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th
Proceedings of the 17 Physics of Estuaries and Coastal Seas (PECS) conference,
Porto de Galinhas, Pernambuco, Brazil, 19–24 October 2014
Langmuir Circulation and Turbulence in Chesapeake Bay
MALCOLM E. SCULLY
1
Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, Woods Hole, MA
02643, USA.
email: mscully@whoi.edi
Keywords: Langmuir Circulation, Turbulence, Mixing
SUMMARY
Measurements made as part of a large-scale experiment to examine wind-driven circulation and mixing in
Chesapeake Bay demonstrate that circulations largely consistent with Langmuir circulation (LC) play an
important role in surface boundary layer dynamics in this estuarine system. Under conditions when the
turbulent Langmuir number is low (Lat < 0.5), the observed low frequency (<1/20 Hz) vertical motions
are characterized by: 1) strong coherence over most of the water column; 2) negative vertical velocity
skewness indicative of strong/narrow downwelling and weak/broad upwelling; 3) strong negative
correlations with the low frequency horizontal velocity in the direction of wave propagation. The
orientation of the regions of surface convergence inferred from the observations are closely aligned with
the dominant direction of wave propagation, which often deviates significantly from the wind direction.
The inferred horizontal spacing between downwelling zones is generally consistent with the depth of the
surface mixed layer (aspect ratio ~ 1), but shows considerable scatter and a lognormal distribution
consistent with surface convergence that occurs randomly in both time and space. Tidal currents, vertical
density stratification and the surface heat flux all modulate the intensity and coherence of the observed
circulations. While strong tidal flows inhibit the development of LC, the surface heat flux can either
inhibit or enhance the observed circulation depending on whether the heat flux is stabilizing or
destabilizing. The circulations we observe appear to be highly variable in time and space and more
analogous to coherent turbulence than the traditionally assumed 2-dimensional wind-aligned pair of
counter rotating vorticies. Consistent with recent results from Large Eddy Simulations, we hypothesize
that wave breaking seeds the flow with vertical vorticity that is tilted over by the stokes drift shear,
initiating a coherent instability consistent with LC. The intensity of the observed circulation is strongly
dependent upon the surface wave height, which is strongly related to both wave breaking and the stokes
drift shear in fetch-limited environments like Chesapeake Bay.
1. INTRODUCTION
There is considerable evidence that the presence of Langmuir Circulation (LC) fundamentally alters the
dynamics of the surface boundary layer in the ocean [1]. There have been a number of proposed
mechanisms for the formation of LC, but the most widely accepted explanation is that the wave-driven
stokes drift tilts vertical vorticity into the streamwise direction, leading to coherent vortices that are
aligned with the direction of wave propagation [2]. The so-called Craik-Leibovich vortex force has been
incorporated into numerous large eddy simulations (LES), which have simulated coherent wind-aligned
vortices that are largely consistent with field observations of LC [3]. Despite the increasing
acknowledgement that LC plays a fundamental role in surface mixed layer dynamics, there are relatively
few detailed field measurements that fully characterize LC. Of the field studies that provide high quality
measurements of LC, none have been conducted in an estuarine environment. Given the presence of both
strong stratification and strong tidal shears, estuarine environments are unlikely locations for LC to play
an important roll in surface mixed layer process. However, as we will demonstrate in this paper, strong
coherent circulations consistent with LC are commonly observed in Chesapeake Bay, and when present,
dominate the mixing in the surface mixed layer.
th
Proceedings of the 17 Physics of Estuaries and Coastal Seas (PECS) conference,
Porto de Galinhas, Pernambuco, Brazil, 19–24 October 2014
2. METHODS
The observations presented in this paper were collected as part of a collaborative research project to
examine wind-driven circulation and mixing in Chesapeake Bay during the fall of 2013. The results
presented below focus primarily on an instrumented turbulence tower that was deployed along the
western shoal in roughly 14m of water. The tower contained a vertical array of six acoustic Doppler
velocimeters (ADVs), 6 CTDs and 12 thermistors. The ADVs were spaced roughly 2m apart in the
vertical and sampled nearly continuously (28 minute burst every 30 minutes) at 32 Hz for 30 days.
Immediately adjacent to the tower was a bottom mounted 1200 kHz acoustic Doppler current profiler
(ADCP) that sampled at 1Hz and recorded a velocity profile every 30 seconds. In order to remove the
high frequency motions associated with surface gravity waves and small-scale turbulence, the ADV data
for each 28-minute burst was lowpass filtered with a cutoff frequency of 1/20 Hz. The lowpass filtered
data were then linearly detrended, removing the mean and effectively bandpassing the data. The resulting
velocity data (denoted with underscore lp) has no high frequency (e.g. surface waves) motions, low
frequency (e.g. tides) motions, and has a mean of zero. We use the rms intensity of the low-frequency
vertical velocity calculated for each burst as a simple metric for the intensity of observed circulation
(denoted <w’>std). The structure and coherence of vertical motions is inferred from the vertical velocity
skewness (γ = <wlp3>/<wlp2>3/2), where the angled brackets indicate burst average. Negative values of γ
are indicative of stronger and narrower downwelling zones that alternate with weaker and wider
upwelling zones—a feature commonly attributed to LC. While we did not directly observed the
horizontal spacing (Lh) of circulation cells, it was estimated from the time between successive
downwelling regions (Td) and the velocity perpendicular to the direction of wave propagation (Vw) so that
Lh = TdVw. The orientation of the circulation also was not directly measured, but inferred by finding the
horizontal rotation angle that minimizes the correlation between low frequency vertical and horizontal
velocity (i.e. most negative correlation). The characteristics of the surface waves including significant
wave height (Hs), dominant wave period (T), wavenumber (k), stokes drift velocity (Us) and the stokes
drift shear (∂Us/∂z) were calculated from the directional wave spectra measured by the uppermost ADV.
Estimates of Us combined with observed shear velocity (u*) were used to calculate the turbulent Langmuir
number Lat = (u*/Us)1/2. The net heat flux through the ocean surface (Q) was estimated from direct
measurements of sensible heat flux (Qh) and latent heat flux (Qe), combined with estimates of net short
wave radiation (Qs) and net longwave radiation (Qb) from the NCEP North American Regional
Reanalysis (NARR) model. With estimates of Q, we estimated the Hoenikker number (Ho = [αgQ]/[ρC kUSu*2]), which represents the ratio of the buoyancy forcing that drives thermal convection to
the vortex force that drives LC.
ρ
3. RESULTS
Circulations consistent with LC are commonly observed in Chesapeake Bay throughout the record. Data
from the bottom-mounted ADCP demonstrates coherent low frequency circulation with strong (> 3 cm/s)
vertical velocities that often extend throughout the water column under strong wind and wave forcing (fig.
1). ADCP backscatter data suggest that the strong vertical velocities advect air bubbles from the surface
downward and advect suspended sediment upward from the bottom. During conditions when Lat < 0.5,
the observed circulations are characterized by negative vertical velocity skewness, indicative of strong
narrow downwelling zones and weaker more broadly distributed upwelling (fig. 2). A commonly noted
characteristic of LC is the presence of an intensified downwind jet associated with the convergent
downwelling regions and a corresponding negative velocity perturbation in the along wind direction
associated with the upwelling regions. If we assume the traditional velocity structure for LC, the time
series of ulp and wlp should be negatively correlated in a coordinate system aligned with the wind,
assuming the structure of the LC laterally advects past our fixed sensors. So, even though the tower data
were collected at a fixed vertical location and do not provide any direct information about the orientation
of LC, we can infer the orientation by finding the rotation angle that minimizes the correlation between ulp
and wlp (i.e. most negative correlation). As demonstrated in figure 3, the lowest correlations generally
th
Proceedings of the 17 Physics of Estuaries and Coastal Seas (PECS) conference,
Porto de Galinhas, Pernambuco, Brazil, 19–24 October 2014
occur for conditions where Lat < 0.5 and show
a spatial and temporal pattern consistent with
the distribution of <w’>std and γ. Consistent
with the observed distribution of γ, the
minimum correlation is most negative at the
second ADV from the surface during strong
wave forcing. The inferred orientation of LC
agrees reasonably well with the observed wind
and wave directions (fig. 3b). However the
LC orientation is consistently 45 degrees to
the left of the wind and the inferred LC
orientation is more consistent with the mean
wave direction. Given that vortex force
hypothesized to drive the observed LC
originates from the stokes drift, we would
expect the orientation of the observed
circulation to be more aligned with the
waves—which is generally what we observe.
Figure 1. Bandpassed ADCP a) vertical velocity; b) acrosswind
velocity; c) alongwind velocity; and d) acoustic backscatter
illustrating coherent circulation consistent with LC.
the observed probability distribution of Lh
is largely consistent with a lognormal
distribution. Estimates of the aspect ratio
also are generally lognormal with a
median of 1.4 and mode of 1. Thus,
while there is considerable scatter, the
observed spacing is generally consistent
with the depth of the surface mixed layer.
It is worth noting that both Lh and the
aspect ratio exhibit large scatter with no
clear relationship with any other
parameter we measured. We believe the
large scatter and lognormal distribution
are consistent with Csanady’s [4]
interpretation that the surface
convergence caused by LC occurs
randomly in both time and space.
Using the methods outlined in section 2, we
also can estimate the horizontal spacing of LC
in our observations (Lh). We detected 773
individual downwelling “events” with a
median inferred spacing of ~17 m. There is
considerable scatter in the estimates of Lh and
Figure 2. a) Turbulent Langmuir number; b) lowpass filter vertical
velocity magnitude; and c) vertical velocity skewness measured by
the 6 ADVs on the turbulence tower.
The presence of density stratification is often
sufficient so that N2 > ∂U/∂z ∂Us/∂z. Under
these conditions we do not observe circulation that is consistent with LC. In the upper portion of the
water column temperature gradients associated with diurnal heating often dominate the stratification, and
we commonly observe diurnal modulation of the LC intensity. For conditions where the surface heat flux
is destabilizing (Q<0), we see evidence that convective mixing enhances LC. This is illustrated by
comparing conditions where Q<0 and where significant wave height is between 0.5 – 0.7 m, but
segregating the data based on the intensity of surface heat loss (fig. 4). We define strong and weak surface
th
Proceedings of the 17 Physics of Estuaries and Coastal Seas (PECS) conference,
Porto de Galinhas, Pernambuco, Brazil, 19–24 October 2014
Figure 3. a) Minimum correlation between horizontal and vertical lowpass
velocity; b) comparison between angle that minimizes (most negative) the
correlation between horizontal and vertical velocity (inferred LC-orientation),
with observed wind and wave direction.
Figure 4. Profiles comparing the intensity of low frequency a) vertical motion
and b) vertical velocity skewness for the conditions summarized in the table.
Colors of text in table correspond to colors in figure.
heat loss by the criteria of Q<-300
W/m2 and 0>Q>-100 W/m2,
respectively. In restricting our
comparison to this range the two
populations have nearly identical
mean value of Hs and Lat, but
significantly different values of
surface heat flux and Ho (see table in
fig. 4). For further comparison, we
also plot the profiles for conditions
where surface heat loss dominates the
LC forcing (Ho > 1). The intensity of
low-frequency vertical velocities is
intensified and values of γ are more
negative in the presence of strong heat
loss. Values of γ exhibit a sub-surface
minimum, with the lowest values
observed at the second ADV from the
surface for conditions where Lat < 0.5.
In contrast, for conditions where Lat >
1 and Ho > 1 the most negative values
γ are observed at the uppermost ADV
and the negative skewness becomes
less negative rapidly with increased
depth, consistent with coherent
structures that do not penetrate deeply
into the water column. The intensity
of low frequency vertical motion is
nearly three times smaller at the
surface for conditions with convection
but no LC (Lat>1 & Ho>1) than when
LC and convection occur
simultaneously. We conclude that a
destabilizing heat flux can augment
the circulation driven by LC, but that
LC is the dominant mechanism
driving coherent low frequency
motions in the surface boundary layer.
4. REFERENCES
[1]
[2]
[3]
[4]
Thorpe, S. A. (2004). Langmuir circulation. Annu. Rev. Fluid Mech., 36, 55-79.
Craik, A.D.D., and Leibovich, S. (1976). A rational model for Langmuir circulations. Journal of Fluid
Mechanics, 73(03), 401-426.
McWilliams, J.C., Sullivan, P.P., and Moeng, C.H. (1997). Langmuir turbulence in the ocean. Journal of
Fluid Mechanics, 334, 1-30.
Csanady, G. T. (1994). Vortex pair model of Langmuir circulation. Journal of marine research, 52(4), 559581.