R.J. Sobey, S.A. Hughes r Coastal Engineering 36 (1999) 1736
34
The LFI-PUV solutions for the Columbia River data have a somewhat tenuous
nature, evidenced by the sharp changes in predicted kinematics in the neighborhood of
times y8, q5 and q8 s. The UV error bands for this record ZFig. 2b. are quite
significant. The specific PUV gauge was designed with the expectation that analysis
would follow the Longuet-Higgins et al. Z1963. linear and global frequency-domain
analysis outlined in Eqs. Z1.Z10.. In this global linear analysis, measurement error is
easily accommodated by spectral smoothing of the Ep u1Z v ,u . through Eu2 u2Z v ,u .
auto-variance and cross-variance spectra andror the Ehh Z v ,u . estimate from Eq. Z7..
Measurement error bands are not so easily dismissed in the local LFI-PUV theory.
LFI-PUV seeks an enhanced representation of the local kinematics, through the direct
use of local PUV measurements in the problem formulation. The local PUV measure-
ments provide the local reality, so that the predictive potential can be significantly
compromised by local measurement error. The Columbia River data set provides a
useful reality check. While the value of the Fig. 9 predictions are arguably tenuous, their
particular value may lie in the identification of UV measurement error bands as a
relevant design issue for PUV instrumentation.
An associated instrument design issue is the attenuation of the fluctuating kinematics
ZP and UV. with increasing depth of submergence and with increasing frequency. The
attenuation increases with both frequency and depth of submergence. Transducer
accuracy is absolute, so that relative accuracy is significantly compromised for deeply
submerged instruments at higher frequencies in deeper water. There is only partial
mitigation for this in the superior accuracy of P measurements, with respect to UV
measurements. The design compromise has been to locate PUV gauges reasonably high
in the water column to avoid this problem as much as possible. The Columbia River
gauge is deployed at y16.8 m where the water depth is 17.6 m, but the Platform Edith
gauge is deployed at only y7.4 m where the water depth is 46 m. The deeper
submergence of the Columbia River gauge contributes to the tenuous nature of the
analysis of this data.
A careful review of the Fig. 9 predictions reveals that the maximum vertical velocity
prediction, 1.59 mrs at q0.5 s, exceeds the maximum horizontal velocity prediction,
1.39 mrs at y0.5 s. In a global steady wave solution, such as the `global Fourier'
solutions in Figs. 4, 6 and 7, the maximum horizontal and vertical velocities will again
not coincide in time, but the maximum vertical velocity magnitude will always be
smaller than the maximum horizontal velocity magnitude. This underlines the local
character of the LFI-PUV methodology. The LFI-PUV solutions in each local window
are independent, and directly reflect the local measured kinematics. There is no global
influence.
A final phase in evaluation of the LFI-PUV methodology would be detailed labora-
tory measurements of kinematics under regular and irregular wave conditions. These
should include a PUV instrument plus the local water surface and Z ua ,w. velocity
component and dynamic pressure measurements at one or more different near-surface
elevations. Suitable laboratory data do not presently exist. Establishing a suitable data
set would be a very major task. It would presumably involve sophisticated three-dimen-
sional laser Doppler instrumentation for the velocity measurements. Pressure is very
rarely measured in a wave laboratory, except at structures where the data would be
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