Bathymetry, Flow Field and Wave Field Measurement in Upper
Yahara River, Madison, WI
Flow Field
The flow field can be discussed as follows:


Bathymetry Mapping
Modeling
Surface Water Modeling System (SMS) is a software to create one-, two, and
three-dimensional hydrodynamic modeling. We used this software to plot the
bathymetry in our study site. The software can make bathymetry grid in
rectangular/Square grids and triangular grids. Triangular grid system was used to
plot the bathymetry to ensure better and more accurate coverage of the area. Detailed
literature on the working of the software is available on line (http://www.emsi.com/SMS/sms_8_1_new_features.html) but the general procedure for making the grid is
as follows:




·
·
Input in the form of x,y,z coordinates of points required to be
mapped.
·
selection of system of interpolation between points to make a
grid.
·
Applying mesh quality checks to ensure max value of interior
angles, maximum allowable vertical slope between the elements etc.
·
Plotting the contours and visual inspection of the bathymetry
grid to find out some undesired nodes and then correcting them before taking
the output to be run in the FVCOM.
The mesh/bathymetry map generated for our study site was as shown
below( the vertical scale has been exaggerated 20 times for better
assimilation)
Bathymetry Mapping
Use of SMS 8.1
(Figure 2 , Bathymetry Mapping )
Surface water modeling software 8.1 (SMS 8.1) was used to plot the
bathymetry. The software can make bathymetry grid in rectangular/Square grids
and triangular grids. Triangular grid system was used to plot the bathymetry
to ensure better and more accurate coverage of the area. Detailed literature
on the working of the software is available on line (http://www.emsi.com/SMS/sms_8_1_new_features.html) but the general procedure for making the
grid is as follows:
Input in the form of x,y,z coordinates of points required to be mapped.
selection of system of interpolation between points to make a grid.
Applying mesh quality checks to ensure max value of interior angles,
maximum allowable vertical slope between the elements etc.
Plotting the contours and visual inspection of the bathymetry grid to find
out some undesired nodes and then correcting them before taking the output
to be run in the FVCOM.
The mesh/bathymetry map generated for our study site was as shown below( the
vertical scale has been exaggerated 20 times for better assimilation):
The area of our major focus was north of bridge at HW 113, which has the
following bathymetry shape:
Modeling
Finite Volume Coastal Ocean Model (FVCOM) has been used to simulate flow
in the river for 3 days and the wave characteristics have been calculated at
following seleted node which represent particular conditions in a specific
reach of the river:
FVCOM was originally developed for the estuarine flooding/drying process
in estuaries and the tidal-, buoyancy- and wind-driven circulation in the
coastal region featured with complex irregular geometry and steep bottom
topography.
Node 639, 510: Entrance to the lake Mendota.
Node 509:
Inside the jetty areas.
Node 516:
Near the Bridges.
Node 843, 921, 875:
Areas in the north of HW 113.
The results for wave characteristics will be discussed the wave field. However, to ascertain the
impact of different Fetch lengths on the resultant wave height (H)and Wave Time period (T) a point up in
the north near the start of River was selected where already some wetland restoration plantation has
been done. The fetch length was considered in five different directions as indicated in the figure below:
JONSWAP method was used to calculate wave height and wave time period. Main steps involved use of
this method are
Step (1) Given F, U10, td
Step (2) Compute F* = g F/U102
t* = gtd/ U10
F* eff = {t*/68.6}1.5
Step (3) if F* < F* eff ~ Fetch Limited
H*s =gHs/ U102 =0.0016(F* eff)0.5 Tp* = gTp/ U10 = 0.286 (F*)0.333
if F* > F* eff ~ Duration Limited
Step (4) Fully developed
H*s =gHs/ U102=0.243
Tp* = gTp/ U10 = 8.13
Inputs



Ua = 5 ,10 ,15 m/sec (assumed)
Duration 1 hour, ( assumed)
Fetch
o North : 368 m
o South : 720 m
t* = gtd/ U10 = 71500
o
o
o
East : 192 m
West : 176 m
South West : 2656 m
Out puts
Ua
(m/sec)
5
10
15
20
Fetch
length
direction (m)
N
368
S
720
E
192
W
176
Limit
Wave Height
Hs (m)
Wave
Time Pd
(sec)
Fetch
Fetch
Fetch
Fetch
0.04
0.04
0.04
0.04
0.67
0.67
0.67
0.67
SW
N
S
E
W
2656
368
720
192
176
Fetch
Fetch
Fetch
Fetch
Fetch
0.04
0.23
0.23
0.23
0.23
0.67
1.58
1.58
1.58
1.58
SW
N
S
E
W
2656
368
720
192
176
Fetch
Fetch
Fetch
Fetch
Fetch
0.23
0.61
0.61
0.61
0.61
1.58
2.60
2.60
1.58
2.60
SW
N
S
E
W
2656
368
720
192
176
Fetch
Fetch
Fetch
Fetch
Fetch
0.61
1.24
1.24
1.24
1.24
2.60
3.71
3.71
3.71
3.71
SW
2656
Fetch
1.24
3.71
Producer scheme
Wind can strongly affect the behavior of water waves (Especially, the wave
period (Ts) and wave height (Hs). In order to account wind into our
calculation, we downloaded the wind information (for Madison area) of October
from NOVVA. The average daily wind speed (‘Ua’) and the wind direction
(‘dir’) are listed in table 1. The average daily wind speed is also listed
in table. The average wind speed for October , 2008 is 5.54 mph (2.47 m/s)
Linear and progressive waves are assumed for our calculation.
The water
depth (d) and surface velocity (v) are obtained from FVCOM. Wave length (L),
relative depth (d/L), wave height (H) due to the water depth (H mean) and the
maxim wave height (Hmax) are calculated as general prosperities. Group
velocity (Cg) is calculated as to determinate how the wave energy propagated.
We also calculated the wave energy density (Ebar) and wave power (p), because
we like to see if wave can be use as an energy source at this region. The
average value for three days is listed in table 4.