 IFS Documentation – Cy43r1 Part VII: ECMWF Wave Model Chapter 1 Introduction Table of contents 1.1 Background 1.2 Structure of the documentation This document is partly based on Chapter III of “Dynamics and Modelling of Ocean Waves” by Komen et al. (1994). For more background information on the fundamentals of wave prediction models this book comes highly recommended.
    [Show full text]
  • The Pennsylvania State University
    The Pennsylvania State University The Graduate School Department of Civil and Environmental Engineering PHYSICS BASED, INTEGRATED MODELING OF HYDROLOGY AND HYDRAULICS AT WATERSHED SCALES A Thesis in Civil Engineering by Guobiao Huang 2006 Guobiao Huang Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2006 The thesis of Guobiao Huang was reviewed and approved* by the following: Gour-Tsyh (George) Yeh Provost Professor of Civil Engineering Thesis Co-Advisor Co-Chair of Committee Arthur C. Miller Distinguished Professor of Civil Engineering Thesis Co-Advisor Co-Chair of Committee Christopher J. Duffy Professor of Civil Engineering Derek Elsworth Professor of Geo-Environmental Engineering Peggy A. Johnson Professor of Civil Engineering Head of the Department of Civil and Environmental Engineering *Signatures are on file in the Graduate School iii ABSTRACT This thesis presents the major findings in the development of the hydrology and hydraulics modules of a first principle, physics-based watershed model (WASH123D Version 1.5). The numerical model simulates water movement in watersheds with individual water flow components of one-dimensional stream/channel network flow, two- dimensional overland flow and three-dimensional variably saturated subsurface flow and their interactions. Firstly, the complete Saint Venant equations/2-D shallow water equations (dynamic wave equations) and the kinematic wave or diffusion wave approximations were implemented as three solution options for 1-D channel network and 2-D overland flow. Different solution techniques are considered for the governing equations based on physical reasoning and their mathematical property. A characteristic based finite element method is chosen for the hyperbolic-type dynamic wave model.
    [Show full text]
  • Hydroinformatics, Fluvial Hydraulics and Limnology 1
    Hydroinformatics, Fluvial Hydraulics and Limnology Nils Reidar B. Olsen Department of Hydraulic and Environmental Engineering The Norwegian University of Science and Technology 3rd edition, 21 January 2003. ISBN 82-7598-046-1 Hydroinformatics, Fluvial Hydraulics and Limnology 1 Foreword The class “Hydroinformatics for Fluvial Hydraulics and Limnology” was offered the first time in the spring 2001 at the Norwegian University of Science and Technology. It is an undergraduate course in the 8th semester (4th year). The prerequisite is a basic course in Hydraulics/ hydromechanics, that includes the derivation of the basic equations, for example the continuity equation and the momentum equation. When I started my employment at the Norwegian University of Science and Technology, I was asked to teach the course and make a plan for its content. The basis was the discontinued course “River Hydraulics”, which also included topics on limnology. I was asked to include topics on water quality and also on numerical modelling. When adding topics to a course, it is also necessary to remove something. I have removed some of the basic hydraulics on the momentum equation, as this is taught in other courses the students had previously. I have also removed parts of the special topics of river hydraulics such as compound sections and bridge and culvert analysis. The compound sections hydraulics I believe can not be used in practical engineering anyway, as the geometry is too simplified compared with a natural river. The bridge analysis is based on simplifications of 1D flow models for a 3D situation. In the future, I believe a fully 3D model will be used instead, and this topic will be obso- lete.
    [Show full text]
  • Coastal Dynamics and Environments on Sandy Hook, New Jersey
    COASTAL DYNAMICS AND ENVIRONMENTS ON SANDY HOOK, NEW JERSEY NORBERT P .. PSUTY & LINDSAY NAKASHIMA Center jor Coastal and Environmental Studies, Rutgers University, New Brunswick, New Jersey GEORGE THEOKRITOFF Department of Geology, Rutgers University, Newark, New Jersey INTRODUCTION l,rl/H'" Sandy Hook is a complex and compound recurved barrier spit located at the norther)} end of the ocean shoreline of New Jersey (Figure 1). The spit is formed . from the northerly transport of beach material derived from the erosion of beaches extending approximately 40 kilometers to the south. The shoreline of Sandy Hook consists of several distinct s,egments with different rates ~nd forms of development. The spit system may be con­ veniently broken down for analysis into a set of sub­ systems, each with differing shoreline orientations to the approach of ocean swell and each experiencing dif­ ferent equilibrium conditions. These subsystems, or beach segments are identified on Figure 1 as numbers 1 through 7. Certain beach subsystems may be further divided into subunits, identified by lower case letters on Figure 1. Each of these experiences slightly different shoreline development. These smaller subunits are strongly affected by man-made beach protection struc­ tures. The effect of these structures in producing longshore movement of sediment through the spit system is considerable, as revealed in the conspicuous erosion downdrift of the beach protection structures in Segments 1 and 50 The majority of high energy deep water waves ap­ Fig. 1 Shoreline Change at Sandy Hook, 1943-1972. proach the region from the east-northeast and east (Saville, 1954). However, wave refraction on the in­ Tides at Sandy Hook are semi-diurnal with a 1.4 shore portion of the continental shelf causes the shallow meter mean range and a 1.7 meter spring range.
    [Show full text]
  • Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model
    830 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 40 Modal Interpretation for the Ekman Destabilization of Inviscidly Stable Baroclinic Flow in the Phillips Model GORDON E. SWATERS Applied Mathematics Institute, and Department of Mathematical and Statistical Sciences, and Institute for Geophysical Research, University of Alberta, Edmonton, Alberta, Canada (Manuscript received 9 July 2009, in final form 29 October 2009) ABSTRACT Ekman boundary layers can lead to the destabilization of baroclinic flow in the Phillips model that, in the absence of dissipation, is nonlinearly stable in the sense of Liapunov. It is shown that the Ekman-induced instability of inviscidly stable baroclinic flow in the Phillips model occurs if and only if the kinematic phase velocity associated with the dissipation lies outside the interval bounded by the greatest and least neutrally stable Rossby wave phase velocities. Thus, Ekman-induced destabilization does not correspond to a coalescence of the barotropic and baroclinic Rossby modes as in classical inviscid baroclinic instability. The differing modal mechanisms between the two instability processes is the reason why subcritical baroclinic shears in the classical theory can be destabilized by an Ekman layer, even in the zero dissipation limit of the theory. 1. Introduction (inviscid) model equations. In particular, KM09 have extended Romea’s (1977) work and showed that Ekman The role of dissipation in the transition to instability destabilization within the Phillips model can occur for in baroclinic quasigeostrophic flow can be counterintu- baroclinic shears that are inviscidly (i.e., in the absence of itive (Klein and Pedlosky 1992). It is natural to assume dissipation) nonlinearly stable in the sense of Liapunov.
    [Show full text]