20th Australasian Fluid Mechanics Conference
Perth, Australia
5-8 December 2016

A dominant near-inertial internal wave field on the Tasmanian Continental Shelf
1

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1

T.L. Schlosser , N.L. Jones , C.E. Bluteau , A.J. Lucas and G. Ivey
1

School of Civil, Environmental and Mining Engineering & Oceans Institute
University of Western Australia, Crawley 6009, Australia
2

Scripps Institution of Oceanography
University of California, San Diego, La Jolla, CA, USA

Abstract

Methods

The Tasmanian Eastern Continental Shelf (TECS) has a complex
internal wave field forced by surface tides and wind. To quantify
these flow fields, we deployed three traditional moorings and two
autonomous profilers on a transect across the relatively narrowshelf for 18 days in February 2015. These moorings provided
temperature and velocity measurements through the watercolumn. Harmonic analysis of the observed velocities indicatesthat time varying near-inertial waves are an order of magnitude
more energetic than internal tides and dominate the internal wave
field. We link variations in near-inertial wave velocities tovariations in the surface wind stress.

Study Site

Introduction
Internal waves are a ubiquitous physical process on densitystratified continental shelves. Internal waves can transport
nutrients and other tracers vertically and horizontally, throughmixing and nonlinear advective processes, thereby modifying the
primary productivity of coastal waters [4, 6]. These baroclinic(depth-varying) processes can be generated by the barotropic(depth-constant) tides, the wind and other processes. When thebarotropic tide forces stratified water vertically over topography,
tidally-forced internal waves originate from the seabed, called theinternal tide [5]. In contrast, wind-forced internal waves originate
at the water-surface [8]. Their frequency is generally similar to
the Coriolis frequency (i.e. near-inertial) and when freely
propagating we call them near-inertial internal waves (NIW) [2].
The internal wave field of a continental shelf is thus dependent
on the local wind and tide forcing, as well as remotely generated
internal waves that propagate on the shelf.
Here we present field observations on the TECS of the internal
wave field and the barotropic tide and wind that force thisinternal wave field. The internal wave field of this shelf has many
unique features and is vastly unstudied, despite widespread
evidence of the importance of internal waves to the physical andbiological dynamics of continental shelves. The TECS
experiences strong and variable winds and its barotropic tidal
range is around 1.4 m. One of the world’s most energetic internal
wave beams also propagates across the Tasman Sea to theTasman Continental Slope [11], which we originally expectedtransferred significant energy to the shelf through internal waves
at the tidal frequency. Instead, we show that NIWs dominate theinternal wave field at this site and are coherent with the local
wind field in the upper water column.

Our study site is in the north-east of the TECS at 41.1°S, where
the shelf is 28 km wide and its depth gradually increases to
200 m at the shelf-break (figure 1a). The continental slope isorientated approximately north-south at an angle of 3° to the east.
The inertial period at this latitude is 18.1 h. Tasmania lies in thepath of the 'Roaring Forties' and therefore experiences
considerable periods of strong westerly winds. The northern limitof the westerly wind belt is commonly approximately 40°S in
winter months and 44°S in summer months [13]. The Bureau of
Meteorology St Helens station has been in operation since 2001.
The Austral summer winds from St Helens are predominantly
towards the north or south, but are strong and variable. During
the Austral summer months the East Australian Current (EAC)
Extension commonly ranges to approximately 42°S [10]. The
EAC Extension transports warm and salty tropical water southfrom north-eastern Australia to the cool temperate waters of the
TECS. An undercurrent transports colder water northwards, with
reduced flow volumes compared to the EAC Extension. We
expect this combination of tide, wind and mesoscale processes
will result in a complex shelf response.
Field Measurements
In total, we deployed six moorings on the TECS for 18 days in
February 2015. However, we present only the measurementsfrom one of the autonomous profilers (WireWalker), deployed at148.5357°E, 41.3854°S, in 114 m of water. We co-located thisprofiler with a bottom-fixed acoustic Doppler current profiler(ADCP, RDInstruments 300 kHz Workhorse). The ADCP
measured pressure, in addition to velocities in 2 m vertical binsthat ensemble-averaged 6 pings per ensemble in 10 second
intervals. We quality controlled and time-averaged thesemeasurements to 2 minute time intervals. The autonomous
profiler sampled the entire water-column approximately every
8 minutes, with a vertical resolution of 25 cm [7]. It measured
temperature and salinity in addition to other physical andbiological variables.

0 1

𝐻𝐾𝐸 = ∫−𝐻 𝜌|𝒖𝑏𝑐 |2 𝑑𝑧………..……..(1)2Here 𝜌 is the water density from the autonomous profiler’smeasurements, 𝐻 is the water depth (114 m) and 𝒖𝑏𝑐 is thebaroclinic velocity. Bold variables indicate a vector quantity,
including both cross- and along-shore components. We use a
depth varying 60-h low-pass filtered water density for our HKE
calculations.
We calculated the wind stress using:𝝉𝒘 = 𝐶𝐷 𝜌𝒗|𝒗|………………………..(2)Here 𝒗 is the wind velocity; 𝐶𝐷 is the drag coefficient, estimatedat 1.410-3 and 𝜌 is the air density estimated at 1.2 kgm-3.
Rotary spectra is a method of separating vector quantities by theirrotation direction, where NIWs rotate cyclonically or counterclockwise in the Southern hemisphere. We quantitatively
compare the coherence of the wind stress and the water velocities
via cross-spectra of the rotary spectra. We compare only thecyclonic components of the wind stress and water velocities. We
use the sine-multitaper method [1, 9], which preserves the low
frequency range. The form of the rotary spectra was given by:−𝑖2𝜋𝜔∆𝑡 |2 …………….(3)𝑆̂(𝜔) = ∆𝑡|∑𝑁
𝑡=1 𝑤𝑡 𝒖𝑏𝑐 𝑒

Where 𝑤𝑡 is the window function as per the sine-multitaper
method, 𝜔 is the frequency, and ∆𝑡 is the sampling interval. The
term 𝒖𝑏𝑐 can also be replaced by 𝝉𝒘 . We use equation 5.205(p.518) in Thompson and Emery [12] to calculate the inner crossspectra between the wind stress and baroclinic velocities rotatingin the same direction, defined as 𝑆̂𝜏+𝑤𝑢𝑏𝑐 for 𝜔 > 0 (cyclonic).
Results and Discussion
Figure 1: (a) Tasmania, Australia, with study site indicated by a redsquare. Wind rose for month of February 2015 recorded at St Helens (redasterisk in b); the direction indicates the direction the wind is blowing
towards. (b) Map of the local bathymetry and mooring locations(crosses). Our paper focuses on the autonomous profiler (red cross). The
arrow indicates mean flow velocity and ellipses indicate flow velocity of
one standard deviation along the major and minor axis of flow direction.

Background Conditions
Over the entire 18-day record, the EAC Extension flowed
southward (blue arrow in figure 1b). The total (barotropic andbaroclinic) velocities flowed generally southwards at 14 cms-1.
During the month of our measurements, measured winds from St
Helens were directed predominantly in the north and south
directions (along-shore, figure 1a). Our shipboard windmeasurements, which we use to calculate wind stress in figure
2b, showed that the wind blew in a similar direction comparedwith the St Helens’ station. We use the shipboard winds for windstress as the ship was generally closer to the mooring site.

Data Analysis
We analysed the measured velocity timeseries from the ADCP
collocated with the autonomous profiler. The barotropic flow is
depth- and density-independent, which we approximate as thedepth-averaged velocity. To derive the baroclinic velocities, we
subtracted the depth-averaged velocity from the total velocity.
We have assumed all wave-like motions at the near-inertial
frequency are freely propagating internal-gravity waves. We
performed harmonic analysis on the baroclinic velocities at thediurnal (D1), semidiurnal (D2) and inertial frequencies. A sliding
harmonic fit was performed on segments of 3 days, withsegments overlapping by all but one time step. We derived asignal-to-noise ratio for all time segments from the harmonic fit
and residual time series and discarded time segments with asignal-to-noise ratio less than three. For each time step, we thenaveraged harmonic amplitudes of the remaining overlapping time
segments. By reducing the segment lengths to 3 days, ourharmonic analysis could only separate the semidiurnal(𝜔~2 cycles per day), near-inertial, and diurnal frequencies(𝜔~1 cycle per day) from each other but not the individual
constituents such as the S2 and M2. Therefore, we use D1 todenote the diurnal K1 and O1 tidal constituents and D2 to denotethe semidiurnal M2 and S2 constituents. Through harmonic
analysis, we have isolated the tidal and near-inertial baroclinic
variations over time and depth.

To separate the dominant tidal constituents, we performed
harmonic analysis of the water surface elevation, measured by
the bottom-mounted ADCPs pressure sensor. The four mostdominant constituents were, in order of reduced influence, thesemidiurnal M2, the diurnal K1, O1 and the semidiurnal S2, withmaximum surface elevations of 35 cm, 12 cm, 8 cm and 7 cm,
respectively. Neap tide is on day 42 and the spring tide is on day
49. The stratification was relatively strong with a buoyancy
period of about 1 min up to day 49, when the stratification
weakened and the buoyancy period increased to 2 min (notshown). For the entire field campaign, the stratification supported
internal waves.
TECS Internal Wave Field
Barotropic tidal velocities were significantly stronger than theirrespective baroclinic velocities; however, the near-inertial
baroclinic velocities at times exceeded the barotropic tidal
velocities. Barotropic tidal velocities reached 11 cms-1 andaveraged 5 cms-1 over the measurement period (figure 2a). The
median and 95th percentile baroclinic tidal velocities were around
2.4 cms-1 and 4.3 cms-1, respectively, for both D1 and D2 (notWe calculated the horizontal kinetic energy (HKE) using:2

shown). At this site, little energy was evident from the externallygenerated M2 tidal beam that propagates onto the Continental
Slope from across the Tasman Sea. The baroclinic NIW
velocities were significantly stronger with median and 95th
percentile magnitudes of 3.4 cms-1 and 9.1 cms-1, respectively(figure 2d). The NIW baroclinic velocities were strongest near
the surface, averaging 6.9 cms-1, while those mid-depths and near
the bottom averaged at 3.5 cms-1 and 3.0 cms-1, respectively(figure 2d). These near-bottom averages, although half of nearsurface estimates, were still larger than the median near-bottom
baroclinic tidal velocities. The mean and maximum baroclinic
NIW velocities therefore exceeded the baroclinic tidal velocities.

frequency approaches the inertial frequency. We considered only
horizontal flow, but rotary coefficients less than one indicates
there may be vertical propagation [3]. The NIW field therefore
rotates cyclonically due to the Earth’s rotation and is not limited
to surface waters.

Figure 3: Rotary coefficient for baroclinic velocities at near-inertial
frequency, calculated from harmonic analysis velocities. A value of one
indicates perfectly circular, cyclonic (counter-clockwise) rotation.

Relating Wind and Bottom Stress to Near-Inertial Waves
We relate the observed NIW near the surface to the local winds
by comparing the induced baroclinic velocity magnitudes infigure 2d with the wind stress in figure 2b. Large wind stresses
that exist for less than the near-inertial period (18 h) and rotate
cyclonically are most effective in creating NIW [8]. Winds
rotated cyclonically and exceeded 0.2 Nm-2 on two occasions:day 41 and 53. Following these two large wind events, the nearsurface NIW velocities increased to over 12 cms-1 and reachedtheir maximum values over the record. Cyclonically rotating
winds with magnitudes around 0.1 Nm-2 occurred more
frequently; following these smaller wind stresses a weaker NIW
response was recorded, with velocities around 6 cms-1 (day 38,
46 and 47). It is likely the near-surface NIW velocities on days
41 and 53 were larger due to the added influence of these prior,smaller wind events as there is little evidence of velocities
decreasing in the mixed layer before the larger wind events. From
day 43 to 45 winds were sustained at over 0.1 Nm-2 and blew
westwards (aligned along x-axis). After these sustained winds thenear-surface NIW velocities were their smallest over the whole
record. We attribute these small velocities to the wind blowing
for over two inertial periods and emphasise that efficient
generation of NIWs requires not only strong winds that rotate
cyclonically, but also winds that periodically relax with afrequency near or less than the Coriolis frequency [8].

Figure 2: (a) Barotropic velocities at all tidal frequencies, (b) wind stress6-hour low-pass filtered, (c) depth-integrated horizontal kinetic energy(HKE) of baroclinic velocities at labelled frequency, and (d) baroclinic
velocity magnitude (cross and along-shore) at near-inertial frequency. In(d) the 60-h low-pass filtered isotherms(°C) are shown in black. Arrowdirection in a-b is geographical (i.e. up is north, left is west).

The HKE conveys the proportion of energy in the different
frequencies (figure 2c). The baroclinic tidal velocities had similar
magnitudes throughout the 18 days, resulting in a nearly constant
HKE with a mean of 35 Jm-2. In contrast, the NIW HKE varied
by an order of magnitude (80 Jm-2) over 4 day periods. Thishighlights the baroclinic near-inertial signal is temporally
variable, due to the non-stationarity of the wind-forcing and otherdynamics to be explored in future work. The mean HKE of thebaroclinic NIW was 106 Jm-2, an order of magnitude larger thanthat of the baroclinic tides. We conclude that NIWs were themost dominant baroclinic motion on TECS during our field
campaign.

The NIW velocity structure at depth is complex. Velocities over
6 cms-1 occurred at depths over 50 m deep during large windstresses (>0.1 Nm-2) for days 41-44, but not days 50-54 (figure2d). On days 46 and 47, the near-surface NIW velocities were
smaller; however, there were four isolated depth layers withvelocities over 5 cms-1. On days 41-44, the thermocline’s
stratification is stronger at 1 min period and corresponded
approximately to the 16°C isotherm. During this period, the large
NIW velocities at depth do not penetrate the thermocline. Afterday 50 the thermocline weakens to 1.5 min period and decreases
to a depth of 90 m on day 50 (~14°C isotherm), then sharply rises
to 50 m on day 53 (~16°C isotherm). We attribute the large
velocities on days 50-54 penetrating to depths of 90 m, below the
16°C isotherm to the weakening in the thermocline’s
stratification. There were also additional periods where NIW
velocities exceeded 5 cms-1 at depths below the thermocline. We
then statistically compare the wind field to the water velocities
through cross spectra.

The rotary coefficient describes both the rotation direction
through its sign (clockwise or counter-clockwise) and the degreeof rotation versus unidirectional flow. A value of one represents
perfect cyclonic circles (counter-clockwise) and zero represents
unidirectional flow. We computed the rotary coefficient from thehorizontal baroclinic harmonic analysis velocities. The rotary
coefficient was close to one for most of the water-column, with asmaller coefficient at approximately mid-depth and close to theseabed (figure 3). A rotary coefficient of one is consistent withtheory, which describes that waves become more circular as their

Inner cross rotary spectra of the cyclonic wind stress and watervelocities revealed the coherence of the two signals, their time3

lag and the energy at certain frequencies. We compare the windstress to the water velocities at two depths. Near the surface,water velocities were coherent with the wind at the near-inertial
frequency (figure 4a), with a phase difference of approximately
32° or 1.6 hours with water lagging wind (figure 4b). Thisconfirms the qualitative relationship explored above between thewind stress and NIW velocities in figure 2. The velocities at
depth were also coherent with the wind at the near-inertial
frequency, however the baroclinic velocities were less coherent
and the variance shared with the wind was weaker at this depth(figure 4c-d). The phase difference was approximately -155°(335°) or -7.8 hours (16.8 hours). For both depths, the inner crossspectra shows the wind energises all frequencies, with thegreatest response at the inertial frequency, as found by otherstudies [8].

Collaboration Award and a UWA ECM Research Development
Award. We acknowledge the anonymous reviewer whose
detailed comments improved the quality of this work. T. L.
Schlosser acknowledges the support of a University PostgraduateAward. We also acknowledge the crew of the R/V Revelle andChief Scientist Professor Rob Pinkel.
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Figure 4: Inner cross-spectra of cyclonic (counter-clockwise) shipboard
wind stress and baroclinic water velocities at 23 m (a-b) and 81 m (c-d)
depth. Horizontal dashed lines in b and d show the 95% significance andall vertical dashed lines mark the diurnal, inertial and semidiurnal
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The TECS field observations demonstrate that NIWs dominate
the internal wave field. The local wind forced the near-surface
NIW, as revealed by a comparison of NIW velocities with thelocal wind stress. Large wind stresses that were sustained for lessthan one inertial period (18 hours) and rotated cyclonicallyappeared to be most effective at generating NIWs, which also
rotate cyclonically in circular motions throughout the watercolumn. The local wind stress was significantly coherent with thewater velocities at the near-inertial frequency, although thecoherence of the signal weakened with increasing depth. Thissuggests other factors were influencing the NIW field at depth,
which requires further analysis.
A more detailed analysis of the NIW dynamics will be the focus
of future work. This work will include an energy balance, theenergy flux variations and the modal separation of NIW on the
TECS. Spatial variations will be analysed across the shelf using
the physical measurements from five other moorings. Our
ultimate goal is to link the NIWs physical dynamics to the
biological response on the shelf.
Acknowledgements
This work was funded by an Australian Research Council
Discovery Project (DP 140101322), a UWA Research4