Contact
E-Mail
JohnDFenton@gmail.com
Home address
St-Ulrichs-Platz 2/4
1070 Vienna
Austria
Phones:
Home +43 1 522 7467
Mobile/Handy/Cellulare:
John +43 664 7313 1035
Cristina +43 650 762 2417
Work
Guest Professor
Institute of Hydraulic Engineering and Water Resources
Management
TU Wien / Vienna University of Technology
Karlsplatz 13/222, 1040 Vienna, Austria
E-mail: john.fenton@tuwien.ac.at
Homepage: https://www.kw.tuwien.ac.at/en/team/visiting-professors/profile/fenton/
Family History
John's mother spent many years researching the Family History
A computer program for calculating rating curves
I have developed a computer program that reads in rating
data for a gauging station or structure and calculates a
rating curve using least squares methods. It has nothing
to do with the old method of trying to fit straight lines
on log-log axes. It seems to work well.
The program and its operation are described here.
All files necessary for the operation of the program are
in http://johndfenton.com/Rating-curves/Program-Files.exe
(it is necessary to copy that link text and paste it into
your internet browser). It is a self-extracting file that,
when downloaded and executed (after your computer maybe
asks you to say that it is acceptable), unpacks the files,
retaining the original file structure, under a directory
of your choice. The program is based on the research
described in two documents:
In those papers a number of different aspects of the
problem are considered, including calculating Rating
Envelopes for scattered data, and the incorporation
of dates of ratings so that one can calculate a rating
curve for any day in the past.
A method for approximating, smoothing, differentiating,
interpolating, or calculating an envelope to data
While working on river rating curves I developed a program
using quadratic or cubic splines. Its primary use was to
approximate noisy data, but the method seems quite flexible
to approximate more-or-less scattered data, or to smooth,
differentiate, interpolate, or calculate an envelope to that
data. An example is Nikuradse's results for resistance
in pipes, which shows variable curvature:
The program and a
supporting theoretical document are described here.
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Collected papers
Recent publications
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A literature review shows that the most
important physical quantities determining
environmental impact of ship waves in a waterway are
the fluid velocities, maximum and minimum water
levels, and size of drawdown events. Fluid velocity
can vary strongly in the vertical so that the usual
measurements at a single point are not enough unless
made near where the effects are most important,
often the bed. Customary use of wave height as a
measure of impact has been misleading, because the
all-important fluid velocity is of a scale given by
wave height divided by wave period. A good and
simple estimate of the surface velocity as a
disturbance scale is shown to be given by the time
derivative of the free surface height. The most
important role of linear wave theory is to explain
and understand the physics and measurement
procedures, such as done here in several places. Its
use for obtaining numerical results is criticised.
Instead, three integral measures of impact are
proposed, all of which use surface elevation
measurements and which require no essential
mathematical approximations or wave-by-wave
analysis. The methods are applied to a study of ship
waves on the Danube River. A number of results are
presented, including examination of the effects of
measurement frequency. After a ship passage, due to
repeated shoreline reflections of the wake waves,
the river is brought into a long-lasting state of
short-crested disturbances, with finite fluid
velocities. The environmental consequences of this
might be important. After the primary and secondary
ship waves it could be called the tertiary wave
system.
- Fenton, J. D. (2019) Flood
routing methods, Journal of Hydrology 570,
251-264.
The hierarchy of one-dimensional equations and
numerical methods describing the motion of floods and
disturbances in streams is studied, critically
reviewed, and a number of results obtained. Initially
the long wave equations are considered. When presented
in terms of discharge and cross-sectional area they
enable the development of simple fully-nonlinear
advection-diffusion models whose only approximation is
that disturbances be very long, easily satisfied in
most flood routing problems. Then, making the
approximation that changes in surface slope are
relatively small such that diffusion terms in the
equations are small, various advection-diffusion and
Muskingum models are derived. Several well-known
Muskingum formulations are tested; one is found to be
in error. The three families of the governing
equations, the long wave equations, the
advection-diffusion and the Muskingum approximations,
are linearised and analytical solutions obtained. A
dimensionless diffusion-frequency number measures the
accuracies of the approximate methods. Criteria for
practical use are given, which reveal when they have
difficulties for streams of small slope, for
fast-rising floods, and/or when shorter period waves
are present in an inflow hydrograph. They can probably
be used in most flood routing problems with an
idealised smooth inflow. However the fact that they
cannot be used for all problems requires a general
alternative flood routing method, for which it is
recommended to use the long wave equations themselves
written in terms of discharge and cross-sectional
area, when a surprisingly simple physical stream model
can be used. An explicit finite difference numerical
method is presented that can be used with different
inflow specifications and downstream boundary
conditions, and is recommended for general use.
- Fenton, J. D. (2018) On
the generation of stream rating curves, Journal
of Hydrology 564, 748 - 757.
Traditional methods for the calculation of rating
curves from measurements of water level and discharge
are criticised as being limited and complicated to
implement, such that manual methods are still often
used. Two methods for automatic computation are
developed using least-squares approximation, one based
on polynomials and the other on piecewise-continuous
splines. Computational problems are investigated and
procedures recommended to overcome them. Both methods
are found to work well and once the parameters for a
gauging station have been determined, rating data can
be processed automatically. For some streams,
ephemeral changes of resistance may be important,
evidenced by scattered or loopy data. For such cases,
the approximation methods can be used to generate a
rating envelope as well, allowing the routine
calculation also of maximum and minimum expected
flows. Criticism is made of current shift curve
practices. Finally, the approximation methods allow
the specification of weights for the data points,
enabling the filtering of data, especially decreasing
the importance of points with age and allowing the
computation of a rating curve for any time in the past
or present.
- Fenton, J. D. (2018) Where "Small is Beautiful'' -
Mathematical Modelling and Free Surface Flows, Chapter 3
in
Free Surface Flows and Transport Processes,
Kalinowska, M. B.; Mrokowska, M. M. & Rowiński, P.
M. (Eds.), Proc. 36th International School of
Hydraulics, Jachranka, Poland, May 2017, Springer.
Mathematical and computational models in river and
canal hydraulics often require data that may not be
available, or it might be available and accurate while
other information is only roughly known. There is
considerable room for the development of approximate
models requiring fewer details but giving more
insight. Techniques are presented, especially
linearisation, which is used in several places. A
selection of helpful mathematical methods is
presented. The approximation of data is discussed and
methods presented, showing that a slightly more
sophisticated approach is necessary. Several problems
in waves and flows in open channels are then examined.
Complicated methods have often been used instead of
standard simple numerical ones. The one-dimensional
long wave equations are discussed and presented. A
formulation in terms of cross-sectional area is shown
to have a surprising property, that the equations can
be solved with little knowledge of the stream
bathymetry. Generalised finite difference methods for
long wave equations are presented and used. They have
long been incorrectly believed to be unstable, which
has stunted development in the field. Past
presentations of boundary conditions have been
unsatisfactory, and a systematic exposition is given
using finite differences. The nature of the long wave
equations and their solutions is examined. A
simplified but accurate equation for flood routing is
presented. However, numerical solution of the long
wave equations by explicit finite differences is also
simple, and more general. A common problem, the
numerical solution of steady flows is then discussed.
Traditional methods are criticised and simple standard
numerical ones are proposed and demonstrated. A
linearised model for the surface profile of a stream
is obtained, also to give solutions without requiring
detailed bathymetric knowledge.
- Darvishi, E., Fenton, J. D. and Kouchakzadeh, S.
(2017) Boussinesq
equations for flows over steep slopes and structures,
Journal of Hydraulic Research 55(3),
324-337.
A finite-slope Boussinesq equation is developed to
model curved transcritical flow over spillways and
broad-crested weirs, even with large slopes. A number
of laboratory experiments were performed with
different transcritical flow problems including
changes in channel gradients and a trapezoidal weir.
The equation and the numerical model were tested using
results from those experiments and from those for a
steep and sharply-curved weir structure, with good
results. They can be used as a computational flume to
determine the head-discharge characteristics of
proposed structures. A novel feature of the equation
and numerical method is that higher derivatives of the
bed topography are best ignored, apparently mimicking
the effects of flow separation in smoothing it.
- Fenton, J. D. (2016) Hydraulics:
science, knowledge, and culture, Journal of
Hydraulic Research 54(5), 485-501.
The processes of thinking, research,
dissemination, and use of research and knowledge in
hydraulics are examined, differentiating it from
hydrology, and suggesting greater use of scientific
methods and theories. At highly technical levels, that
is already done, but it is suggested that there is
room for a greater simplicity of approach, based on
scientific rigour, recognising that much of what is
done in hydraulics is modelling. This would make
understanding, access to, and participation in
research easier for members of the profession. A
number of recommendations and conclusions are made.
The article has a critical tone, but its main
intention is to be helpful to individual hydraulicians
and to the profession at large. Suggestions are made
as to how the profession might use the Web to give
open access to research findings and to create an open
resource for hydraulics knowledge, as connection by
colleagues in all countries is now possible and
feasible.
- Fenton, J. D. and Darvishi, E. (2016) Discussion of
"Minimum specific energy and transcritical flow in
unsteady open-channel flow" by Oscar Castro-Orgaz and
Hubert Chanson, Journal of Irrigation and Drainage
Engineering 142(10), http://ascelibrary.org/doi/10.1061/(ASCE)IR.1943-4774.0001077
We show that there is no justification for the
Singular Point Theory of Massé (1938) for calculating
transitional flows between sub- and super-critical
flows.
This was given the 2018 Best Discussion Award by the Journal of Irrigation and
Drainage Engineering.
- Fenton, J. D. (2015) Basic physical processes in
rivers, Chapter 1 in
Rivers – Physical, Fluvial and Environmental
Processes, (eds) Paweł Rowiński and Artur
Radecki-Pawlik, Springer.
The governing long wave equations for a curved
channel can be developed with very few limiting
approximations, especially using momentum rather than
energy. The curvature is then shown to be rarely
important and is subsequently ignored. Wave periods,
imposed by boundary conditions, are asserted to be
fundamental. Long waves have speeds and propagation
properties that depend on period, and there is no such
thing as a single long wave speed. Examination of
dimensionless equations and solution of linearised
equations using wave period shows a novel
interpretation of terms in the momentum equation: the
”kinematic” approximation and wave are misnomers: the
approximation lies not in the neglect of inertial
terms but is actually a very long period one. The
outstanding problem of river modelling, however, is
that of resistance to the flow. A large data set from
stream-gaugings is considered and it is shown that the
state of the bed, namely the arrangement of bed grains
by previous flows, is more important than actual grain
size. A formula for resistance is proposed which
contains a parameter representing bed state. As that
state is usually changing with flow, one can not be
sure what the resistance actually will be. This
uncertainty may have important implications for
modelling. The momentum principle is then applied also
to obstacles such as bridge piers, and a simple
approximation gives greater understanding and a
practical method for incorporation in river models.
Finally, river junctions are considered, and the
momentum approach with the very long period
approximation shows that they can be modelled simply.
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Lectures in hydraulics, numerics, and maritime
engineering
The most recent set of lecture notes here are those for a
course on River Engineering at the Vienna University of
Technology in 2021-2022: Home Page
Lecture notes as slides in colour
Lecture notes for printing in
small format, B\&W
This is an introduction to
hydraulics. True energy conservation is presented, and
Bernoulli's equation is left to a subsidiary (and
occasionally useful) role. It is an integrated momentum
equation which is valid along a streamline and whose
"constant" varies across streamlines. It is absurd to
expect to apply it in fully-turbulent three-dimensional
situations - for example the flow from a reservoir to a
tap in a house. It is much more intellectually honest
simply to use conservation of energy, which is more easily
derived and is a more plausible model of most hydraulic
problems.
A final year elective subject,
dealing with elementary oceanography, water wave theory,
tsunami, and coastal engineering
An introduction to numerical methods, presenting theory
and applications largely using the optimisation package in
Microsoft Excel.
This is a set of notes describing the application of
numerical methods. There are some innovations.
Coastal and Ocean Engineering - Steady water waves
A computer program ("Fourier") that solves the problem of
steadily-progressing waves over a flat bottom is described
and made available here: Fourier
Programs that implement Stokes and cnoidal theories are
also available. The instructions file for all is Instructions.pdf.,
which is also included in Fourier.zip. The
latest changes are shown as highlighted comments.
The three wave programs are
- A Fourier approximation method whose only
approximation lies in truncating the number of terms in
the approximating series: Fourier.zip -
current version, 23 July 2015.
- An implementation of cnoidal theory, which is based on
series expansions in shallowness, requiring that the
waves be long relative to the water depth : Cnoidal.zip -
current version, 20 March 2015 (to be unpacked in a
sub-directory of the Fourier one). This is an
approximation, and not as applicable to higher waves as
the Fourier method. It can be used as a check on that
method - for long waves that are not high, both should
give the same results.
- An implementation of Stokes theory, requiring that the
waves be not too long relative to the water depth: Stokes.zip -
current version 20 March 2015 (to be unpacked in a
sub-directory of the Fourier one). This is also an
approximation, and not as applicable to higher waves as
the Fourier method. It can be used as a check on that
method - for waves that are not high or long, both
should give the same results.
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