3.1 Modelling Methods
The ideal would be a modelling system in which all these variables would be reproduced
and which would allow them to interact freely. That is far beyond present capabilities. All
methods of modelling involve compromise—often quite drastic—between major forces.
In the case of physical modelling, reduction in size results in increase in relative
importance of viscous and surface tension forces whereas the effect of both may be small
in the prototype. Estuaries must be modelled at small horizontal scale because of their
physical size. These scales are such that flows would be laminar in a model built to a
homogeneous scale. To overcome this defect, vertical scales are made larger than
horizontal scales, often by an order of magnitude.
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This is essential in order that tidal
currents can be reproduced satisfactorily; but such scale distortion prevents similarity of
propagation and breaking of waves. It can also cause severe misrepresentation of
horizontal and vertical mixing processes
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which affect distribution of salt and pollutants
(particulate, solute or thermal).
Numerical models represent prototype conditions on a grid of points in plan so that,
instead of having continuously varying solid boundaries as in nature and in physical
models, boundary values are only stated at intervals. Similarly, variations of parameters
with time are estimated at intervals that are short compared with a tidal period but in
some cases are long compared with wind-induced waves and swell and are very long
compared with turbulent fluctuations. Modelling of wind-induced waves and of tides
requires different compromises to be made. Tides are ‘long’ waves in ‘shallow’ water in
which vertical accelerations are very small compared with gravitational force per unit
mass. In the case of wind-generated waves and swell, vertical accelerations cannot be
ignored. Tide-and wind-generated waves are each modified by passage through ‘shallow’
water. In the absence of significant tidal currents, wave energy E per unit plan area is
propagated at the wave group celerity c
g
.
Group celerity changes as waves pass into shallow water or encounter moving water,
causing wave height to change. Local changes in wave speed cause directional changes in
the wave front (refraction). Changes in wave height along a wave front cause wave
energy to spread laterally (diffraction). When waves move onto a sloping shallow bed
and approach the point of breaking, they slow down and exert a force on the bed with a
resulting change in flux of momentum. Radiation stresses then cause changes in mean
water level and generate wave-induced currents.
A further complication is that waves and tides consist of an infinite range of
components. In the case of tides, the components of the tide-generating forces can be
measured and their effect predicted with precision. However, shallow water and
reflection from coastlines cause local changes which are usually orders of magnitude
greater than the effect of direct tide-generating forces. These local effects can be
predicted with quite high accuracy. Seasonal effects, which can cause changes in mean
sea level with periods of the order of a year, can be measured over several years and
mean variations found. Meteorological effects also cause short-term variations with
periods of the order of days. Seasonal and meteorological effects must necessarily have
large random components which prevent accurate forecasting. Tides can be predicted
fairly well in regions where the astronomical tide causes large shallow-water tides.
Developments in hydraulic engineering–5 138