ENVIRONMENTAL FLUID MECHANICS
University of Texas at Austin, Department of Civil, Architectural & Environmental Engineering
 
 

Ph.D. Dissertation, Stanford University,

Dept. of Civil and Environmental Engineering, 1997

Numerical Simulation of Nonlinear Free-Surface Waves on a Turbulent Open-Channel Flow

by Ben R. Hodges

This dissertation provides the development and application of a Large-Eddy Simulation method for free surface flows where the viscous boundary layer beneath the water surface is resolved in an orthogonal boundary-fitted coordinate system. (235 pages). See also the papers Hodges & Street (1999) and Hodges & Street (1998) below.

Note, the dissertation loads very slowly in Adobe Acrobat 6.0 as the version of PostScript produced from LaTex in 1997 is not optimized for pdf conversion. It is suggested that you save this to your local hard drive to view with Acrobat rather than trying to view in a browser plug-in (which may lock up your machine!)

Download: Entire dissertation: PDF (7.8 MB)

Download: Text and grayscale figures only: PDF (2 MB)

Download: Color plates only, pp. 176-184 PDF (5.8 MB)

Below are the journal and peer-reviewed conference papers that I have authored or co-authored. For those papers that do not have links, please email me and I will be glad to send you a reprint.

Technical Reports on CWR-ELCOM and info on other ELCOM papers can be found back on another web page

I occasionally get requests for copies of my dissertation. It is too big to email and I don't have any hard copies printed up for distribution, so I have made a PDF version that is downloadable at right.

 

 

2006

Hydrostatic and non-hydrostatic modeling of internal waves (2006) - The capabilities of both hydrostatic and non-hydrostatic internal wave models using primitive equations are compared to laboratory experiments. It is shown that the hydrostatic bore has similar characteristics to the leading wave of a non-hydrostatic train of solitary waves, which may provide a basis for subgrid-scale internal wave closure schemes for hydrostatic models.

<web abstract> <pdf of first page not yet available>

Wadzuk, B.M., and B.R. Hodges (2006), “Hydrostatic and non-hydrostatic modeling of internal waves,” submitted to Journal of Engineering Mechanics, (March, 2006)

A grid-switching strategy for computing high-frequency, high wave number motions embedded in geophysical flows (2006) - The effects of altering the model grid when an internal wave transitions from linear hydrostatic behavior to nonlinear non-hydrostatic behavior is examined.

<web abstract> <pdf of first page not yet available>

Botelho, D., J. Imberger, C. Dallimore, and B.R. Hodges (2006), “A grid-switching strategy for computing high-frequency, high wave number motions embedded in geophysical flows,” submitted to International Journal for Numerical Methods in Fluids (February, 2006).

Baroclinic stability of two-level semi-implicit numerical methods for the 3D shallow water equations (2006) - The TRIM method for baroclinic flows is shown to be unstable in the inviscid limit for a Crank-Nicolson discretization of the barotropic term. Theoretical stability for predictor-corrector methods is examined.

<web abstract> <pdf of first page not yet available>

Rueda, F.J., E. Sanmiguel-Rojas, and B.R. Hodges (2005), “Baroclinic stability of two-level semi-implicit numerical methods for the 3D shallow water equations,” submitted to Journal of Computational Physics, (November, 2005).

Numerical error assessment and a temporal horizon for internal waves in a hydrostatic model (2006) - Methods for quantifying basin-wide numerical diffusivity and numerical viscosity in a closed-basin stratified flow are proposed. It is demonstrated that a hydrostatic model has a limited temporal horizon for reasonable representation of internal wave dynamics.

<web abstract> <pdf of first page >

Hodges, B.R., B. Laval, and B.M. Wadzuk, Numerical error assessment and a temporal horizon for internal waves in a hydrostatic model,Ocean Modelling, 13(1):44-64, doi:10.1016/j.ocemod.2005.09.005

Identification of submerged large woody debris from single-beam echo soundings (2006) - Statistical methods for separating the LWD signal from the background bathymetry in a river channel data set are investigated. Scale-space analysis methods are found to be too complex and inaccurate. A method of discrimination based on standard deviation is proposed and is shown to be simple and effective.

<web abstract> <pdf of first page not yet available>

White, L. , B.R. Hodges, B. Austin, and T. Osting, (2006), "Identification of submerged large woody debris from single-beam echo soundings,” , Journal of Hydroinformatics, 8(1):1-12.


2005

Drifter modeling and error assessment in wind driven currents (2005) - A new approach is developed for modeling drifters that includes the dynamics of forcing on the drifter body. Prior methods of error assessment for drifter performance are analyzed and a new "Circle Assessment" method is proposed that provides improved quantitative analyses.

<web abstract> <pdf of report (2.5 MB)>

Furnans, J.E., B.R. Hodges, and J. Imberger (2005), Drifter Modeling and Error Assessment in Wind Driven Currents, CRWR Online Report 05-5, Center for Research in Water Resources, University of Texas at Austin, 172 pages, http://www.crwr.utexas.edu/online.html.

Geospatial representation of river channels (2005) - A method of using curvilinear channel coordinates (see Hodges & Imberger 2001, below) is adapted into a GIS representation to provide a method of creating a smooth, flow-oriented mesh from bathymetry sampling or river cross-sections.

<web abstract> <pdf of first page>

Merwade, V.M., D.R. Maidment and B.R. Hodges, Geospatial representation of river channels, ASCE Journal of Hydrologic Engineering, 10(3):243-251 (2005).

Filtering the signature of submerged large woody debris from bathymetry data (2005) - Digital filtering methods for separating the LWD signal from the background bathymetry in a river channel data set are investigated. Linear filters are shown to be difficult to consistently apply. A method using nonlinear filters is proposed. It is shown that a scaling analysis can be used to remove the analyst's judgement from the selection of the filter scale

<web abstract> <pdf of first page>

White, L., and B.R. Hodges, Filtering the signature of submerged large woody debris from bathymetry data, Journal of Hydrology, 309:53-65, (2005).

Grid-scale dependency of subgrid-scale structure effects in hydraulic models of rivers and streams (2005) - Subgrid-scale heterogeneity creates difficulties for hydraulic modeling because the effects of turbulence propagate upscale, resulting in turbulence models that implicitly require different calibrations at different grid scales. We explore new approaches to addressing this issue.

<web abstract> <pdf of McMat2005 conference paper (256kb)>

<pdf of UT Graduate Student Conference paper (200kb)> <pdf of poster (260kb)>

Fu, S. and B.R. Hodges, Grid-scale dependency of subgrid-scale structure effects in hydraulic models of rivers and streams, Mechanics and Materials Conference 2005 (McMat 2005), June 1-3, 2005, Louisiana State University, Baton Rouge, Electronic Proceedings (CD-ROM), 5 pgs.

Fu, S. and B.R. Hodges, A hybrid RANS and LES model for studying the flow around large woody debris in a river, University of Texas at Austin Engineering Graduate Student Research Conference, April 28, 2005, 4 pgs.

Improved techniques for gravity current modeling (2005) - Shallow estuaries present problems for modeling the fate of thin layer gravity currents. This paper reflects some of our initial work in this area.

<web abstract> <pdf of McMat2005 conference paper (50 kb)>

Kulis, S. and B.R. Hodges, Improved techniques for gravity current modeling, Mechanics and Materials Conference 2005 (McMat 2005), June 1-3, 2005, Louisiana State University, Baton Rouge, Electronic Proceedings (CD-ROM), 4 pgs.


2004

Hydrostatic and Non-hydrostatic Internal Wave Models (2004) - An investigation of the errors resulting from using the hydrostatic approximation in modeling internal waves.

<web abstract> <pdf of report (3.2 MB)>

Wadzuk, B.M and B.R. Hodges, Hydrostatic and Non-hydrostatic Internal Wave Models, CRWR Online Report 04-09, Center for Research in Water Resources, University of Texas at Austin, (2004), 77 pages, http://www.crwr.utexas.edu/online.html.

Modeling a Plunging Underflow (2004) - This is an extension of the work Dallimore et al., 2003 (see below). In this paper the method for coupling a 2D benthic boundary layer model to a 3D model is extended to handle plunging underflows.

<web abstract> <pdf of first page>

Dallimore, C.J., J. Imberger and B.R. Hodges, “Modeling a Plunging Underflow,” ASCE Journal of Hydraulic Engineering, 130(11): 1068-1076, (2004).

Accuracy order of Crank-Nicolson discretization for hydrostatic free surface flow (2004) - This examines the use of C-N discretization in CWR-ELCOM for the free surface, and derives a correction term that is necessary to preserve formal second-order accuracy. Of particular interest is a demonstration accuracy of the free surface solution for free waves is less than second-order when the barotropic CFL is greater than unity. Some initial results associated with this paper were presented at a conference

<more info>. <web abstract>. <pdf of first page>

Hodges, B.R., “Accuracy order of Crank-Nicolson Discretization for Hydrostatic Free Surface Flow,” ASCE Journal of Engineering Mechanics, 130(8): 904-910 (2004).

Hodges, B.R., “A second-order correction for semi-implicit shallow water methods,” 16th ASCE Engineering Mechanics Conference, July 16-18 2003, University of Washington, Seattle, Electronic Proceedings (CD-ROM ).

Numerical diffusion and dissipation in hydrostatic models in internal waves (2004) - We demonstrate that numerical diffusion of mass and dissipation of energydo not monotonically decrease with grid resolution in a hydrostatic internal wave model. Instead, changing the grid scale changes the horizontal length scale of small waves produced through nonlinear steepening in the absence of nonhydrostatic pressure.

<web abstract> <pdf of EM2004 conference paper>

Hodges, B.R., and S. K. Delavan, “Numerical diffusion and dissipation in hydrostatic models in internal waves,” 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, Newark, Electronic Proceedings (CD-ROM ), 4 pgs..

Isolation of hydrostatic regions within a basin (2004) - This paper demonstrates how a hydrostatic model can be used to predict regions of expected non-hydrostatic behavior.

<web abstract> <pdf of EM2004 conference paper>

Wadzuk, B.M , and B.R. Hodges, “Isolation of hydrostatic regions within a basin,” 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, Newark, Electronic Proceedings (CD-ROM ).

Lake Kinneret surface circulation with particle tracking (2004) - Preliminary results of model results for drifters in Lake Kinneret are presented.

<web abstract> <pdf of EM conference paper>

Furnans, J.E., B.R. Hodges and J. Imberger, “Lake Kinneret surface circulation with particle tracking,” 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, Newark, Electronic Proceedings (CD-ROM ).


2003

Coupling an underflow model to a 3D hydrodynamic model (2003) - To solve problems of "numerical convective entrainment" when high-density water flows under low-density water, we develop a method to couple a 2D benthic boundary model to 3D CWR-ELCOM. It is demonstrated with field data from Lake Ogawara, Japan, and Lake Kinneret, Israel, that the coupled model maintains coherent underflow characteristics that cannot be captured by a 3D model alone.

<web abstract> <pdf of first page>

Dallimore, C., B.R. Hodges, and J. Imberger, "Coupling an underflow model to a 3D hydrodynamic model." ASCE Journal of Hydraulic Engineering 129: (10): 1-10, (2003).

Reducing Numerical Diffusion Effects with Pycnocline Filter (2003) - A methodology is proposed to counter the cumulative effects of numerical diffusion for models of density-stratified systems. The accumulation of even small amounts of diffusion over a long simulation can signifcantly distort the properties of internal waves. This journal paper is related to a prior conference paper

<web abstract> <pdf of first page>

Laval, B., B.R. Hodges, and J. Imberger, "Reducing Numerical Diffusion Effects with Pycnocline Filter." ASCE Journal of Hydraulic Engineering 129: (3): 215-224 (2003).

Modeling Circulation in Lakes: Spatial and Temporal Variations (2003) - The effects of spatial and temporal variations in the wind field are examined with the CWR-ELCOM model and field data. The mixed-layer algorithm in CWR-ELCOM is improved with a mixing time-scale to provide temporal invariance in results as the time step is changed.

<web abstract> <pdf of first page> <download paper from L&O (420KB)>

Laval, B., J. Imberger, B.R. Hodges, R. Stocker, “Modeling Circulation in Lakes: Spatial and Temporal Variations,” Limnology and Oceanography, 48:(3):983-994 (2003).

Comparing hydrostatic and nonhydrostatic Navier-Stokes models of internal waves (2003) - Preliminary results for modeling hydrostatic and nonhydrostatic internal waves are presented and discussed. A related paper was presented at Texas Water 2003

<web abstract> <pdf of EM2003 conference paper 273 KB>

Wadzuk, B.M., and B.R. Hodges, “Comparing hydrostatic and nonhydrostatic Navier-Stokes models of internal waves,” 16th ASCE Engineering Mechanics Conference, July 16-18 2003, University of Washington, Seattle, Electronic Proceedings (CD-ROM )

Wadzuk, B.M. and B.R. Hodges 2003, "The Limitation of the Hydrostatic Approximation for Nonlinear Internal Waves." Proceedings of Texas Water 2003, April 1-4, 2003, Corpus Christi, TX.

A second-order correction for semi-implicit shallow water methods (2003) - This examines the use of C-N discretization in CWR-ELCOM for the free surface, and derives a correction term that is necessary to preserve formal second-order accuracy. This was the precursor to the paper on C-N methods in 2004 (see above).

<more info>

Hodges, B.R., “Accuracy order of Crank-Nicolson Discretization for Hydrostatic Free Surface Flow,” ASCE Journal of Engineering Mechanics, 130(8): 904-910 (2004).

Hodges, B.R., “A second-order correction for semi-implicit shallow water methods,” 16th ASCE Engineering Mechanics Conference, July 16-18 2003, University of Washington, Seattle, Electronic Proceedings (CD-ROM ).

 


2002

Impacts of Hydrological Changes on Phytoplankton Succession in the Swan River, Western Australia (2002)- The CWR-ELCOM hydrodynamic code is linked to the CAEDYM water quality code (also developed at CWR) to examine the species succession in the Swan River and how changes in the catchment during European settlement and development may have altered the ecosystem behavior.

<web abstract> <pdf of first page>

Chan, T.U., D.P. Hamilton, B.J. Robson, B.R. Hodges, and C. Dallimore. "Impacts of hydrological change on phytoplankton succession in the Swan River, Western Australia." Estuaries 25: 1406-1415, (2002).


2001

Simple curvilinear method for numerical methods of open channels (2001) - A Cartesian grid model (CWR-ELCOM) can be converted into a curvilinear model with relatively small effort through the use of a perturbation expansion approach - which is valid as long as the width of the system is smaller than the large-scale radius of curvature (a typical case for rivers and narrow reservoirs). This also allows estimation of the scales of error for models which "straighten" the curves in a river. Reprints are available on request. This paper is complemented by a more detailed technical report <more info>. A related paper on straightening reservoir bathymetry was also presented at a conference <more info>.

<web abstract> <pdf of first page>

Hodges, B.R., and J. Imberger. "Simple curvilinear method for numerical methods of open channels." Journal of Hydraulic Engineering 127: (11): 949-958, (2001).

Model bathymetry for sinuous, dendritic reservoirs (2001) - We apply the methods developed in Hodges and Imberger (2001), above, to develop an approximate "straightened" bathymetry that can be used for 3D reservoir modelling.

<web abstract> <pdf of paper>

Waduzk, B. and B.R. Hodges, “Model bathymetry for sinuous, dendritic reservoirs,” 6th Workshop on Physical Processes in Natural Waters,” University of Girona, Catalonia-Spain, 27-29 June 2001, pp. 205-209 .


2000

Modeling basin-scale internal waves in a stratified lake (2000) - The advanced mixed-layer model algorithm used in CWR-ELCOM is described, and the model's ability to represent the large internal wave signatures in Lake Kinneret, Israel, is demonstrated. Direct comparisons to extensive field data are made, with very favorable results. Reprints are available on request.

<web abstract> <pdf of first page>

Hodges, B.R., J. Imberger, A. Saggio, and K. B. Winters,"Modeling basin-scale internal waves in a stratified lake." Limnology and Oceanography 45:(7):1603-1620, (2000).

The effects of freshwater flows and salinity on phytoplankton biomass and composition in an urban estuary, the Swan River, Western Australia (2000) - Preliminary results of field and modeling studies on the Swan River are reported. See Chan et al (2002) above for the more complete analysis.

Hamilton, D.P., T.U. Chan, B.J. Robson and B.R. Hodges, “The effects of freshwater flows and salinity on phytoplankton biomass and composition in an urban estuary, the Swan River, Western Australia,” Proceedings, 3rd International Hydrology and Water Resources Symposium, Nov. 2000, Vol 1, pp. 114-119 .

Recirculation and equilibrium displacement of the thermocline in a wind-driven stratified lake (2000) - Analysis of effects of vertical recirculation on the internal wave setup due to wind forcing. It is shown that underpredicting the depth of the surface-mixed layer in a vertically-recirculating system can result in undepredicting the initial setup of the internal seiche.

<web abstract> <pdf of paper>

Hodges, B.R. “Recirculation and equilibrium displacement of the thermocline in a wind-driven stratified lake,” Fifth International Symposium on Stratified Flows, Vancouver, Canada, July 7-11, 2000, pp. 327-330 .

Numerical diffusion in stratified lake models (2000) - Preliminary development of a technique for ad hoc correction of numerical diffusion. See paper Laval et al. (2003), "Reducing Numerical Diffusion Effects with Pycnocline Filter

<web abstract> <pdf of paper>

Laval, B., B.R. Hodges, and J. Imberger, “Numerical diffusion in stratified lake models,” Fifth International Symposium on Stratified Flows, Vancouver, Canada, July 7-11, 2000, pp. 343-348 .

Modeling the hydrodynamics of stratified lakes (2000) - Review of principle advances in modeling. Delivered as invited plenary lecture at Hydroinformatics 2000.

<web abstract> <pdf of paper>

Hodges, B.R., J. Imberger, B. Laval, J. Appt, “Modeling the hydrodynamics of stratified lakes,” Proceedings of Hydroinformatics 2000 (CD-ROM), Iowa Institute for Hydraulic Research, University of Iowa, July 23-27, 2000 .


1999 and earlier

On simulation of turbulent nonlinear free-surface flows (1999) - A moving-grid fractional-step method in boundary-fitted curvilinear coordinates is used with dynamic large-eddy simulation (LES) to model the turbulent flow beneath a water wave. It is pointed out that the nonlinear kinematic boundary condition, when filtered using LES, provides subgrid-scale correlations that are similar to the Leonard, Cross and Reynolds terms of LES. These terms have not been considered in any models to date. THis work is based on my dissertation (Hodges, 1997, see top of this page)

<web abstract> <pdf from journal: doi:10.1006/jcph.1998.6166 >

B.R. Hodges and R.L. Street, “On simulation of turbulent nonlinear free-surface flows,” Journal of Computational Physics, 151:425-457, (1999).

Wave-induced enstrophy and dissipation in a sheared turbulent current (1998) - Taking the results from my dissertation (Hodges, 1997; see top of this page) a step further, we analyzed how the surface waves distort the fluctuating enstrophy in the current.

<web abstract> <pdf of paper>

Hodges, B.R. and R.L. Street, Wave-induced enstrophy and dissipation in a sheared turbulent current ,”Wave-induced enstrophy and dissipation in a sheared turbulent current, in M.C. Thompson and K. Hourigan (editors), Proceedings of the Thirteenth Australasian Fluid Mechanics Conference, Monash University, Melbourne, Australia, 13-18 Dec. 1998. Vol II, pp. 717-720.

Other conference papers that were precursors to my dissertation:

B.R. Hodges and R.L. Street, “Three-dimensional, nonlinear, viscous wave interactions in a sloshing tank,” in Proceedings of the Fluids Engineering Summer Meeting, Vol. 3, FED-Vol. 238, ASME, pp. 361-367, (1996).

B.R. Hodges, R.L. Street and Y. Zang, “A method for simulation of viscous, nonlinear, free-surface flows,” in Twentieth Symposium on Naval Hydrodynamics, National Academy Press, pp. 791-809, (1996).

 

 
©2006 Ben R. Hodges • last updated April 19, 2006

UT College of EngineeringDept of Civil EngineeringEWRE CRWREFM Home