The dynamic response to oceanic
and atmospheric forcing in a
stratified Arctic fjord
Or:
Wave induced drift in boundary trapped
internal waves, with application to the
Arctic region
PH.D PROJECT EIVIND STØYLEN
EIVIND.STOYLEN@GEO.UIO.NO
DEPT. OF GEOSCIENCES, METOS SECTION
UNIVERSITY OF OSLO
Wave drift
 Stokes (1847): Stokes drift
in the direction of wave
propagation. Non-viscous
 Longuet-Higgins (1953):
Additional Eulerian drift
from viscosity.
Wikipedia
Target:
• Long interfacial boundary trapped waves in the
Arctic
–
–
–
Tidally induced internal Kelvin waves under ice
Interfacial motion from changing wind conditions
Stokes interfacial edge waves in thin dense bottom layer
• Common:
• Propagation of waves along boundary
• Yields systematic transport of pollutants and biological
material near topographic features
The Kelvin wave
 Reduced gravity model
under ice
 Forced by tides
interacting with
topography
 Applications



Barents Sea
Van Mijenfjorden,
Svalbard
Baffin Bay, Canada
Theory
 Straight coast. Linear solution :
~
  Ae x  y / a cos(kx  ly  t )
 Separate motion in mean and
fluctuating part:
~
U  U U , UL  US UE
 Integrate in vertical, average
over wave period. Result:
 fVE  c12 x  (3 / 2)c1U Sx  cD U E U E / H12
fU E  c12 y  0
U Ex  VEy  U Sx
UE 
H 1
cD
c1 Ae c  y / a
VE   [C1 (1  e  2 y / a ) e  2x  C2 (1  e  y / a ) e x ]
 Wave forcing as divergence of
Stokes drift. Similar to
radiation stress from L.H. for
surface waves
 Stress on mean motion
modelled as drag
 Eulerian drift both along coast,
and normal to coast due to
friction
Støylen and Weber (2010),
JGR, in press
Numerical test
 Linear motion:
Test in a box, two-layer
model, a=4.5 km
 Open west boundary, tidal
forcing
 Narrow constriction
generate waves in
pycnocline

 Drift simulation
Upper layer reduced
gravity iterative solution
 Wave forcing from
previous result
 Outflow, return current
and boundary trapped

Top: Wave solution, Two-layer model simulation. Open
west boundary
Bottom: Mean drift, reduced gravity mode. Forcing from
linear wave solution
Wind induced motion
 Typical fjord summer-autumn
Ice free conditions
 Wind direction either in or out of the fjord
 Strong stratification from glacier melting

 Pileup of water from unidirectional wind
Depression of pycnocline
 Wind changes, interfacial disturbance propagates in the same
manner as the tidally induced Kelvin wave
 Change in wind induces cyclonic near shore transport (f>0)

Simulation: Van Mijenfjorden
 Plots show typical autumn scenario
for salinity and wind
 z-coordinate model (MITgcm) to
resolve pressure gradient forces
accurately in upper layer
 (Unable to successfully apply a coordinate model to this problem
setup)
Eklima.no, Kangas (2000)
Preliminary results
 Initially at rest
 8 m/s wind
from west
 After 6 hrs not
much change
in pycnocline
 Significant
after 30 hrs
The Stokes interfacial edge wave
 Outflow of dense bottom
water along the eastern
Greenland coast. (Similar
situations in the Antarctic)
 Interfacial edge waves in the
lower layer
 Analytical model. Reduced
gravity with infinite upper
layer
 Frequency splitting from
Coriolis, waves propagate
both ways
Section across Denmark Strait (Smith
(1976)). The dense bottom layer is
confined to the western slope
My thesis so far and challenges ahead
 Work on Kelvin wave finished and published
 Numerical runs for wind driven motion in progress

Comparison with field data?
 Work on theory for wave induced drift in wind-generated
interfacial waves (closely related to previous work)
 Development of theory for nonlinear drift in Stokes
interfacial edge waves in progress
 Connect the topics under the umbrella of arctic coastal
processes
Thank you