YELLOW SEA INTERNAL SOLITARY WAVE VARIABILITY
A. WARN-VARNAS, S. CHIN-BING AND D. KING
Naval Research Laboratory, Stennis Space Center, MS 39539, USA
E-mail: varnas@nrlssc.navy.mil
J. HAWKINS
Planning Systems Inc., Slidell, LA 70458, USA
K. LAMB
University of Waterloo, Waterloo, Ontario, Canada N2L3G1
M. TEIXEIRA
Polytechnic University of Puerto Rico, San Juan, PR 00919, USA
Our studies are centered in an area south of the Shandong peninsula where the observations of Zhou, Zhang and Rogers [1] showed an anomalous drop in acoustical
intensity at 630 Hz. For this region ocean-acoustic modeling studies are performed in
conjunction with available SAR observations of internal solitary waves. Acoustic field
intensity calculations show that for some frequencies a redistribution of acoustic energy
to higher modes occurs.
1 Introduction
The initial interest in the region of the Yellow Sea south of the Shandong Peninsula
arose from acoustical measurements of shallow-water sound propagation. Acoustical
measurements performed by Zhou et al. [1], over a period of several summers, showed
an anomalous drop in acoustical intensity of about 20 dB at a range of 28 km for acoustic
frequencies around 630 Hz. The transmission loss was found to be time and direction
dependent. The authors postulated the existence of solitary waves in the thermocline
and, using a gated sine function representation of them, performed transmission loss
calculations using an acoustic parabolic equation (PE) model. The simulation results
from this hypothetical case showed that an anomalous transmission loss could occur
at a frequency of around 630 Hz when acoustical waves and solitary waves interact.
Computer simulations subsequently confirmed [2] that the resonant like transmission loss
is caused by an acoustical mode coupling due to the presence of solitary waves, together
with a corresponding larger bottom attenuation for the coupled acoustic modes. In the
acoustical calculations the existence of solitary waves has so far been only postulated for
the area south of the Shandong Peninsula. This paper addresses this issue by considering
solitary wave generation and propagation in the region together with an acoustical field
interaction.
409
N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 409-416.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
410
A. WARN-VARNAS ET AL.
Figure 1. Location of the region south of the Shandong peninsula with the track of RADARSAT1
measurement indicated by the black line. The smaller black lines reflect the orientation of the
internal bores and solitary wave trains relative to the direction of propagation.
2
Region
The present study is located south of the Shandong peninsula and will be referred to as
the Shandong area, Fig. 1. The arrow shows the direction of an observed solitary wave
train with Radarsat1 SAR. At the beginning of the arrow there is a relatively steeper slope
at the location where the first internal bore is observed, Digital Atlas of Choi [3]. The
lines across the arrow indicate the along crest direction of the wave packets. The variable
angle of the lines suggests refraction along the shelf break. We obtained summer SAR
observations, for the Shandong area, from Radarsat1 ScanSAR with a 500 by 500 km
wide resolution. The observations were acquired on August 8, 1998 and processed at the
Alaska SAR Facility. The pixel spacing is 100 m. Figure 1 shows the track location,
of the observations, with the topographic features in the background. The results of the
Fourier spectral analysis of the SAR images are summarized in Table 1, where the solitary
wave trains are labeled from left to right. The listed wavelengths are for the most intense
spectral peaks that occur for packets 2, 3, and 4 . For packet 5 there is not enough signal
above background for determining a wavelength at which an energy peaking occurs. The
411
YELLOW SEA INTERNAL SOLITARY WAVE VARIABILITY
Table 1. Parameters of SAR observations.
Solitary wave train #
Bore 2
P1
P2
P3
P4
P5
Distance (km) 0
Phase speed C (m/s)
Dominant
wavelength (m)
36–46
0.8–1.03
72–93
0.8–1.05
132
1.098
178
1.03
226
1.075
272
1.03
630
930
1600
2300
Fourier analysis reflects the wavelength around which most of the energy is concentrated.
The set of wavelengths that we obtained for the solitary wave trains is 630 m, 930 m,
1600 m, and 2700 m, Table 1. The last two wavelengths mark an appreciable increase
relative to the first two.
3
Modelling results
The Lamb [4] model is used for simulating the generation and propagation of solitary
waves in the Yellow Sea. It consists of the Boussinesq equations with the Coriolis force in
a two-dimensional cross-bank plane. In the along-bank direction, the velocity is included
but the derivatives are neglected (2.5 dimensional representation). The equations of the
model are:
Vt + V·∇V − fV × k = −∇P − ρgk
ρt + V·∇ρ = 0
∇·V = 0 ,
(1)
where V is the velocity vector, ∇ the gradient operator subscript t denotes the time
derivative, ρ the density, P the pressure, g the gravitational constant, f the Coriolis
parameter, and k the unit vector along the z direction that is perpendicular to the surface.
The flow is forced by specifying a semidiurnal tidal velocity at the left boundary of
the form Vt sin(ωt) where ω is the M2 tidal frequency assumed to have a 12.4 h period.
The strength of the semidiurnal tidal current in the shallow water, Vt , varies between 0.6
and 1.2 m/s, typical of values in the Shandong region.
The parameters for the different model runs are given in Table 2. We consider here
case 2. For this case, the pycnocline is at a depth of 15 m, a peak barotropic tidal velocity
of 0.7 m/s is used, and the deep water depth is 70 m. The density is specified on the
basis of climatology and available data. Each tidal cycle generates a wave propagating
on the shelf and a wave packet propagating away from the shelf. This behavior is seen
in other areas. At 63 hours or 5.1 semidiurnal tidal cycles into the simulation there are
Table 2. Simulation parameters: hd is pycnocline depth, H(m) water depth, Vt is the tidal strength,
Topo is the topography type a being for cases with a finger ; dH is the length of the computational
domain.
Case
1
2
3
hd (m)
15
15
15
H(m)
70
70
70
Vt (m/s)
1.2
0.7
0.35
Topo
a
a
a
dH (km)
150
240
240
412
A. WARN-VARNAS ET AL.
Figure 2. Simulated sigma-t density distributions for case 2 in Table 1 at 5.1 semidiurnal tidal
periods.
four well developed wave packets with a fifth starting to form, Fig. 2. Note that the first
three wave packets from the shelf show a dramatic increase in amplitude. This is largely
due to the response over the shelf edge increase in time, as discussed in Lamb [4]. The
third and fourth packets from the shelf are more similar in size (when compared at similar
stages of their evolution). The individual waves in each packet grow in size for a while
and then start to decay. They also get further apart. This is particularly apparent in the
further away packets from the shelf . The decrease in amplitude may be partly due to
numerical dissipation.
For comparison with SAR, the tuned simulation with a 15 m pycnocline, case 2 in
Table 2, is used. Table 3 shows the calculated wavelengths at the various horizontal
locations. At around 100 km the wavelength is 420 m. The measurements, Table 1,
show a 630 m wavelength at the location. In the vicinity of 130 km to 140 km the
model results yield a wavelength of 810 m, underpredicting the data value of 930 m. At
around 170 km the modeled wave train is displaying an increased spacing between waves
that is most pronounced towards the back of the wave packet. The resultant wavelength
Table 3. Model results.
Wave train
Tidal cycle
Distance (km)
Wavelength (m)
1
6.1
63
335
2
6.1
102
420
3
6.1
143
810
4
6.1
178
2300
5
6.1
195
3300
YELLOW SEA INTERNAL SOLITARY WAVE VARIABILITY
413
due to this increased spacing is around 2300 m, Table 3. The corresponding wavelength
in the measurements is around 1600 m, Table 1. This is a situation where the model
overpredicts the wavelength instead of underpredicting it. This, also, marks an increase
in the measured wavelengths from the previous locations, that indicates wavelengths of
630 m and 930 m with comparable spatial incremental distances. This suggests a change
in the behavior of the measured solitary wave trains from type A to type B configuration
that results in a sudden increase in wavelength size. The model results at ranges greater
than 170 km also indicate such a phenomena.
4
Acoustic model results
The acoustic effects of these solitary waves can be simulated by applying Dr. Michael
Collins’ acoustic PE propagation model, FEPE, to selected environmental “snapshots”
generated by the Lamb model. A selected scenario and the corresponding acoustic simulation are shown in Fig. 3. The upper figure is the ocean environment after 71 hours.
This environment was generated by the Lamb model assuming a tidal strength of 0.7 m/s,
and validated by comparing with SAR observations. The lower figure shows the acoustic
loss that occurs when a 925 Hz acoustic source is placed at the position indicated by the
red dot (located on the left hand side of each figure). Clearly, the acoustic transmission
is greatly affected by the first two solitary wave packets that are closest to the acoustic
source.
Figure 4 (upper figure) shows the transmission loss at a receiver depth of 30 m for the
Figure 3. A selected solitary wave packet environment generated by the Lamb mode, and the
corresponding acoustic simulation.
414
A. WARN-VARNAS ET AL.
60
Transmission Loss (dB)
70
80
90
100
110
120
0
20
40
60
80
Range (km)
100
120
140
160
60
Transmission Loss (dB)
70
80
90
100
110
120
0
20
40
60
80
Range (km)
100
120
140
160
Figure 4. Transmission loss at a receiver depth of 30 m when the solitary wave packet is present
(upper figure) and when it is not present (lower figure).
925-Hz case shown in Fig. 3, and for the same scenario, but at two adjacent frequencies,
875 Hz and 950 Hz. There is a loss in transmission at 925 Hz, but not at 875 Hz nor
at 950 Hz. The lower figure in Fig. 4 shows the transmission loss for the three source
frequencies when the solitary wave packets are removed from the simulation. The loss
is virtually identical for the three source frequencies. For the selected environmental
scenario and acoustic parameters, there is a significant loss in acoustic signal at 925
Hz that is not seen at surrounding frequencies. This loss is due to the presence of the
solitary wave packets. Figure 5 shows the corresponding wave number analysis at 925
Hz (upper figure) and 950 Hz (lower figure) for the simulations with and without the
solitary wave packets. The solitary wave packets had only a slight acoustic effect at 950
Hz and this is confirmed in the upper figure of Fig. 5 which shows only slight mode
conversion and mode loss. The lower figure of Fig. 5 shows that at 925 Hz the acoustic
modes were greatly affected by the presence of the solitary wave packet, with practically
every mode experiencing mode conversion and mode loss. Our results tend to confirm
the resonance hypothesis of Zhou et al. We have performed numerous simulations that
indicate that solitary wave packets can cause acoustic mode conversion (from lower-order
to higher-order modes) followed by loss due to ocean bottom attenuation (with the higherorder modes having higher bottom attenuation). The results shown in Figs. 3, 4, and 5
415
YELLOW SEA INTERNAL SOLITARY WAVE VARIABILITY
0.3
Intensity (a/u)
0.25
925 with
0.2
925 without
0.15
0.1
0.05
0
4.1
4.08
4.06
4.04
4.02
4
k(1/m)
3.98
3.96
3.94
3.92
3.9
0.3
Intensity (a/u)
0.25
950 with
0.2
950 without
0.15
0.1
0.05
0
4.1
4.08
4.06
4.04
4.02
4
k(1/m)
3.98
3.96
3.94
3.92
3.9
Figure 5. Wave number analysis at 925 Hz (upper figure) and 950 Hz (lower figure) for the
simulations with and without the solitary wave packets.
are somewhat different in that higher bottom attenuation is not a required mechanism.
Rather, it appears that massive mode conversion occurs, from discrete propagating modes
to continuous evanescent modes, resulting in a significant loss in acoustic signal. This
new finding is currently under investigation.
5
Conclusion
We have shown that generation and propagation of internal solitary waves can occur along
a southeastern track off the Chinese coast located south off the Shandong peninsula. SAR
imagery shows the presence of internal solitary waves along the same track and suggest’s
their generation in the, shallower, shelf break region. Model results indicate generation of
internal solitary wave in the same off shelf area. The tuned model simulation and the SAR
data both exhibit the presence of two behavior states, A and B that have corresponding
solitary wave train characteristics. The two states of behavior A and B could be due
to short vs. long time behavior. These states of behavior are evolved by the dynamics
of the ocean and the model. The modelled soliton wave amplitudes and wave lengths
are within a factor of 2 (or better) of amplitudes and wavelengths derived from SAR
data. The simulated phase speeds range from 0.73 m/s to 0.83 m/s. The phase speeds
estimated from the measurements range from 0.8 m/s to 1.1 m/s. This suggests that the
model formalism does contain dynamics similar to the ocean. Acoustic simulations were
performed on several internal solitary wave environments generated by the Lamb model.
Large unexpected acoustic losses were observed and were attributable to the solitary wave
fields. The results tend to confirm the resonance hypothesis developed by Zhou et al.
416
A. WARN-VARNAS ET AL.
Acknowledgements
This work was supported by the U. S. Office of Naval Research through the U. S. Naval
Research Laboratory base program, PE 62435N. The U. S. Naval Research Laboratory
provided technical management.
References
1. Zhou, J.X., Zhang, X.Z. and Rogers, P.H., Resonant interaction of sound wave with internal
solitons in coastal zone, J. Acoust. Soc. Am. 90(4), 2042–2054 (1991).
2. Chin-Bing, S.A., King, D.B. and Murphy, J.E., Numerical simulations of lower-frequency
acoustic propagation and backscatter from solitary internal waves in a shallow water environment. In Ocean Reverberation, edited by D.D. Ellis, J.R. Preston and H.G. Urban
(Kluwer Academic Press, Dordrecht, The Netherlands, 1993) pp. 113–118.
3. Choi, B-H., Digital atlas for neighboring seas of Korean Peninsula. Available on compact
disk, 1999. E-mail: bchoi@yurim.skku.ac.kr
4. Lamb, K., Numerical experiments of internal wave generation by strong tidal flow across a
finite amplitude bank edge, J. Geophys. Res. 99(C1), 848–864 (1994).