Abstract:
We examine the interactions and feedbacks between bathymetry, waves, currents, and
sediment transport. The ﬁrst two pro jects focus on the use of remote sensing techniques
to expand our knowledge of the nearshore. Due to the plethora of snap-shot data that is
available from satellites and their distribution via Google Earth, having a method that
can determine bathymetry from spatial wave patterns would be very valuable. Utilizing
remotely-sensed wave refraction patterns of nearshore waves, we estimate bathymetry
gradients in the nearshore through the 2D irrotationality of the wave number equation.
The model, discussed in Chapter 2, uses an augmented form of the refraction equation
that relates gradients in bathymetry to gradients in wavenumber and wave angle through
the chain rule. The equations are cast in a form that is independent of wave period,
so can be solved using wavenumber and direction data from a single snapshot rather
than the normally-required time series of images. Synthetic testing of the model using
monochromatic waves on three bathymetries of increasing complexity, showed that the
model accurately estimated 2D bathymetry gradients, hence bathymetry, with a mean
bias of 0.01 m and mean root mean square error over the three beaches of 0.17 m for
depths less than 5 m. While the model is not useful for cases of complex seas or small
refraction signals, the simpliﬁed data requirement of only a single snapshot is attractive.
The model is perhaps best suited for shorter period swell conditions (wave periods of 8-10
seconds), for example, where strong refraction patterns are visible and wave number, k,
and wave angle, θ, are easily extracted from a single frame image.
Secondly, remotely sensed images of wave breaking over complex bathymetry are used
to study the nonlinear feedbacks between two-dimensional (horizontal), 2DH, morphol-
ogy and cross-shore migration rates of the alongshore averaged bar. We ﬁrst test a linear
model on a subset of 4 years of data at Palm Beach, Australia. The results are discussed
in Chapter 3. The model requires eight free parameters, solved for using linear regression
of the data to model the relationship between alongshore averaged bar position, x, along-
shore sinuosity of the bar, a, and wave forcing, F = H 2
o . The linear model suggests that
2DH bathymetry is linked to cross-shore bar migration rates. Nevertheless, the primary
limitation is that variations in bar position and variability are required to be temporally
uncorrelated with forcing in order to achieve meaningful results. For large storms, this is
indeed the case. However, many smaller storms seen at Palm Beach show that changes
in bar position and variability are correlated with forcing and bar interaction dynamics
are not separable from bar - forcing dynamics.
In Chapter 4 a nonlinear model is subsequently developed and tested on the same data
set. Initial equations for cross-shore sediment transport are formulated from commonly
accepted theory using energetics-type equations. Cross-shore transport is based on the
deviations around an equilibrium amount of roller contribution with the nonlinearity
of the model forcing sediment transport to zero in the absence of wave breaking. The
extension to 2DH is based on parameterizations of bar variability and the associated 2DH
circulation. The model has ﬁve free parameters used to describe the relation between
alongshore averaged bar position, x, 2DH bar variability, a, and wave characteristics
(wave height, H , wave period, T , and wave angle, θ). The model is able to span multiple
storms, accurately predicting bar migration for both onshore and oﬀshore events. The
longest individual data set tested is approximately 6 months. Using manually determined
values for the coeﬃcients, bar position is predicted with an R2 value of 0.42 over this
time period. The eﬀect of including a 2D dependency both increased rates of onshore
migration and prevented highly 2D systems from migrating oﬀshore under moderate
wave heights. The model is also compared against a 1DH version by setting the 2D
dependency term to unity and using the same values for the ﬁve free parameters. The
1DH model showed limited skill at predicting onshore migration rates, suggesting again
that the inclusion of 2DH terms is important.
The last pro ject (Chapter 5) explored the utilization of changes in bathymetry,
∆h/∆t, to gain further understanding of the feedbacks between 2D sediment transport
patterns, Qx and Qy , with respect to existing bathymetry in the nearshore. The model
is based on the 2D continuity equation that relates changes in bathymetry to gradients
in the cross-shore, ∂ Qx /∂ x, and the alongshore, ∂ Qy /∂ y, directions. The problem is
under-determined, having two unknowns (Qy and Qx) and only one known (∆h/∆t)
such that a series of constraints must be applied in order to solve for transport. We as-
sume that that the cross-shore integral of Qx is closed, such that no sand enters or exits
the system in this direction. By conservation of mass, this requires changes in volume
of the cross-shore transect to be due to longshore gradients in Qy . We test six rules
for distributing Qy : three rules describing the initial longshore transport (Qr
y ) and three
describing the cross-shore distribution of the excess volume component (Qe
y ). Initial re-
sults suggest that requiring sediment to travel down slope (Qry = f (βy )) is an intuitive
choice for describing transport of distinct perturbations. However, in one example ﬁeld
test this method did not perform well and the approach may need further reﬁnements.
Alternatively, having Qrx and Qry depend on spatial correlation lags between two sur-
veys showed good results for identifying transport associated with alongshore migrating
features. This method, however, did not do well under strict onshore migration of 2D
features, where alongshore transport was not predicted. A hybrid approach, using both
the down-slope constraint and spatial correlation lags may provide more robust predic-
tions of sediment transport patterns in complex environments. Due to the lack of closed
boundaries in the alongshore, knowledge of Qy (x, y0 ) is required to obtain sensible net
sediment transport patterns. Alternatively, spatial patterns of the transport gradients
(∂ Qy /∂ y, ∂ Qx /∂ x), which ultimately determine bar migrations provide useful insight
into the system behavior without requiring Qy (x, y0 ).