Nonhydrostatic effects of nonlinear internal wave propagation in the South China Sea Zhonghua Zhang

1
Nonhydrostatic effects of nonlinear internal wave
propagation in the South China SeaZhonghua
Zhang and Oliver B. FringerEnvironmental Fluid
Mechanics LaboratoryDept. of Civil and
Environmental EngineeringStanford University24
May 2007Support ONR Grant N00014-05-1-0294
2
SAR Imagery from internalwaveatlas.com (Global
Ocean Associates)
South China Sea
Convergence (rough)
Convergence (rough)
Divergence (smooth)
Surface
Propagation direction
3
Nonlinear Internal waves in the SCSMain
Questions

• How are the internal waves generated?
• Is the nonhydrostatic pressure important for
  computing the internal wave propagation?

4
Evidence from observations
Isotherm displacements at mooring B1 are due
to nonlinear waves generated at L1, 31 hours
earlier, which is the time it takes for the
first-mode internal tide to propagate from
station L1 to B1. Lagged peak displacements
correspond to generation during peak ebb (ebb is
defined as positive currents in the figure).
Data from Steve Ramp, NPS
5
2D simulations with SUNTANS
Levitus stratification
28 C
Depth at sill DS 200 m
3 C
Ocean depth D0 3500 m
Barotropic forcing at diurnal frequency
Radiation of first-mode baroclinic wave. Sponge
layers are also employed to damp internal waves
at the boundaries.
6
Case with Frsill0.27
Isotherms 16, 20, 24, 28 degrees C
7
Case with Frsill1.60
Isotherms 16, 20, 24, 28 degrees C
8
Beginning of ebb tide
t10
End of ebb tide
t2T/2
LT/2c1
Beginning of flood Lee wave release
t3T/2
Arrival at B1
t4t3LB1/c1
DtLB1/c1
9
Lee wave vs. flood wave
15o Isotherms after 2 tidal periods
First flood
First ebb
Fr0.25
Increasing Fr
Stronger ebb pushes peak of depression farther
from the crest of the sill.
Fr3.00
After 2 tidal periods, the flood wave has
propagated roughly 2.5 mode-1 wavelengths,
while the ebb wave has propagated roughly 1
mode-1 wavelength. The crests of the flood
wave with increasing amplitude have propagated
further because of amplitude dispersion, while
the crests of the ebb wave have been delayed due
to the excursion of the peak of the depression
during the ebb.
10
Nonhydrostatic effects (Frsill1.60)
Nonhydrostatic code
Isotherms 16, 20, 24, 28 degrees C
Hydrostatic code
11
Nonhydrostatic-Hydrostatic Comparison
Dispersion in the hydrostatic model is purely
numerical. The numerical dispersion is much
smaller than the physical, nonhydrostatic
dispersion, which leads to excessive steepening
of the front. The oversteepened front is
diffused due to grid-scale numerical diffusion,
and this causes a reduction in the wave
amplitude. Reduction in the wave
amplitude reduces the amplitude dispersion and
thereby reduces the speed of propagation of the
wavetrain.
15o C isotherm after 3 tidal periods.
12
Using the KdV equation as a model
Initial wave Half-sine wave (first-mode internal
tidal wavelength) with amplitude 70 m.
13
Computed vs. Modeled (KdV) Results
SUNTANS
KdV
14
Conclusions

• Generation mechanism lee-wave release
• Nonlinear wavetrains in the SCS are likely
  generated as a result of the formation of large
  lee waves of depression in the Luzon Strait which
  are "released" at the end of the ebb tide and
  subsequently propagate into the SCS.
• Nonhydrostatic effects
• Accurate simulation of the evolution of weakly
  nonlinear wavetrains requires a nonhydrostatic
  model.
• The hydrostatic model has insufficient dispersion
  (roughly ¼ that of the nonhydrostatic model), and
  this dispersion is purely numerical.
• The lack of sufficient dispersion leads to
  oversteepening and excessive numerical diffusion,
  which reduces the amplitude of the wavetrain, and
  this in turn causes a reduction in the
  propagation speed of the wavetrain.

15
Evidence from observations
16
Response at B1 as F of u/c1
17
Generation Mechanism