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uniquorn

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Inertial oscillations
« on: July 24, 2021, 11:12:48 AM »
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

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Re: Inertial oscillations
« Reply #1 on: July 24, 2021, 11:17:18 AM »
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

Quote
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.

Quote
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.

« Last Edit: July 24, 2021, 07:25:21 PM by uniquorn »

uniquorn

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Re: Inertial oscillations
« Reply #2 on: July 24, 2021, 11:24:38 AM »
rammb of the restless sea beneath the centre of high pressure today.  9.5MB
https://col.st/nuZix

uniquorn

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Re: Inertial oscillations
« Reply #3 on: July 24, 2021, 01:20:00 PM »
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

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Re: Inertial oscillations
« Reply #4 on: July 24, 2021, 01:36:40 PM »
http://oceanmotion.org/html/resources/coriolis.htm

Quote
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

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Re: Inertial oscillations
« Reply #5 on: July 24, 2021, 11:59:24 PM »
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

Quote
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?

Quote
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

« Last Edit: July 25, 2021, 01:48:16 AM by uniquorn »

Tor Bejnar

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Re: Inertial oscillations
« Reply #6 on: July 25, 2021, 01:57:03 AM »
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.)
Arctic ice is healthy for children and other living things.

kassy

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Re: Inertial oscillations
« Reply #7 on: July 30, 2021, 10:38:03 PM »
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.
Þetta minnismerki er til vitnis um að við vitum hvað er að gerast og hvað þarf að gera. Aðeins þú veist hvort við gerðum eitthvað.

uniquorn

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Re: Inertial oscillations
« Reply #8 on: August 07, 2021, 04:54:23 PM »
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
Quote
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

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Re: Inertial oscillations
« Reply #9 on: August 07, 2021, 05:19:11 PM »
Quote
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

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Re: Inertial oscillations
« Reply #10 on: September 13, 2021, 04:21:44 AM »
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.