Inertial oscillations

[uniquorn]

Starting the thread with a 'thought experiment' explanation using two screenshots from http://faculty.washington.edu/luanne/pages/ocean420/notes/inertial.pdf
© 2005 Susan Hautala, LuAnne Thompson, and Kathryn Kelly.  All rights reserved.

Hopefully they don't mind me sharing some of it here, posted as images to easily include the static graphics

[uniquorn]

A more detailed analysis is available here
http://www.cleonis.nl/physics/phys256/inertial_oscillations.php

Which starts with an example of one of my favourite topics

A drifting buoy set in motion by strong westerly winds in the Baltic Sea in July 1969. When the wind has decreased the uppermost water layers of the oceans tend to follow approximately inertia circles due to the Coriolis effect. This is reflected in the motions of drifting buoys. In the case there are steady ocean currents the trajectories will become cycloides.
The inertia circles are not eddies; a set of buoys close to each other would be co-moving, rather than revolve around each other

and includes many animations.

Understanding of the physics of inertial oscillation is the key to understanding how the rotation of the Earth affects the oceanic and atmospheric dynamics. Inertial oscillation is the simplest, purest case. Usually the motion of air mass is affected by both pressure gradient and Coriolis effect. Inertial oscillation shows how water mass and air mass move when there is no pressure gradient to begin with, and no buildup of pressure gradient in the course of the motion.

[uniquorn]

rammb of the restless sea beneath the centre of high pressure today.  9.5MB
https://col.st/nuZix

[uniquorn]

From http://www.cleonis.nl/physics/phys256/inertial_oscillations.php
the period of oscillations in the Arctic is roughly 12.2hrs, frustratingly close to tidal periods. So in the example below from Mosaic P236, jun27-jul24, it's not easy to separate the probable tidal component from the inertial oscillations. Any fast fourier transfomers out there?

P236 almost gets grounded on jul22 and is possibly free floating now.

[uniquorn]

http://oceanmotion.org/html/resources/coriolis.htm

Description

This model depicts the motion of an object sliding on the surface of a smooth sphere whose size and rotation speed are identical to the Earth. You select the starting speed and direction of the object and click on the map to see the trajectory of the object over a week of time. The object is subject to the Coriolis acceleration, an acceleration caused by the rotating system of reference.
   

Rules to remember for the Coriolis acceleration are:

    The acceleration is perpendicular to the object velocity so the acceleration will change only the direction of the velocity and not its magnitude.
    In the Northern Hemisphere, objects curve to the right as they travel.
    In the Southern Hemisphere, objects curve to the left as they travel.

[uniquorn]

The Coriolis Effect – a conflict between common sense and mathematics
Anders Persson, The Swedish Meteorological and Hydrological Institute, Norrköping, Sweden
https://www.lextalus.com/pdf/The%20Coriolis%20Effect.pdf

Introduction: The 1905 debate
Hundred years ago the German journal “Annalen der Physik”, the same 1905 volume where Albert Einstein published his first five ground breaking articles, provided a forum for a debate between three physicists, Denizot, Rudzki and Tesař on the correct interpretation of the Coriolis effect, in particular how it manifested itself in the Foucault pendulum experiment. The debate was complicated by many side issues, but the main problem was this:

if the pendulum’s plane of swing was fixed relative to the stars, as it was often said, why then was not its period of rotation the same, one sidereal day (23 hours and 56 minutes), everywhere on earth and not only at the poles?
 
Instead the period was 28 hours in Helsinki, 30 hours in Paris and 48 hours in Casablanca, i.e. the sidereal day divided by the sine of latitude. At the equator the period was infinite; there was no deflection. This could only mean that the plane of swing indeed was turning relative the stars. But how could then, as it was also said, a ‘fictitious’ inertial force be responsible for the turning?

Hundred years later, Einstein’s five 1905 “Annalen der Physik” papers are common ground in the elementary physics education whereas teachers and students, just like Denizot, Rudzki and Tesař, struggle to come to terms with the Coriolis effect.

This article will try to explain the complex and contradictory understanding of the deflective mechanism in rotating systems. But first it might be appropriate to remind us what is generally agreed on.

tldr?

Coriolis’ 1835 paper did not do away with erroneous intuitive explanations. The paper was highly mathematical and not easily accessible.

In 1847 the French mathematician Joseph L. F. Bertrand (1822-1900) suggested to the French Academy a “simplified” derivation. He combined two “common sense”, but erroneous, assumptions:
a) the deflective acceleration is due to conservation of absolute velocity and
b) the deflective acceleration on a rotating turntable is constant and only due to the Coriolis effect.
The first assumption underestimates the Coriolis effect and the second overestimates it - so the errors cancel out (fig.20). 

Fig. 20: Joseph Bertrand and his “simplified” derivation. An object on a turntable at a distance R from the centre of rotation is moving radially outwards with a constant speed Vr= ∆R/∆t . Due to the rotation Ω the object is subject to a deflective acceleration a, which is assumed constant. The deflected distance ∆S during ∆t can be expressed both as ∆S=a(∆t)2/2 and ∆S=Ω ∆R∆t which yields a=2ΩVr.             

Bertrand’s derivation became popular and entered meteorology in the 1880's.
If we today are grappling to understand the Coriolis effect, one source of confusion is this “simple” but deceptive derivation, which appears to justify two frequent misconceptions.

added some spaces to make it more readable and the last emphasis

[Tor Bejnar]

So what some of us thought was tidal forces is actually inertial oscillations.  It makes sense: tidal forces are minimal/nonexistent far from shore.  (Somebody reminded us of this a year ago or so.)

[kassy]

Some large scale stuff:

Eddy Killing in the Ocean

Eddies are circular currents that wander around the ocean like spinning tops, ranging from tens to hundreds of kilometers in diameter. They mimic weather systems in the atmosphere and serve as a feeding grounds for sharks, turtles, and fish. Eddies often spin off major ocean currents and typically die within a matter of months.

Some fundamental questions in physical oceanography center around the life cycle of eddies: What gives rise to them, and how do they die? “It’s a big puzzle that’s been long-standing in the community,” said fluid dynamicist Hussein Aluie from the University of Rochester, N.Y.

Aluie and his colleagues found that when it comes to eddy killing, the planet’s winds are partly to blame.

Their innovative analysis of satellite data suggests that wind sucks energy out of the ocean from features smaller than 260 kilometers—features that include most eddies. Wind continually extracts about 50 gigawatts of energy from eddies around the world. The team published their research in Science Advances in July.

...

Although it’s long been suspected that wind zaps eddies of their spin, the latest study provides a seasonal signal and an estimate of wind power loss in major currents. Although wind may be a killer of eddies, it supercharges larger-scale ocean circulation. Wind adds about 970 gigawatts of energy to features larger than 260 kilometers, the recent research found.

Eddies boost ocean heat intake, ocean mixing at the surface, and the exchange of gases with the atmosphere, so calculating these processes relies on accurate depictions of eddies in computer models.

details see:
https://eos.org/articles/eddy-killing-in-the-ocean

It is a bit off topic but uniquorn likes eddies so hopefully he won´t mind.
On the large scale they meet somewhere.

[uniquorn]

So what some of us thought was tidal forces is actually inertial oscillations.  It makes sense: tidal forces are minimal/nonexistent far from shore.  (Somebody reminded us of this a year ago or so.)

I wonder what happened to u300673?

<>
Have you considered inertial oscillations (e.g. https://tc.copernicus.org/articles/6/1187/2012/tc-6-1187-2012.pdf) ?

Sea ice inertial oscillations in the Arctic Basin
F. Gimbert, D. Marsan, J. Weiss, N. C. Jourdain and B. Barnier
Received: 30 April 2012 – Published in The Cryosphere Discuss.: 18 June 2012
Revised: 24 September 2012 – Accepted: 1 October 2012 – Published: 24 October 2012

Abstract.
An original method to quantify the amplitude of inertial motion of oceanic and ice drifters, through the introduction of a non-dimensional parameter M defined from a spectral analysis, is presented. A strong seasonal dependence of the magnitude of sea ice inertial oscillations is revealed, in agreement with the corresponding annual cycles of sea ice extent, concentration, thickness, advection velocity, and deformation rates. The spatial pattern of the magnitude of the sea ice inertial oscillations over the Arctic Basin is also in agreement with the sea ice thickness and concentration patterns. This argues for a strong interaction between the magnitude of inertial motion on one hand, the dissipation of energy through mechanical processes, and the cohesiveness of the cover on the other hand. Finally, a significant multi-annual evolution towards greater magnitudes of inertial oscillations in recent years, in both summer and winter, is reported, thus concomitant with reduced sea ice thickness, concentration and spatial extent

[uniquorn]

Have you considered near-inertial oscillations?

No they haven't. I've suggested it multiple times though and provided the semi-diurnal frequency using excel's spline fit to the discretized half hour buoy data in the Yermak Plateau area. Uniq provides fresh data links in #1176 but no one followed through. Project SHEBA went to some lengths to observe this effect; for a serious fluid dynamical treatment, the R Pinkel papers cover it.

From the recommended link above (Sea ice inertial oscillations in the Arctic Basin by F. Gimbert et al 2012):

"The effect of the Coriolis force on geophysical fluid dynamics has been studied for more than a century. Interestingly, the first studies of oceanic inertial oscillations (Ekman, 1905) were prompted by the observations of Nansen, made during the Fram’s journey along the Transpolar drift, that sea ice was moving with a 20–40º angle to the right of the wind direction (Nansen, 1902).

"Indeed, as the Coriolis force acts perpendicularly to the particle velocity, it induces a deviation of the trajectory to the right in the Northern Hemisphere. This deviation generates inertial
oscillations, characterized by a frequency of f = 2 sin(latitude in radians) cycles per day, close to a semi-diurnal frequency cycles per day in the Arctic."

The sine function takes on the value 1 at 90º giving two 12 hour cycles per day. After than it falls off slowly to zero at the equator. At Arctic latitudes, the frequency falls off quite slowly but remains quite distinguishable from tidal frequencies (not a big consideration at the Polarstern's location).

Lat   Sine(lat)   Sub-diurnal
90   1.0000   12.000
89   0.9998   12.002
88   0.9994   12.007
87   0.9986   12.016
86   0.9976   12.029
85   0.9962   12.046
84   0.9945   12.066
83   0.9925   12.090
82   0.9903   12.118
81   0.9877   12.150
80   0.9848   12.185
79   0.9816   12.225
78   0.9781   12.268
77   0.9744   12.316
76   0.9703   12.367
75   0.9659   12.423
74   0.9613   12.484
73   0.9563   12.548
72   0.9511   12.618
71   0.9455   12.691
70   0.9397   12.770

A free online scan of Nansen 1902 is at the links below; amazon sells a hard copy of the book for only $545.95. Despite text search, I have not been able to locate Nansen actually saying anything about ice drift angle with respect to wind direction. That seems to have been discussed only in volume III of Nansen's report (which is exhausively detailed) and only available for $35.

https://www.amazon.com/Norwegian-expedition-1893-1896-scientific-results/dp/1130729486

Ekman 1905 is an out of print book available on Johns Hopkins microfilm which can be read at the second link below.

Nansen, F.: Oceanography of the North Polar basin: the Norwegian
North Polar Expedition 1893–96, Scientific Results, 3, 1902.

https://www.biodiversitylibrary.org/item/57263#page/14/mode/1up
https://archive.org/details/norwegiannorthpo02framrich/page/n233/mode/2up?

Ekman, W.: On the influence of the earth’s rotation on ocean currents., Ark. Mat. Astron. Fys., 2, 1–52, 1905.

https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/33989/31151027498728.pdf?sequence=80&isAllowed=y

[oren]

A bit late response but still thanks for this thread. I recall well the discussions mentioning inertial oscillations, but had a hard time wrapping my head about why exactly it was happening and why it was similar to tidal effects. Now having read it all in one piece I (think I) finally understand.

[uniquorn]

Probable example of anti-clockwise inertial oscillation in the southern hemisphere from finding Endurance episode18

[Tor Bejnar]

Thanks, Uniquorn, I thought this was likely the case.

[uniquorn]

Springtime ice motion in the western Antarctic Peninsula region
Cathleen A. Geiger, Donald K. Perovich
https://www.sciencedirect.com/science/article/abs/pii/S0967064507003062

Abstract
Oscillatory motion of sea-ice is examined using two ice-drifting buoys separated by 1° latitude near 66°S during the winter to spring transition in the Marguerite Bay region west of the Antarctic Peninsula. The buoys’ motions exhibit spectrally distinct periods (12.87±0.04 and 13.03±0.04 h, respectively) despite highly correlated motion between them (r2 is 0.62 and 0.81 for u and v, respectively). The periods shift with latitude and nearly match the local inertial periods (13.00 and 13.10 h, respectively).
 The oscillations are further examined with respect to the kinematics involved in the breakup process of sea-ice. These include hourly resolved manifestations of circular trajectories, semi-circular oscillations with compressed trajectory cusps, and “accordion-like” compressions along straight-line trajectories. Oscillations are found in all trajectory types over the lifetime of both buoys (several months). Traditional circular and semi-circular oscillations are particularly prominent during two episodes, one of which is preceded by strong wind events and a substantial decrease in ice thickness and concentration. These episodes combine with seasonally warming temperatures to break up and melt the sea-ice cover.
 We discuss potential relationships between the degradation of the ice pack during spring breakup and the increase in energy at near-inertial frequencies including the appearance of a non-linear cascade of energy within the ice from the low frequencies (commensurate with storms and fortnightly tides) to semi-diurnal frequencies. We further comment on the implications this type of high-frequency motion has on local biological ecosystems.
 Specifically, we find that sea-ice semi-diurnal oscillations are at their peak during the final decay of sea-ice just before springtime primary productivity begins. Hence, the oscillatory motion of sea-ice not only serves as an effective mixing agent within the ice–ocean mixed layer, but also serves as an effective seeding platform for distributing phyto- and zooplankton overwintering within and around the ice floes.

[uniquorn]

http://www.cleonis.nl/physics/phys256/inertial_oscillations.php
Why the oscillations are called inertial oscillations

Generally, inertial motion is asscociated with uniform motion along a straight line, and the motion depicted in the animation is far from uniform: it's not along a straight line and the velocity isn't constant. But there is another sense of 'inertial motion' that does apply in the case of inertial oscillation. In general, motion is referred to as 'inertial motion' when an accelerometer doesn't register any acceleration. Accelerometers onboard a satelite in orbit do not register acceleration since both the accelerometer casing and the movable parts inside are identically influenced by the Earth's gravitation. Orbital motion is free fall motion, the satellites are falling towards the Earth all the time - but they don't get there because they also have sufficient tangential velocity to overshoot the Earth all the time.

In the case of a buoy or a weather balloon that is moving along with inertial oscillation an onboard accelerometer would not register acceleration in the direction parallel to the local surface. Of course the accelerometer will register the gravitational acceleration that is associated with the local vertical component of the gravitational force; the buoy is supported by its buoyancy, the buoyancy support prevents it from "going with the flow" of the local vertical component of the gravitational acceleration. But the accelerometer won't register an acceleration parallel to the surface. The motion of the object parallel to the surface is motion that is "going with the flow" of gravitational acceleration, and then an accelerometer doesn't register acceleration. This illustrates again that it's useful to think of inertial oscillation as a form of orbital motion.

Picture 15. Animation
Inertial oscillation over the surface of an oblate speroid.
 

[uniquorn]

Enhancing Sea Ice Inertial Oscillations in the Arctic Ocean between 1979 and 2019
Danqi Yuan, Zhanjiu Hao, Jia You, Peiwen Zhang, Baoshu Yin, Qun Li and Zhenhua Xu
https://doi.org/10.3390/w15010152   Published: 30 December 2022

Abstract
As the Arctic Ocean continues to warm, both the extent and thickness of sea ice have dramatically decreased over the past few decades. These changes in ice have an impact on sea ice motion, including sea ice inertial oscillations (SIIO). However, the spatial pattern and temporal variations of Arctic SIIO remain poorly understood. In this study, the spatiotemporal characteristics of Arctic SIIO between 1979 and 2019 are revealed based on the sea ice drifting buoy dataset from the International Arctic Buoy Program (IABP). The results indicate the significant enhancement of SIIO during 1979–2019, with the trend of 7.84 × 10−3 (±3.34 × 10−3) a−1 (a−1 means per year) in summer and 1.92 × 10−3 (±0.80 × 10−3) a−1 in winter. Compared with the first 30 years, the magnitude of SIIO in 2009–2019 increases by 66% in summer and 21% in winter. Spatially, the remarkable enhancement of SIIO during 2009–2019 is found in most of the Arctic Ocean. Especially in summer, SIIO are significantly intensified in marginal seas, including the Beaufort Sea, East Siberian Sea and Laptev Sea, which is mainly correlated with the decrease of sea ice concentration in recent years. This study is anticipated to provide insights for spatiotemporal variation of Arctic sea ice inertial motion in recent decades.

extract:

There are two main hypotheses for the increasing trend of SIIO over the past 41 years: strengthening external forcing and the thinning ice cover. Wind forcing is an important external factor driving sea ice motion. More than 70% of the variances of sea ice motion on the days-to-weeks timescales can be explained by local geostrophic wind [38,39]. Based on the wind data from four atmospheric reanalysis products (including the JRA, ERA-Interim, NCEP and NCEP-2), Spreen et al. [37] discovered that the wind speed in the Arctic Ocean slightly increased during 1992–2009 with a trend of 1–2% per decade. Zhang et al. [25] also drew a similar trend (increasing by 0.9% per decade) of Arctic wind speed during 1979–2019 based on the ERA-5 dataset. Regionally, the increase in wind speed was identified over most of the Arctic Ocean, with the most significant increase in the central Arctic Ocean, where the increasing trend of wind speed can partly account for the increased sea ice drift [37]. However, the changes of SIIO in the central Arctic Ocean are not significant (more details will be displayed in next section). While in other regions, the thinning ice cover is more likely to be the reason for the kinetic ice drift. Observation results from submarine sonars (1958–1976) and satellite sensors (2011–2018) showed that the average thickness of Arctic sea ice has decreased by 2.0 m (or 66%) over the past six decades. During 1999–2017, the multiyear ice also decreased more than 50% [5]. The thinning ice cover implies the decrease in mechanical strength and the increase in ice deformation and fracturing [40]. Consequently, the multi-annual variation of SIIO is mainly associated with the decrease in sea ice thickness.

4. Discussion
The analysis from the IABP buoy dataset shows an enhancement of SIIO in the Arctic Ocean between 1979 and 2019. It should be noted that there is a heterogeneity in the spatial sampling of the IABP buoy dataset. A question arises as to whether the SIIO growth trend obtained in this study can reveal a realistic evolution of SIIO rather than the artificial aliases of the uneven spatial sampling of buoys. Gimbert et al. [29] have discussed this issue and indicated that the increase in M values during 1979–2008 cannot only be caused by the irregular sampling. In addition, the number of buoy data files has dramatically increased after 2008. It is necessary to explore this issue again owing to the extension of the time span of the IABP dataset. The new summer and winter datasets of M during 1979–2019 are constructed under the null hypothesis [29], which supposes a dataset satisfying the following condition: there is no temporal variation, but the spatial sampling of buoys at different locations in different periods will affect the overall trend estimated from this dataset. The construction step is as follows: for any buoy position at a given season, represented by the coordinate (Xj, Yj), all points in a circular region centered (Xj, Yj) and with a radius of 200 km are considered to compute the M0 values based on Equation (9). Figure 8 compares the multi-annual variations and trends of M0 values under the null hypothesis and M values shown in Figure 4. The trend of M0 values for 1979–2019 is 1.14 × 10−3 (±1.61 × 10−3) a−1 in summer and −0.004 × 10−3 (±0.33 × 10−3) a−1 in winter, accounting for 14.5% and −0.2% of the trend of M values in summer and winter, respectively. Consequently, the spatial heterogeneity of buoy sampling is not the reason for the increase in M values derived from the IABP buoy dataset. The increase in M values does indicate that the SIIO have been strengthening in the Arctic Ocean from 1979 to 2019.
  Another problem is the contamination of tidal signals. In the whole Arctic Ocean, the semi-diurnal tidal period is close to the inertial period. Compared with other oceans, Arctic tides are weaker. The barotropic tidal model shows that there is weak tidal activity in the central Arctic Ocean but strong tidal amplitude over the Arctic continental shelves [46,47]. In this study, the data in the areas shorter than 150 km away from the coasts is excluded to avoid some aliases due to tides. However, high-value zones of M¯¯¯¯ near New Siberian Islands are found in both seasons, more remarkably in the winters of 1979–2008 (Figure 6), which may be a joint result of inertial and semi-diurnal tidal oscillations. As mentioned in Section 2.2, the normalized amplitude of the rotary spectrum at the inertial frequency is used to represent the SIIO strength, although it contains the semi-diurnal tidal component. Relatively strong tides near New Siberian Islands probably make us overestimate the magnitude of SIIO in these regions. Two cases of buoy trajectories (ID: 3004, 26 June 1999 to 25 July 1999; ID: 53095, 23 November 2019 to 22 December 2019) are displayed in Figure 9. For both cases, strong SIIO can be identified from the buoy tracks and the spectrum peaks at the inertial frequency f ≈−2 cycles d−1. The semi-diurnal oscillation is evidenced by the peak at f ≈ 2 cycles d−1, whose amplitude is, respectively, 4.41 km d−1 for buoy (ID: 3004) and 8.83 km d−1 for buoy (ID: 53095). It can be seen from Figure 9b,d that although there is an obvious tidal peak, its contribution is far less than that of the near inertial motion, which ensures that the method used in this paper is feasible and reliable.
  In the Arctic Ocean, the presence of sea ice can substantially modulate energy input from the wind to the ocean [48,49]. The insulating effect of sea ice can damp the strength of internal waves generated by winds. With decreasing sea ice in recent decades, several works have discovered the increasing trend of near-inertial energy in the upper Arctic Ocean [50,51]. Furthermore, the complexity of sea ice morphology, especially the existence of ice ridges, directly strengthens the dynamic coupling process between the upper ocean and sea ice [52], thus significantly affecting the upper layer mixing. In global oceans, near-inertial waves and internal tides greatly contribute to diapycnal mixing [53,54,55], resulting in the redistribution of oceanic heat and momentum. Although the change of mixing effects has a direct impact on the Arctic circulation and water mass distribution [56], the effect of rapid sea ice decline on internal wave processes and its mixing effects are still poorly understood. This inspires us to focus on the process under the ice next and understand the interaction between atmosphere, the ice and the ocean based on the existing knowledge of SIIO.

[uniquorn]

Year on Ice Gives Climate  Insights   October  12,1999
https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/EO080i041p00481-01

Inertial  oscillations of the  ice  cover were  common  during summer,  though  for  the  most  part  there  was  little direct  impact  on  ice-ocean energy  exchange, since the  ice  and  mixed  layer oscillated  in  phase. 

[johnm33]

My favoured view of tides is that they are mostly harmonics driven by the repeating distortion of earths crust. Some effects are driven by the co-orbitting of the earth-moon system, that is the moon does not properly 'orbit' the earth but together they sort of stitch their way around the year. In the Arctic they are reactive to the 'sound boxes' of the Nordic seas and Baffin whose delivered pulses do not coincide with the sun/moons positions in any direct way, afaics. So is it possible that inertial oscillations do coincide with sun/moon movements? I guess a reasonable test would be to look at stats from january, when the sun is closest, at a time when the moon is furthest from the equator to see if it exceeds expectations. Or from july at a time when the moon is far south, I'm assuming these are times of peak and trough in terms of tangential pull on the ice, especially if at times of new or full moon respectively.

[uniquorn]

Inertial oscillations in January and July would likely be more affected by thicker/thinner ice and less/more open water than distance of the moon from the equator imho.

[johnm33]

Inertial oscillations in January and July would likely be more affected by thicker/thinner ice and less/more open water than distance of the moon from the equator imho.

Agreed but that's why I chose times when more, and less, movement than ice conditions would suggest may occur. What I forgot was that the suns gravity is so much stronger than the moons and obviously won't be above the horizon in January.

[uniquorn]

Evidence of Abrupt Transitions Between Sea Ice Dynamical Regimes in the East Greenland Marginal Ice Zone
Daniel M. Watkins, Angela C. Bliss, Jennifer K. Hutchings, Monica M. Wilhelmus
First published: 31 July 2023    https://doi.org/10.1029/2023GL103558

Extract:

5 Sub-Daily Sea Ice Variability, Inertial Oscillations, and Tides

We now quantify the apparent tide-like oscillation seen in Figure 1. We select 20-day segments of buoy trajectories from four distinct bathymetric regions: the Nansen Basin (NB), the Yermak Plateau (YP), East Greenland Channel (GC), and East Greenland Shelf (GS) (Figure 4a–4d). Rotary spectra show distinct characteristics, with strong signals in both semi-diurnal and diurnal frequency bands everywhere except the deep Nansen Basin (Figures 4a and 4e) indicating that tidal currents play an important role in sub-daily sea ice velocity variability. In the northern hemisphere, inertial oscillations are clockwise (CW), which manifests as higher spectral power in the CW direction than in the counterclockwise (CCW). The peak in the semidiurnal band for the Nansen Basin trajectories is small but exists in both CW and CCW components. This suggests the possibility of tidal effects on ice motion even in pack ice well away from the shelves. We note as a topic for future research that the east-west velocity component displays a regular semi-diurnal oscillation that is not apparent in the north-south velocity component.

The spread of spectral power across the array (indicated by the shading and dotted lines in Figure 4) is smaller in the NB and YP than in the channel and shelf, reflecting both the coherence expected in pack ice and the area sampled. The CCW semi-diurnal peak is narrow and strong in the GC suggesting a clearer influence of semi-diurnal tides. Over the GS, the diurnal band is no longer distinct, while the semi-diurnal CW band remains strong but increases in spread. Since the shelf region includes a wider range of buoy locations, it is possible that interacting tidal waves and varied bottom topography dilute the tidal signal. Sensor failure and sensor retrieval results in a smaller sample size (26 buoys) representing a region nearly twice as large as the region sampled over the YP, further contributing to the spread in the spectral peak.

The harmonic model assumes that hourly velocity anomalies occur at a limited set of tidal frequencies. When the harmonic model performs well, we interpret that the sub-daily sea ice velocity is consistent with tidal forcing. Tidal constituents are typically estimated from measurements of ocean currents or sea surface height, not sea ice motion; we expect that the additional variability due to imperfect momentum transfer between the surface current and the motion of the ice pack will make the estimate of tidal variability more uncertain. It is therefore notable that we find such strong tidal signals in the ice motion. Implied maximum currents of between 0.1 and 0.2 m/s are seen over the shelf, channel, and plateau, consistent with other tidal current speed estimates (Padman & Erofeeva, 2004; Padman et al., 1992; Vasulkar et al., 2022). These speeds are close to the total drift velocity, hence, tidal currents are likely a major component of ice motion in these regions. For the Yermak Plateau, more than 80% of the sub-daily variance is explained by the tidal currents. The strong change in ocean forcing from the Nansen Basin onto the Yermak Plateau implies a sharp gradient in the ice velocity, inducing deformation. This is confirmed in Figure 1, where we see diurnal oscillation in both divergence and maximum shear that coincides with arrival of the MOSAiC array at the edge of Yermak Plateau.

Inertial oscillations are difficult to differentiate from semi-diurnal tidal variability at high latitudes. Not only are individual semi-diurnal tidal components very close to the inertial period, but tidally generated waves can become inertially trapped. Confidence that the semi-diurnal cycles can be attributed to tides comes from the relatively long 20-day time window used for estimating tidal constituents, and the presence of strong peaks in the CCW band of the rotary spectra. The presence of inertial oscillations in addition to the tidal variability is indicated by the strong CW peaks in the rotary spectra as well as the timing of increases in sub-daily velocity anomalies following brief periods of strong winds, such as occurred on August 15th.

6 Discussion and Conclusion
The MOSAiC ice drift observations capture a broad range of summer ice dynamics in a historically undersampled region. The spatial coverage in our study allows us to document the imprint of differences in ocean forcing on sea ice dynamics across distinct bathymetric regions with unprecedented fidelity. Ice drift has a strong stochastic component due to the interaction of highly variable wind and ocean forcing. The particular path taken by the MOSAiC observatory resulted in a month-long residence over the tidally active Yermak Plateau. Gradients in velocity due to the abrupt transition between the basin and tidally active plateau impose strain on the ice, enhancing deformation. Subsequent low wind speeds, decreasing ice concentration, and the proximity of boundary currents resulted in ocean currents dominating the drift through the Fram Strait. Following transit through the Fram Strait, intermittent high drift speed events result from strong wind events, and both tides and inertial oscillations affect the subdaily drift velocities. Low ice concentration late in the summer resulted in the MOSAiC observatory being more sensitive to changes in atmosphere and ocean forcing, unconstrained by internal ice stresses.

Our results emphasize the importance of small-scale, sub-daily motion for ice dynamics (Heil et al., 2008; Itkin et al., 2017). We show that a substantial fraction of observed sea ice velocity at hourly timescales occurs at tidal and inertial frequencies. Characteristics of this variability are distinct within regions defined by bathymetry. Uncertainty in bathymetry combined with sparsely located tide gauges means that tides are poorly constrained throughout the shallow Arctic marginal seas. Models of sea ice drift that fail to take mesoscale ocean variability and tides into account will systematically underestimate drift variability and deformation. The range of dynamical regimes captured during the MOSAiC drift provides a challenging test case for next-generation, tide-resolving coupled sea ice models.

My emphasis

[uniquorn]

Sea Ice Stories
Forecasting ICE DRIFT: inertial oscillations