506 CHAPTER 8. LABORATORY MEASUREMENT AND ANALYSIS
A sensitivity analysis indicated that Method II was the most accurate
and Method III was the least accurate. For all methods, estimates of incident wave height were more accurate than estimates of reflection coefficient.
Isaacson discussed the shortcomings of each method and under what conditions (gauge spacing) the methods would fail. The paper did not compare
the methods using actual measurements from a wave flume.
8.4.2 Reflection Analysis of Irregular Waves
Determination of incident and reflected irregular wave spectra can be accomplished by analyzing time series records collected using the following
instrument deployments:
1. Spatially-Separated Wave Gauges: This wave reflection analysis method uses time series records of sea surface
elevation from two or more stationary wave gauges placed
in a line parallel to the direction of wave travel.
2. Vertical Array: This method uses time series records
of horizontal velocity and sea surface elevation collected
from a current meter and wave gauge arranged in a vertical
array.
3. Co-Located Velocities: This method uses time series
records of horizontal and vertical water velocity components obtained from a current meter at a single location.
All three methods are based on linear, irregular wave theory, thus nonlinear wave interactions are not represented in the analyses. Furthermore,
the methods are restricted to the two-dimensional case, i.e., long-crested
waves generated and reflected at normal incidence in a wave flume. Several
of the methods are derived in the following sections.
Basic Linear Equations
The first-order velocity potential for irregular, linearly superimposed reflected waves in two dimensions on a flat bottom is given as (e.g., Dean and
Dalrymple 1984)
oo
<£( * ,-M)
= ]T1=1
aJtg cosh fc,(/i 4- z)
(Ti
cosh(^jh)
sin(fc,x — ait + q,)
0^,0 cosh ki(h + z)
ai
cosh(fct/i)
sin(fctx + ad + c/jJ
(8.27)
A sensitivity analysis indicated that Method II was the most accurate
and Method III was the least accurate. For all methods, estimates of incident wave height were more accurate than estimates of reflection coefficient.
Isaacson discussed the shortcomings of each method and under what conditions (gauge spacing) the methods would fail. The paper did not compare
the methods using actual measurements from a wave flume.
8.4.2 Reflection Analysis of Irregular Waves
Determination of incident and reflected irregular wave spectra can be accomplished by analyzing time series records collected using the following
instrument deployments:
1. Spatially-Separated Wave Gauges: This wave reflection analysis method uses time series records of sea surface
elevation from two or more stationary wave gauges placed
in a line parallel to the direction of wave travel.
2. Vertical Array: This method uses time series records
of horizontal velocity and sea surface elevation collected
from a current meter and wave gauge arranged in a vertical
array.
3. Co-Located Velocities: This method uses time series
records of horizontal and vertical water velocity components obtained from a current meter at a single location.
All three methods are based on linear, irregular wave theory, thus nonlinear wave interactions are not represented in the analyses. Furthermore,
the methods are restricted to the two-dimensional case, i.e., long-crested
waves generated and reflected at normal incidence in a wave flume. Several
of the methods are derived in the following sections.
Basic Linear Equations
The first-order velocity potential for irregular, linearly superimposed reflected waves in two dimensions on a flat bottom is given as (e.g., Dean and
Dalrymple 1984)
oo
<£( * ,-M)
= ]T1=1
aJtg cosh fc,(/i 4- z)
(Ti
cosh(^jh)
sin(fc,x — ait + q,)
0^,0 cosh ki(h + z)
ai
cosh(fct/i)
sin(fctx + ad + c/jJ
(8.27)