JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. C2, PAGES 33213336,
FEBRUARY 15, 1994
Tidal propagation in strongly convergent channels
Carl T. Friedrichs
1 and David G. Aubrey
Department
of Geology and Geophysics,
Woods Hole Oceanographic
Institution,
Woods Hole, Massachusetts
Abstract.
Simple first and secondorder
analyticsolutions, which diverge markedly
from classical
views of cooscillating
tides, are derived
for tidal propagation
in strongly
convergent
channels. Theoretical predictions compare well with observations
from
typical examples of shallow, "funnelshaped"
tidal estuaries. A scaling of the governing
equations
appropriate
to these channels
indicates
that at first order, gradients
in cross
sectional area dominate velocity gradients
in the continuity equation and the friction term
dominates acceleration
in the momentum equation. Finite amplitude effects, velocity
gradients due to wave propagation,
and local acceleration
enter the equations at second
order. Applying this scaling,
the firstorder governing equation becomes a firstorder
wave equation, which is inconsistent
with the presence
of a reflected wave. The solution
is of constant
amplitude andhas a phase speed near the frictionless wave speed,
like a
classical
progressive wave,yet velocity
leads elevation by 90 ø,
like a classical
standing
wave. The secondorder
solution at the dominant
frequency
is also a unidirectional wave;
however,
its amplitude
is exponentially modulated. If inertia is finite and convergence
is
strong, amplitude
increases
along channel, whereas
if inertia
is weak and convergence
is
limited, amplitude decays. Compact solutions
for secondorder
tidal harmonics quantify
the partiallycanceling
effects of (1) time variations
in channel depth, which slow the
propagation
of low water, and (2) time variations
in channel width, which slow the
propagation
of high water. Finally, it is suggested
thatphase speed, alongchannel
amplitude growth, and tidal harmonics
in strongly convergent
channels are all linked by
morphodynamic
feedback.
1. Introduction
1.1. Classical
Tidal
Cooscillation
In this paper a new asymptotic solution
is presented
for
the barotropic
tidal wave in strongly convergent channels.
The type of wave described here, which paradoxically
exhibits properties
of bothstanding
andprogressive
waves
simultaneously, occurs
in real tidal estuaries such as the
Thames and the Tamar in the United Kingdom and the
Delaware in the United States
(Figure 1). Like a classical
progressive wave, this wave does not appreciabl'y
grow or
decay along channel, and its phase speed
is nearly equalto
the frictionless wave speed. Like a classical standing wave,
it produces currents which are slack near high and low
water. Unlike either wave, however,the dynamic balance
which produces this asymptotic solution is strongly
frictional. This new solution and its governing equation are
markedly different from the classical view of damped
tidal
cooscillation, yet some of its properties may be confused
with classical results. It is useful, therefore, to review
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 Three '10
 Dr.XiaoHuaWang
 Geodesy, Delaware, Tide, Convergent Channels, tidal propagation

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