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24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Wash Waves Generated by
Ships Moving on Fairways of Varying Topography
Tao Lange, Rupert Henn2 & Som Deo Shaman
(~VBD - European Development Centre for Inland and Coastal Navigation, 2Institute of Ship
Technology and Transport Systems, Mercator University, Duisburg, Germany)
ABSTRACT
Using the computer program BEShiWa, based on
extended Boussinesq's equations for the far-field
flow and slender-body theory for the near-ship flow,
the wash waves generated by ships were investigated
taking account of varying topographies. It appears
that for the time being the shallow-water approxima-
tion based on Boussinesq-type equations is a useful
method for combining all effects associated with the
nonlinear and unsteady nature on the one hand and
the large-domain feature on the ether hanr1 of wash
problems. A good agreement between computations
and measurements was achieved for waves far from
the ship in a rectangular channel as well as for 2D
wave propagation over an uneven bottom. Further-
more, it was found that the propagation of wash
waves depends significantly on bottom topography,
ship speed, and motion history.
INTRODUCTION
Recently, increased attention is being paid to wash
waves by ferry operators, naval architects, marine and
environmental consultants, and port and waterway
authorities. Such wash waves can affect the safe
operation of other floating bodies near the shoreline
or the bank and endanger human life on beaches.
Moreover, they can cause environmental damage, for
instance, bank erosion.
Strong wash waves can be generated by a
fast ship at high speeds or by a large ship at moderate
speeds, operating on a near-shore fairway or on an
inland waterway. The resulting wash-wave system is
basically nonlinear due to the wave characteristics in
shallow water and usually unsteady due to the non-
uniform seabed or inland waterway topography.
Moreover, the major part of the wash wave system
consists of divergent waves which can travel over a
long distance without loss of energy until close to the
shore.
Due to the great interest in wake-wash ef-
fects, a considerable amount of research effort has
been devoted to the wash problem during the last few
years. In model experimental studies the focus has
been on designing low-wash ships and acquiring
reliable data for validation, see, e.g., Zibell and Grol-
lius (1999), MacLarlane and Renilson (1999), and
Koushan et al.~2001~. Also full-scale measurements
have been taken, aiming at deriving recommendations
for safe ship operation as well as finding possibilities
of ship monitoring in sensitive operational areas, see,
e.g., Feldtmann and Garner (1999), and Bolt (2001~.
In numerical simulations the focus has been on de-
veloping efficient methods. For a ship moving on
water of uniform depth the linear theory can be ap-
plied usefully in the subcritical and the supercritical
speed range, see, e.g., Doctors et al.~2001~. For these
steady cases a steady nonlinear free-surface panel
method can also be used, see, e.g., Raven (20004. The
wave generation by a ship moving in a channel at a
transcritical speed, on the other hand, can be well
predicted using Kadomtsev-Petviashvili (KP) type
equations, see, e.g., Chen and Sharma (1995), where
the near-ship flow is approximated by an extended
slender-body theory. This KP approximation has been
extended by Chen and Uliczka (1999) for ships mov-
ing in natural waterways with transversally varying
water depth. But a basic restriction of the KP equa-
tion is that it is not valid for truly unsteady cases,
caused, for instance, by varying topography along the
ship's track. A more general shallow-water approxi-
mation are equations of Boussinesq type, which are
valid for almost arbitrarily unsteady cases. In Jiang
(1998) a set of modified Boussinesq's equations,
which are valid not only for long waves but also for
waves of moderate length, was applied to compute
ship waves in shallow water, using slender-body
theory to approximate the near-ship flow. In Yang et
al.~2001) Boussinesq's equations based on a suitable
reference level were used for computing ship waves
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Representative terms from entire chapter:
wash waves
in shallow water but the near-ship flow was repre-
sented by a mean transverse velocity from slender-
body theory instead of using the near-field velocity at
the reference level. A hybrid approach, comprising
the coupling of a steady nonlinear panel method for
the near-ship flow to a Boussinesq solver for the far-
field wave propagation, has been introduced by Ra-
ven (2000~. However, it is useful only for steady
problems.
It should be noted here that due to the non-
linear and unsteady nature as well as the large-
domain feature of the wash problems, they can be
neither solved well by the linear wave theory nor
approximated efficiently by a nonlinear singularity-
method, even less by a finite-volume method due to
the huge computational domain required. To cover all
effects mentioned above an efficient method for the
time being seems to be a shallow-water approxima-
tion based on Boussinesq-type equations, in which
the 3D governing equations for the inviscid fluid are
first treated analytically in the vertical direction and
the resulting 2D equations then solved numerically in
the horizontal plane. In an extensive study by Jiang
(2001) a computer program BEShiWa, standing for
Boussinesq's Equations for Ship Waves, has been
developed with the following features:
- extension of the shallow-water equations of Bous-
sinesq type to longer and shorter waves over an
uneven bottom,
— inclusion of the near-ship flow into the shallow-
water equations either through the law of conser-
vation of mass or through a free-surface pressure
distribution equal to the hydrostatic pressure on
the hull bottom or through a unified shallow-water
theory,
— implementation of suitable boundary conditions,
and
— application of numerically efficient and robust
methods.
In the present study, we focus on the wash-
wave systems generated by a Panmax containership
and a fast inland passenger-ferry. Special attention is
paid to the interaction between ship waves and bot-
tom topography, aiming to find practical criteria for
safe ship operation (speed and distance to shoreline)
as well as for fairway maintenance (dredging depth
and frequency) with regard to the wash effects.
BRIEF MATHEMATICAL DESCRIPTION AND
NUMERICAL APPROXIMATION
Coordinate System
For describing the flow generated by a ship sailing in
shallow water over a general topography, a right-
handed earthbound coordinate system Oxyz is used.
The origin O lies on the undisturbed water-plane. The
x-axis points in the direction of ship's forward mo-
tion; the z-axis, vertically upwards.
Field Equations
Considering water as incompressible and inviscid, the
wave generation by ships in shallow water can be
approximated by the well-established shallow-water
wave theory, see Jiang (2001) for a review. Assuming
that the water depth is small in comparison to the
wave length and that the wave amplitude is small in
comparison to the water depth, the wave field can be
well described by shallow-water equations of Boussi-
nesq type. In the present study, Boussinesq's equa-
tions based on the mean horizontal depth-averaged
velocity for an uneven bottom, without additional
terms for correcting the dispersion relation, are ap-
plied:
+( +hx>)u+(~+h')(ux +vy)+(~
On vertical channel sidewalls, if any, the
condition of no-flux or, equivalently, perfect reflec-
tion holds.
Initial Conditions
In compliance with the unsteady nature of the flow,
the ship is assumed to start from rest and accelerate
uniformly to a final velocity like in a model towing
tank. As may be expected, the final wave system is
found to be influenced by the acceleration rate, espe-
cially in case of trackwise varying topography. This
is because the waves caused by the accelerating ship
with a rather arbitrarily assumed starting point can be
reflected by the bottom topography and then interact
with the waves generated by the ship at steady speed.
Approximation of the Near-Ship Flow
The main interest in the present study lies in the wave
propagation far from the ship. So a slender-body
theory is applied to approximate the near-ship flow.
Starting from the general formulation of the depth-
averaged mean transversal velocity for a slender body
in Jiang (2001), and additionally taking account of
the asymmetric effect caused by nonuniform channel
topography, the boundary condition on the longitudi-
nal ship-centerline (the mathematical dividing line
between the near-field and the far-field) relevant to
the far-field flow reads
vie - Or = Ah + ~ ~ [(V - u0 );oBX + hBuox
+ VSx - (unsex ] + vo
with the port-starboard mean values of the longitudi-
nal velocity component u0= to 2 IN of
the transversal velocity component
2C`xy XS,e= (uly~o+ - ammo- Arc, and of the
wave elevation `~0= to 2 IN . The hull
sectional area is denoted by S(x), and the beam by
B(x). The sectional blockage coefficient C(x) can be
calculated by a 2D boundary element method in ad-
vance, see, e.g., Taylor (1973~. xbOW and xs~errl are the
longitudinal positions of the bow and stern, respec-
tively. Moreover, the Kutta condition is implemented
at the stern through
U1 0+ = al o_
Physically, it means that the longitudinal velocities
on the two sides of the hull have to be identical at the
ship stern to ensure that there is no pressure jump.
Numerical Solution Technique
To solve this initial-boundary value problem gov-
erned by Boussinesq's equations, an implicit Crank-
Nicolson scheme is implemented as usual. But it
encounters some difficulties arising from the nonlin-
ear terms and the linear high-order terms. The devel-
oped solution technique comprises:
— Crank-Nicolson scheme of high-order accuracy
for the time and space discretization,
— approximation of the state values of the nonlinear
terms by means of Taylor series expansion,
— SOR iterative solution of the resulting sparse
equation system,
— overrelaxation to accelerate the convergence, and
— local and global filtering to suppress numerical
oscillations and instabilities.
RESULTS AND DISCUSSION
Example Ships
Two example ships are investigated in the present
study. One is an inland passenger ferry that operates
on the river Rhine and in a sheltered region of vary-
ing water-depth; this aims at finding suitable criteria
for fast-ship operations. The other is a Panmax con-
tainer ship; this is intended to predict the wash-waves
typical of large ships operating on a near-shore fair-
way or near a harbor. The main dimensions of both
ships are listed in Table 1.
Table 1: Main dimensions of investigated ships
Inland Passenger Ferry Panmax Container Vessel
EWL 39.3 m 280 m
B 8.8 m 32.2 m
T 1.2m 11 m
Representative Waves in a Large Shallow-Water
Region
To demonstrate the capability of the computer pro-
gram BEShiWa to predict ship waves over a huge
computational domain, Figure 1 shows three repre-
sentative wave systems generated by the subject
inland passenger-ferry moving in an unbounded shal-
low-water region of uniform depth. The computa-
tional domain was of 17.5 ship lengths long and 7.5
ship lengths wide, taking advantage of transverse
symmetry. The grid size was lm x lm, yielding a
total of 210,000 grid points. The CPU time required
for a typical run was about 23.5 hours for 4,500 time
steps.
At a subcritical speed, Fnh= 0.7 in graph (a),
the wave system is steady and close to a Kelvin-
Havelock wave pattern with pronounced transverse
waves. At critical speed, Fnh= 1.0 in graph (b), the
3
wave system is characterized by significant divergent
waves. Long-time simulations showed that no asymp-
totic steady state could be reached at transcritical
speeds. For the same speed in a (finite-width) chan-
nel, so-called solitons, which are perfect transverse
waves propagating ahead of the ship, were generated
in accordance with observations in model tanks and
full-scale, see, e.g., Jiang (2001~. Similar unsteady
response to steady excitation has been observed in
other nonlinear problems. In fact, for a nonlinear
system governed by Boussinesq's equations, there is
no guaranty that the asymptotic solution would be
steady and independent of the initial conditions. At a
supercritical speed, Fnh= 1.5 in graph (c), the final
wave system comprises only divergent waves, no
initial transverse waves generated during the accel-
eration phase could keep up with the ship. The as-
ymptotic wave system is again steady relative to the
ship.
a) Fnh = 0 7
b)Fnh= 1.0
4
c) F~,h = 1.5
Figure 1: Representative wave systems generated by the subject inland passenger-ferry in shallow water
Validation of Waves at a Large Distance from the
Ship
To validate the computational results from BEShiWa,
especially at a large distance from the ship, Figure 2
compares the computed wave records (dashed lines)
with those measured (solid lines) in the Duisbur~
Shallow-Water Towing Tank (VBD) for the inland
ferry model. At the design speed of Fnh = 0.873 the
following observations can be made: (i) The agree-
ment is quite satisfactory near the ship (y = 6 m) and
pretty good ahead of the ship. (ii) The consistently
improving agreement (in both amplitude and phase)
with increasing proximity to the channel sidewall
demonstrates the usefulness of the present solution
method for predicting far-field wash-waves. (iii) The
relatively large discrepancy in the ship's wake may
have been caused by the running submergence of the
transom stern which was not explicitly accounted for
in the present computer program. Luckily, transverse
waves on the ship's track are not relevant to the wash
problem. (iv) Multiple upstream solitons ahead of the
ship are not visible. However, other computations
have shown that shape and speed of the wave ahead
of the ship do depend on the initial acceleration pat-
tern.
Influence of Channel Section Shape on Wash Waves
Figure 3 shows wave patterns generated by the inland
passenger-ferry moving at critical speed (referred to
the water depth along the channel centerline). Three
different channel section shapes are presented to
display the influence of transversally varying bottom
topography on wash waves, namely, a rectangular
5
channel section in graph (a), a trapezoidal channel
section in graph (b), and a polygonal section consist-
ing of a deepened fairway in a shallow channel in
graph (c), all three of the same depth at the centerline
and the same width overall. In all cases the ferry runs
along the channel centerline. It is seen that unlike the
rectangular channel (a) perfect solitary waves could
be generated neither in the trapezoidal channel (b)
nor in the deepened fairway (c), although a perfect-
reflection condition was implemented on the side-
walls in all cases. An important observation is that
the highest waves occur either near the sidewall in the
trapezoidal channel (b) or in the shallow region be-
side the deepened fairway (c). These high waves
could affect the safe operation of other floating bod-
ies near the bank or possibly cause bank-erosion.
Effects of Initial Ship Acceleration
Since wave elevation and wave energy both propa-
gate in shallow water at the same velocity, an initial
disturbance would also travel at the same speed. This
leads to an interaction of waves generated in the
initial acceleration phase with those later generated
by the ship at its asymptotic speed. Due to the possi-
ble scattering of initial waves by the longitudinal
bottom-topography, the resulting wave pattern could
depend on the ship acceleration or deceleration. To
examine this effect, two simulations were performed
for the subject container ship moving on a near-shore
fairway. The contour plot of the investigated fairway
is given in Figure 5. The wave patterns generated are
shown in Figure 6 (a) and (b) for the case of slow and
fast acceleration, respectively. As expected, the larger
the acceleration, the higher the initial waves observed lated wave probes (locations marked in Figure 5~.
ahead of the main wave system generated by the Moreover, an interaction of waves generated in the
steady ship motion. Within the main wave system, acceleration phase with those later generated by ship
the initial acceleration influences strongly the so- at constant speed can be noticed in the transition
called primary wave but only weakly the trailing between the deepened and shallow regions, see graph
waves. This phenomenon can be clearly observed in 7(a), where the higher harmonic waves are missing
Figure 7 showing wave records taken by four simu- totally in the slow-acceleration case.
[m] ~ I ~ ~ ~ ~ I ~ ~ y=6m ~
-0.5 ~ <~ ~ ~ NX /~ ___
-1 1 ----------- -----1-------- -1-------- --------- I
-200 -150 -100 -50 Stern O Bow 50 100 150 [m] 200
[m] ~ ~ ~ / ~ ~ ~ I y=15m 1
.0.5--~ ~ ~ N!/_ or ~ ~ ~
-1 r--------~---------l------__l____ ~~~r~ ~~ ~~ It l
-200 -150 -100 -50 0 50 100 150 [m] 200
1 r--------l---------l------__l_____ ~~~r~-- ~ It lo lo l
[m] ~ ~ ~ ~ _ ~ ~ ~ ~ y=25m
0.5 ~ f ;~ A__, __ _ ~ ~ ,._ I
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
-200 -150 -100 -50 0 50 100 150 [m] 200
[m] _ ~ ~ 3Sm
1 1 1 1 1 1 1 1 1
-200 -150 -100 -50 0 50 100 150 [m] 200
1 r--------l---------l------__l_____ ~~~r--- ~ It lo lo l
m|
1 1 1 1 1 1 1 1 1
-200 -150 -100 -50 0 50 100 150 [m] 200
Figure 2: Comparison of wave records (replotted as profiles in shipbound coordinates) of the subject ferry at
Fnh = 0.873 as measured in the VBD ~ ~ and calculated by the computer program BEShiWa (-- -)
6
a) Contour plot of the wave pattern in a rectangular channel with uniform water-depth h = 5 m
b) Contour plot of the wave pattern in a trapezoidal channel with maximum water-depth h = 5 m
c) contour plot of the wave pattern in a channel with a deepened fairway (h = 5 m) and shallow banks (h = 3 m)
Figure 3: Influence of transversally varying bottom topography on the wave pattern generated by the subject inland
passenger-ferry moving at constant speed As = 7 m/s (corresponding to local Fnh = 1 on the channel centerline)
z
_} ~
Y- 1
LL: .
'i l
-
'1
50 m ~
-
Figure 4: Channel section shapes for cases (b) and (c)
7
Figure 5: Contour plot of the bottom topography (locations of the four wave probes (a)~d) marked)
a) Slow acceleration
b) High acceleration
Figure 6: Contour plots of wave patterns generated by the subject containership at a speed V=8.35 m/s in a near-
shore fairway (Note: Here the direction of motion is from right to left)
8
0.4 -
0.3 -
0.1 -
O -
-0.1
-0.2
-0.3
0.3
0.2
0.1
,_ O
-0.1
-0.2
-0.3
-0.4 -
0.3
0.25
0.2
0.15
0.1
-
,= 0.05
or
-0.05
-0.1
-0.15
-0.2—
0.5
0.4
0.3
0.2
0.1
o
-0.1
-0.2
-0.3 - .
..... . .. _~ . .
0.2- / ~
, .
WN
1 \K
wave probe (a)
...
0 50 100 150 200 250 300 350
t [s]
1 ~
~ 1 M7'
wave probe (b)
0 50 100 150
1\
1~
~ _~ ~ ~
~ \\ ~
200 250 300 .. 350
t[s]
wave probe (c)
0 50 100 150 200 250 300
.
1 1\ 1
1 ~ ~ ,
_- ~
1 ~ '
1 . ..... .............. 1
t [s]
wave probe (d)
~ I 1 1 1
0 50 100 150 200 250 300 t [s]
Figure 7: Wave records showing the influence of initial ship acceleration ~ fast, ----slow acceleration)
9
Interaction of Wave Generation and Propagation
with Bottom Topography
As discussed by Feldtmann and Garner (1999), a
suitable artificial ramp in a wash-sensitive region
could reduce the wash. The main idea is to minimize
the passing time from a supercritical speed in a shal-
low region to a subcritical speed in a deeper region or
vice versa so that the large wave generation in the
transcritical speed range may be avoided or at least
reduced. Figure 9 demonstrates the wave generation
and propagation over a fairway with a ramp such as
shown in Figure 8. The ferry speed was assumed to
be constant at 8 m/s. Before the subject ferry arrives
at the ramp it moves at a supercritical speed. So the
wave pattern has pronounced divergent waves ac-
companied by transverse waves caused by the initial
acceleration, see graph (a). As soon as the ferry
crosses over the ramp a strong interaction of the su-
percritical wave-pattern occurs with the ramp, and the
wave pattern changes its form as seen in graph (b).
This interaction continues until the ferry has moved
far beyond the ramp, see graphs (c) to (d). Finally,
there is a wave pattern typical of the subcritical speed
in the deeper region, and the wake waves over the
ramp almost disappear from the calculation domain
due to the no-reflection condition implemented on the
open truncation-boundaries to each side, see graph
(e).
Of period 2.02 s and amplitude 0.02 m propagate over
the upward slope of the bar, the nonlinear effect in-
creases and, hence, higher harmonics are generated,
see records of wave probes located at x = 26.04 m
and 28.04 m. These higher harmonics become
quickly free over the downward slope, see records of
wave probes located at x= 30.44 m and 37.04 m.
There is remarkable agreement between calculation
and measurement as long as the higher harmonics do
not get free. Thereafter, a strong interaction between
the primary waves and the free waves makes the
latter equally important. Since the free wave has
approximately half the wave length of the primary
one, the dispersion relation of the classical set of
Boussinesq's equations needs to be corrected, as
discussed by Dingemans (1997~. Similar results were
obtained for primary harmonic waves of period
2.525 s and amplitude 0.029 m, see Figure 11.
CONCLUSION
For predicting the wash waves generated by ships a
method based on Boussinesq-type equations for the
far-field flow and on slender-body theory for the
near-ship flow yields satisfactory results. It covers all
relevant effects associated with the nonlinear and
unsteady nature as well as with the large-domain
feature of the wash problems. Any neglect of these
effects would lead to a poorer approximation.
Since the propagation of wash waves sig-
Validation of Wave Propagation over Uneven nifir~nt]~~ ~~ ~~ i-- ~
Bottom
To validate the computation of the wave propagation
over an uneven bottom, a measurement performed at
Delft Hydraulics (Dingemans, 1994) with a 2D bar-
type bottom topography as shown in Figure 12 was
numerically simulated. A wavemaker generates a
harmonic wave train propagating from left to right in
a wave channel. Figure 10 compares the cal~,l~.~1
.~ . _ ~ . At .C ~
_ ~~$ ·t,J~. _= ~1_ ~~4A~ ~~
wavy; It;~;~lUb WItIt ~r~e measured by wave probes at
6 different locations. As the harmonic primary waves
=
/~///////~/////~)
Lit
Cal
milcantly depends on bottom topography, ship speed
and motion history, any measures for reducing wash
waves deduced from computational predictions need
to be validated by experiments. At the same time,
however, this strong dependence opens up possibili-
ties of formulating suitable criteria for safe ship op-
eration (speed and distance to shoreline or river bank)
, management (con-
struction and maintenance).
as well as for effective fairway
I////
50
20
_ _
30 _
Figure 8: Schematic of the subject ramp (all dimensions in m)
10
(a) wave pattern generated by the subject ferry in the shallow region before the ferry moves over the ramp
(b) interaction of the supercritical wave-pattern with the ramp as the ferry crosses over the ramp
(c) wave pattern as the ferry leaves the ramp behind
(d) evolution of the wave pattern while the ferry moves beyond the ramp
(e) wave pattern of the ferry at subcritical speed in the deeper region
Figure 9: Evolution of the wave pattern generated by the subject inland passenger-ferry moving at a constant speed
of 8 m/s over a fairway with a ramp as shown in Figure 8.
11
0,03
0,02
0,01
0,00
-0,01
-0,02
-0,03
o
0,04
0,03
0,02
E 0,01
0,00
-0,01
-0,02
A AA
0,06
0,04
E 0,02
0,00
-0,02
-0,04 _
o
5 10 15 20
0.04
E 0,02
0,00
-0,02 1
-0,04 —
0,04
E 0,02
0,00
-0,02
-0,04
0.04
0.02
-0.02
20 25 30 35 40 45 50
Y = ;^~A ndm
10 15 20
0 5
0,06
-0.04
0 5
25 30 35 40
x = 26.04 m
45 50
10 15 20
15 20 25
x = 37.04m
.
~\ ~
. ~ it,
it'
An
25 30 35 40 45 50
-30.44 m
30 35 40 45 50
10 15 20 25 30 35 40 45 t [s] 50
Figure 10: Records of wave elevation at 6 different wave-probe locations for an initially harmonic wave of period
2.02 s and amplitude 0.02m propagating over an uneven bottom (see Figure 12) as measured by Dingemans
and calculated using BEShiWa (- - -)
12
x = 9.44 m
O,04
0,03
0,02
0,01
0,00
-0,01
-0,02
-0,03
-0,04
0,10
O,08
0,06
E 0~04
0,02
0,00
-0,02 _
-0,04
o
0,12
0,10
0,08
_ 0,06
E 0,04
0,02
0,00
-0,02
-0,04 _
o
0,10
0,08
0,06
E 0~04
0,02
0,00
-0,02
-0,04 _
o
0,08
0.06
15 20 25 30
5 10
...... .-
:~
~ V
~ r ~
it' ~
.
15
it
[~
As
on
' 1
0,04
E 0,02
0,00
-0,02
-0,04
-0,06
0 5 10
0,08
0,06
0,04
0,02
E BOO
-O,02
-O,04
-0,06
-0,08
o
15 20 25 30 35 40
x = 37.04m
Figure 11: Records of wave elevation at 6 different wave-probe locations for an initially harmonic wave of period
2.525 s and amplitude 0.029 m propagating over an uneven bottom (see Figure 12) as measured by Dingemans ~—
and calculated using BEShiWa (- - -)
o
-0.2
_ -0.4 -
-0.6
ens
\
_
-1 _
0.00 5.00 10.00 15.00 20.00 25.00
x [m]
30.00 35.00 40.00 45.00
Figure 12: The two-dimensional bar-type bottom topography investigated by Dingemans
REFERENCES
Bolt, E.: "Fast ferry wash measurement and criteria," Proceedings of the FAST 2001, Southhampton, UK, 2001.
Chen, X.-N. and Sharma, S.D.: "A slender ship moving at a near-critical speed in a shallow channel," Journal of
Fluid Mechanics 291 (1995, S. 263-285. - Presented at the 18th Int. Congress of Theoretical and Applied Mech.,
Haifa, Israel, 1992.
Chen, X.-N. and Uliczka, K.: "On ships in natural waterways," Proceedings of the RINA International Conference
on Coastal Ships and Inland Waterways London 1999.
~ ,
Dingemans, M.W.: "Comparison of computations with Boussinesq-like models and laboratory measurements,"
MAST-G8M note, H1684, Delft Hydraulics, 1994.
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15
DISCUSSION
Stephane Cordier
Bassin d'Essais des Carenes, France
Ships inland waterway are confronted with
changes in maneuvering behavior in shallow or
restricted waters.
Could you please tell us how this method can be
used or extended to improve the prediction of
maneuvering forces for ships in restricted water?
AUTHORS' REPLY
We thank Dr. Cordier for his question. For
predicting the maneuvering forces on ships in
restricted water, we need only to improve our
approximation for the near-ship flow. Currently,
we examine the possibility of coupling the
BEShiWa program with different methods, such
as with a panel program or a Euler solver or a
RANSE solver. We hope to present our new
results in the near future.
DISCUSSION
L.J. Doctors
University of New South Wales, Australia
I would like to express my appreciation to the
three authors for a most interesting paper on the
subject of wave generation, a matter of interest
to many researchers who are aiming to reduce
the potential damage done by high-speed ferries
as well as traditional vessels, travelling near
coastlines and river banks.
The plots in Figure 1, in particular, are excellent
for displaying the wave patterns created by the
vessel at the various depth Froude numbers.
It is encouraging, also, to observe the good
comparison between the measured and calculated
wave profiles in Figure 2. It is particularly
impressive to see the calculations for the non-
uniform bottom topography in Figure 3 and
Figure 1 1.
Referring specifically to Figure 2, could the
authors comment on the likely relative accuracy
of the BeShiWa (Boussinesq's Equations for
Ship Waves) program, compared with, say, a
more traditional linearized-free-surface method,
in which no depth averaging is effected? That is,
what sacrifice has been made in losing the details
of the vertical distribution of the transverse
velocities within the flow domain, in order to
obtain the very impressive capabilities of
BeShiWa?
Secondly, can the authors verify that the effects
of sinkage and trim are not included in their
work? No doubt this would require a full near-
field calculation (presumably not done here).
The discusser feels that the effects of sinkage
and trim are probably not important in most
cases of practical interest.
AUTHORS' REPLY
We greatly appreciate Professor Doctors's
comments and questions.
The accuracy of predicting ship-wave
propagation in shallow water by using the
BEShiWa program is generally remarkable or at
least practically acceptable in comparison with
model tests. Till now, no attempt has been done
by us to compare with a traditional linearized-
free-surface method. A simple answer here
would be that we do not have such a linear code.
However, we would emphasize again our
statement that due to the nonlinear and unsteady
nature of ship waves in shallow water the linear
theory remains to be a restricted approximation.
Furthermore, it should be clarified that the
vertical distribution of the transversal velocity
components is explicitly described as an
analytical function of the averaged horizontal
velocity in the Boussinesq's shallow-water
theory. So the vertical effects are not neglected,
but analytically approximated in the BEShiWa
program.
Coming now to the second question, the effect of
the sinkage and trim as well as the free surface
elevation are simultaneously included in our
near-field solution, see paragraph
"Approximation of the Near-Ship Flow". As
shown by Jiang (1998), the sinkage and trim
could be well predicted by the BEShiWa
program. The agreement of our calculations with
model measurements was good not only in the
subcritical speed range, but also in the
transcritical and supercritical one.
DISCUSSION
H.C. Raven
MARIN, The Netherlands
This is an interesting paper on a topical subject.
The extensive results illustrate the richness of
wave phenomena occurring
in practical
situations; and show how strongly the particulars
of the waterway determine which wave effects
dominate and whether any wash problems will
occur.
In order to predict these phenomena, there is a
need for a computational tool that incorporates
the essential features and has reasonable
efficiency. Boussinesq-type models seem to go a
long way toward that objective, as the
applications illustrate.
My question is on the boundary condition at the
ship hull; which is the one that generates the
waves. In the present work, a 'slender-body' type
condition is used: the passage of the ship
imposes a lateral velocity distribution, which is
averaged over the entire water depth. This is
consistent with Boussinesq theory; but
intuitively one would expect that this is less
accurate for higher water depth / draught ratio's.
Could the authors comment on their experience
in this regard, and mention the water depth /
draught ratio for the good results in Fig. 2?
Secondly, is there a way to compute and
incorporate the dynamic trim and sinkage in this
method?
AUTHORS' REPLY
We thank Dr. Raven for his comments,
particularly for his indication of our consistent
approximation in using the Boussinesq's
equations for the far-field flow and an extended
slender-body theory for the near-ship flow. We
agree with his presumption that our method is
less accurate for higher ratios of water-depth to
ship draught in the absolute sense of the
increased water depth, but not in the relative
sense of the ratio. For instance, the ratio for the
good agreement in Figure 2 was approximately
4. The crucial parameter for using the BEShiWa
program is the depth Froude number which
should not be below the associated lower limit
defined by Jiang (2001~.
For the answer to the second question we refer to
our reply to Professor Doctors on the previous
page.
DISCUSSION
H. S. Choi
Seoul National University, Korea
In this paper, you have used the depth-averaged
Boussinesq equations to describe wave field
generated by ships moving on Fairways.
Have you ever compared your numerical results
with those obtained by FEM based on ON
equations, which, for example, we presented at
the 1 8th SNH in Ann Arbor, 1990?
AUTHORS' REPLY
We thank Professor Choi for the reference of his
work with the generalized Green-Naghdi (GN)
equations. In comparison with the Boussinesq's
equations the Green-Naghdi theory takes account
of the fully nonlinear effects. As discussed by
Jiang (2001), the application of the classical
Boussinesq's equations for most practical cases
is not limited by the nonlinear treatment but by
the dispersion treatment. Various methods are
derived in the work cited for the improvement of
the dispersion relation of the Boussinesq's
equations. Numerically we prefer the numerical
more efficient Boussinesq approximation.
