(1)
Zhou Jifu and Li Jiachun
Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China
Abstract: A sediment transport model is proposed in this paper to simulate sediment motion induced by storm surges. The model is applied to an ideal rectangular harbor. Sediment transport processes and bathymetric evolution are investigated for different typhoon tracks. The simulated results demonstrate that bed changes are influenced greatly by the typhoon track.
Keywords: storm surge, sediment transport, typhoon track, harbor
It is of practical importance to study storm surge induced sediment transport. In most coastal regions, severe dune erosion due to storm surges may cause great economic loss and environmental hazards (D.J.Walker & M.Y.Rana, 1999). Sedimentation caused by storms may result in waterway blockage time and again, although storms only last for days or even hours. For example, the navigation waterway in the Yangtze River Estuary, East China, was obstructed during the No. 8310 typhoon process in 1983.
Over the past decades, many researchers have studied sediment transport in coastal areas. But most of them merely focused on the normal weather conditions. Researchers who study storm surges are exclusively concerned with sea level changes during storms (Lighthill,J., et al 1993; John Noye, 1995). Fewer scientists investigate mechanisms of sediment transport induced by storm surges.
In this paper, we have established a sediment transport model for typhoon induced sediment motion, which may account for both flow field and sediment trasportation. The sediment transport model proposed by the authors (Zhou Jifu & Li Jiachun, 2000; J.Zhou, J.Li & H.Liu, 2000) is used to calculate sediment concentration and bathymetric evolution in an ideal rectangular harbor. The influences of typhoon tracks are investigated.
In the Cartesian Coordinates system, storm induced currents are governed by the following equations:
(1)
(2)
(3)
where z is the
sea surface level, H=h+z is the
total water depth, h is the water
depth beneath the still water level, (u,v) are the depth averaged components of velocity in the direction
of x,y respectively,
is the density of the sea water, f is the Coriolis parameter, g is the acceleration due to gravity, p is the atmospheric pressure,
and
are the surface wind stress and
the bottom stress components respectively, which are parameterized by
conventional quadratic law. The pressure distribution is described by Fujita and
Takahashi models. And the wind field is formulated by superposing the gradient
wind and the motion induced by typhoon itself (Bao, 1991).
This model has been applied to an open sea domain, which is 600 km long along coast and 192 km wide seawards. The simulated peak surges for different pressure drop DP and wind radius R were compared with Wang¡¯s numerical results (Bao, 1991) in Fig.1, showing good agreements between them.
Fig. 1 Peak surges corresponding to different pressure drop DP and wind radius R
To
predict sediment transportation, we further use the passive scalar transport
model proposed by the authors (see Zhou Jifu & Li
Jiachun, 2000; J.Zhou, J.Li & H.Liu, 2000). The governing equation of sediment
transport in the model is written as:
(4)
where
is sediment concentration,
are horizontal sediment
diffusivity,
is a source term. It is closely
related to the exchange mechanism of suspended load and bed load, and can be
expressed as follows:
(5)
Here,
is the density of sediment
particles.
is the settling velocity.
is sediment concentration at the
bottom.
is the so-called entrainment
function, representing sediment flux in volume entrained up from the unit bed
area per unit time. The turbulent bursting-based entrainment function derived by
Cao,1997 is used.
Based
on mass conservation law, the bed deformation obeys the following equation:
(6)
where
is the bed elevation and
is the dry specific weight of bed
material.
It is assumed that the motion is generated from
at rest and the water is clear. Then, we have
everywhere at the initial moment.
The initial water level is set to the hydrostatic height corresponding to the
initial pressure field.
Along the coastline, the non-slip condition for the current velocity and zero sediment flux are used. At the open boundaries, the water level is prescribed by hydrostatic principle, and sediment concentration is set to zero.
An ideal 100km square harbor (the square EFGH in Fig.2) is
presumed. To avoid the influence of the boundary as possible, the calculated
domain is extended to a 500km square.
In Fig.2, |AB|=400km, |BC|=500km, and the solid line represents the coast. The
upwind scheme is used to discretize the governing equations. The domain is
meshed with space steps
,
and refined ones
,
in the harbor. The time step is
for current calculation,
for sediment transport and bed deformation.
To explore the influences of typhoon tracks on sediment transport and bed deformation in the harbor, five typical typhoons are supposed, each of which originates at the place 400km away from the mouth center and moves towards the harbor. The incident angle a, defined as the angle formed by the track and axis x, varies every 45o from 90o to 270o (Fig.2). The fundamental parameters of the typhoon are as follows: the maximum wind radius is 48km; the pressure drop at its center is 50 hPa; and the moving speed is 5 m/s, i.e. 18 km/hr. So that, the typhoon passes the harbor mouth center at t=22.22hr.
Fig. 2 The sketch of calculated domain and the inclination of different typhoon tracks.
During storms, severe wind stress forces water to circulate and sediment to suspend. Fig. 3 shows the variation of sediment concentration (the dashed line) at the mouth center during a storm process. For comparison, the current speed (the solid line) at the mouth center is also plotted. When the typhoon is far from the harbor, wind shear stress at the sea surface is weak. Correspondingly, the bottom shear stress is too small to initiate sediment particles. As the typhoon is approaching, the bottom shear becomes stronger and hence the sediment concentration is increasing gradually. The two peaks both in wind speed and sediment concentration are attributed to the existence of relatively calm typhoon eye. However, owing to the inertia of sediment, the concentration follows the current with a time lag as we may obviously see in Fig.3.
In Fig.4 plotted are the concentration contours in the harbor at several moments during the storm with a=180o, exhibiting the variation of sediment concentration over the whole harbor. Obviously, the concentration in the whole harbor varies with time in an analogous manner as that at the mouth center displayed in Fig.3. That is, the concentration increases with the approach of the typhoon and decreases with its departure.
Fig.3
Time series of velocity and sediment concentration at the mouth center. The
storm moves at the speed of 18km/hr., a=180o, R=48km, Dp=50hPa
Fig.4 Contours of sediment concentration in the harbor at different time. The storm moves at the speed of 18km/hr.,a=180o,R=48km, Dp=50hPa
In the horizontal plane, the characteristics of the concentration distribution rely on the wind field. In the north semisphere, wind vectors to the right of the typhoon center are larger than that to the left. Therefore, sediment concentration in the right area is greater than that in the left area. The water body with high concentration is about one radius distant from the typhoon center. Near the track of the typhoon center, sediment concentration is rather low due to the weak wind in this region.
In this part, we investigate sea bottom processes during storms with different typhoon tracks. To do so, we consider the five typhoon tracks as shown in Fig.2. Each typhoon lasts for 48 hours.
We assume a plane bottom of the simulated domain with depth of h0(x,y)=10m beneath the still water level. When a typhoon passes through the harbor, the bed will deform and the water depth beneath the still water level will change to, say, hn(x,y). The difference Dh= h0(x,y) ¨C hn(x,y) represents scour (if Dh<0) or deposition (if Dh>0) thickness. Integrating Dh over the whole domain, we obtain the scour or deposition volume in the harbor:
A positive (or negative) Vsd means aggradation (or degradation) of the harbor bed. In the following table is listed Vsd in the case of the five typhoons. It is seen that aggradation occurs when the typhoon originates north or east of the harbor, and a typhoon from the south degrades the bed.
Influence of the typhoon track on the scour or deposition volume in the harbor
|
a( o ) |
90 |
135 |
180 |
225 |
270 |
|
Vsd (Mm3) |
-46.23 |
-26.97 |
23.34 |
73.84 |
73.43 |
Fig.5 shows bed aggradation or degradation distribution in the harbor. We find that aggradation begins at the northeast corner and grows gradually southwest. On the other hand, degradation develops from the southeast corner to the northwest region. Little change happens in the bed near the track. Let¡¯s analyze the variation of sediment flux profile along the mouth section:
to elucidate the implied mechanism. Obviously, the sign of q depends on the current velocity component u at the mouth section. If the current carries sediment into the harbor, q is negative. In contrast, q is positive for seaward sediment delivery. Fig.6 displays the sediment flux profile along the mouth section at seven moments in the typhoon process with a=135o and
Fig.5 Contours of scour (negative) and deposition (positive) thickness ( in meters) in the harbor for different typhoon tracks.
Fig. 6 Time-dependent sediment flux profile along the mouth section.
a=225o. The flux is negligible if the time is beyond the range 18hr.<t<32hr. Owing to the time lag between sediment concentration and current speed processes (see Fig.3), the seaward blowing wind exports more sediment from the harbor via the south subsection and the inward blowing wind imports less sediment from the open sea via the north subsection in the case of a=135o (Fig.6a). Therefore, bed degradation occurs in the southeast part of the harbor as shown in Fig.5a. Analogously, Fig.6b accounts for bed changes demonstrated by Fig.5c as a=225o.
In this paper, we have proposes a model to investigate sediment transportation induced by storms in an ideal rectangular harbor with flat bed. The influences of typhoon tracks are addressed. The numerical results imply that sediment concentration process follows the current albeit with a time lag; the inward blowing wind generally causes bed aggradation and the seaward blowing wind results in bed degradation.
In order to understand more clearly the mechanism of sediment transport caused by typhoons, further work should be done to explore the effects of marine soil property, sea bed topography, tide role as well as typhoon strength.
Acknowledgement
This study is financially supported by China National Natural Science Foundation (No.19802020 and No.10002023).
References
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