Project Name TO EDIT....

Project (long title)Wind stress resonance and deep ocean energy transfer - laboratory experiments
Campaign Title (name data folder)16ResEk
Lead AuthorYosef Ashkenazy
ContributorJoel Sommeria, Samuel Viboud, Miklos Vincze, Nora Fenyvesi, Pierre Augier
Date Campaign Start07/11/2016
Date Campaign End25/11/2016

0 - Publications, reports from the project

1 - Objectives

Turbulent mixing in the deep ocean is an essential process to maintains the deep ocean circulation -- without it the abyssal ocean would have been stagnant -- yet, the key aspects of its actual underlying dynamics are far from being understood. There are two main comparable sources of deep ocean energy, winds and tides. These increase the vertical mixing by several orders of magnitudes, maintaining the meridional overturning circulation. There are additional sources of energy to the deep ocean and the common feature for the different energy sources of the abyssal ocean is the large uncertainties associated with them.

According to the seminal paper of Ekman [1905] wind induced currents are restricted to the upper ocean (first hundred meters or so) and decay exponentially with depth. However, this model is based on the simplistic assumption that the winds are constant, both in space and time. In fact, winds are stochastic by nature and vary on a wide range of temporal and spatial scales. They can generate internal waves, instabilities, and eddies, that eventually radiate into the abyssal ocean. Thus, although the Ekman layer model provides the basic understanding on the effect of the Coriolis force on surface currents, it is clear that additional processes that are related to the wind have to be taken into account.

Winds are sometimes periodic. As such, when their frequency matches the inertial (Coriolis) frequency, they can resonate with the currents induced by them. Resonance conditions are satisfied when the winds at 30 degree latitude have diurnal frequency, when the characteristic frequency of a storm matches the Coriolis frequency, or when the tides' frequency matches the Coriolis frequency. In addition, stochastic wind that has temporal correlations can lead to enhanced currents, depending on the strength of the correlation. Recently we have investigated the effect of the resonance of the wind with the Coriolis force on ocean currents and, in particular, on the abyssal ocean kinetic energy (KE). We carried out oceanic General Circulation Model (GCM) simulations and provided analytic solutions and approximations for the currents as a function of depth for a finite depth ocean under the action of periodic and stochastic wind that exhibits temporal correlations. We showed that in both cases the wind induced currents are significant in the deep ocean and contribute significant KE to the abyssal ocean.

The goal of the proposed lab experiments is to verify the validity of the theory of the Ekman resonance reported by previous studies and by Ashkenazy et al (2015) and Ashkenazy (2015) are applicable to real water flow. Part of the main concerns regarding the analytic and numerical results of the effect of periodic and stochastically correlated wind stress is the choice of the viscosity coefficient. In the numerical model and the analytic approximation a constant eddy parameterized viscosity coefficient was assumed. This is obviously not accurate assumption as the vertical viscosity coefficient may depend on may factors including the local eddy activity and the local stratification which lead to large variations of the viscosity coefficient both horizontally and vertically. In addition, other effects like the boundary friction were ignored in our previous analytic and numerical studies. Thus, the proposed lab experiment will strengthen significantly the applicability of the theory to real ocean dynamics in general and to deep ocean circulation in particular.

The usage of such a large platform is justified by the fact that the effect of the lateral boundary layers and the curvetrure of a smaller tank can markedly modify the flow (as observed in our preliminary experiments that utilized a tabletop-size rotating laboratory tank at the Eotvos University, Budapest). Also the fact that investigation involving a horizontally oscillating top top lid are possible at the CORIOLIS platform makes it the perfect facility to study the resnance effect which -- besides its aformentioned importance for oceanography -- can also be thought of as a natural extension of the earlier investigations of Ekman layer turbuence, initiated by spinning up and spinning down the very same laboratory tank, as reported by Sous, Sommeria, and Boyer (2013).

Based on the previous studies in the tank, we intend to focus on the velocity fields ca. 1 m away from the outer wall of the tank, where the lateral sidewall effects were found to be negligible. We intend to utilize wide field Particle Image Velocimetry (PIV) to observe velocity decay rates after spin-up. Theoretically (as shown by Ashkenazy, Gildor and Bel (2015)), in the presence of the aforementioned resonant libration, the Ekman layer `explodes' (i.e. invades the total water depth, whereas typically its thickness is of the order of few millimeters) which would largely increase the velocity decay rates, meaning that the system reaches solid body rotation faster.Besides the large-scale observation of this transient phenomenon, we would also utilize stereo-PIV to obtaim small scale mean and fluctuation velocity components, to determine e.g. the changes of the cross isobar angle (45 degrees in the classic laminar Ekman theory and half that large for turbulent Ekman layers) and thus the development of the Ekman spiral at various depth levels.


2 - Experimental setup:

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2.1 General description

3 - Instrumentation and data acquisition

3.1 Instruments



4 - Methods of calibration and data processing

5 - Organization of data files

All data related to the project are in: \\SERVAUTH4\share\project\coriolis\2016 or \\\share\project\coriolis\2016

  • 0_DOC: miscellaneous documentation and reports
  • 0_MATLAB_FCT: specific matlab functions
  • 0_PHOTOS: photos of set-up
  • 0_PIV
    • Each ‘PIV’ folder contains subfolders for each of the 3 PIV cameras: Dalsa (sometimes Falcon1 – it’s the same thing); PCO2; PCO3 [these are named after the different brands of camera]. Other folders include PCO2.png and PCO3.png which contain processes images of the PCO cameras that are in a non-bespoke format. Other folders that can be within the Camera folder include: Dalsa.sback; Dalsa.sback_1; PCO2.png.civ; PCO2.png.civ_1; PCO2.png.civ_2; PCO2.png.sback: PCO2.png.sback_1; PCO3.png.sback_1. .sback files refer to those files where the background has been subtracted, then civ_1 contains images with the first PIV iteration as processed in UVMAT (Joel’s code) and shows the raw data – with or without the rejected vectors; vectors are shown in four colours, blue = best, green = medium, red = poor, and pink = false. A box can be clicked to hide the false vectors. Civ_2 uses a spline interpretation to interpolate between vectors, so long as they are close enough to the surrounding vectors. Then interpolates all the vectors onto a regular grid. Times for the .png images are in the XML files, or netcdf files.
  • 0_Processing: UVP processing scripts in Matlab
  • 0_REF_FILES: files of general use (calibration data, grids ...)
  • EXP1, EXP2, folder for each experiment with names given in the table below. The names refer to ‘fix’ for non-rotating fixed case, ‘rot’ for rotating case, ‘str1’ for the first straight position (also called position X1), and ‘apex 2’ , for the apex in bend 2 (also referred to as position X4).
    • Within each experiments, there is a folder with PIV imagery called ‘Camera’, one for ADV data – ‘ADV’, one for UVP data – ‘UVP’, and one for the data coming directly off of the Coriolis table control system ‘LABVIEW’. Some experiments also contain an ‘Images’ folder or a ‘Gopro folder’ containing Gopro videos.
      • Each ‘Camera’ subfolder contains subfolders for each of the 3 PIV cameras: Dalsa (sometimes Falcon1 – it’s the same thing); PCO2; PCO3 [these are named after the different brands of camera]. Other folders include PCO2.png and PCO3.png which contain processes images of the PCO cameras, that are in a non-bespoke format. Other folders that can be within the Camera folder include: Dalsa.sback; Dalsa.sback_1; PCO2.png.civ; PCO2.png.civ_1; PCO2.png.civ_2; PCO2.png.sback: PCO2.png.sback_1; PCO3.png.sback_1
      • Each ‘ADV’ subfolder, contains two sub-folders: ‘nkt_files’ containing raw Nortek files, and the ‘mat_files’ are the exported raw data in Matlab format.
      • Each ‘UVP’ subfolder contains two folders – one with the experiment name (which is the downstream velocity data) recorded downstream of the velocity inflection downstream of bend apex 2, and one with experiment name ‘_cross’ which contains the cross-stream UVP data recorded at bend apex ‘2. These two folders contain text files for each of the probes. The convention is that Probe 1 is the basal probe, with each subsequent probe being successively higher. There are also .mfprof files which are the raw UVP data in native format. All probes are also integrated into single Matlab files. Lastly, there is a Logfile with the header file for the UVP detailing all of the parameters used in the run.
      • Each ‘LABVIEW’ subfolder contains: 1) a .lvm file which is a text file and contains a time-stamp, two voltages for the Conductivity probe on the traverse (C0 – Conductivity, and T0 – temperature [this latter one doesn’t work]), a Trig_cam heading representing the Trigger for the PIV Cameras, Conductivity probe in the input box (C1 and T1), and C2 (this was conductivity for a second probe in the input box which was briefly used before breaking. There is always a record for this but it is just background noise. 2) _position.lvm file which is an XYZ file with a times for the movement of the traverse. 3)Some folders also contain files. These are netcdf files and contain the vector data from the processed PIV images.

6 - Table of Experiments:

No stratification, periodic forcing.
Experiment NameVelocity amplitude [cm/s]Forcing frequency $\omega$ [rad/s]Correlation exponent $\gamma$ (for "noisy" runs)Rotation Rate $\Omega$ [rad/s]Remarks
Exp0150.4188n.a.0.2094Too many tracers on top
Exp0250.4188n.a.0.2094Too few tracers on top
Exp032.50.4188n.a.0.2094Looks laminar
Exp0450.4188n.a.0.2094repetition of Exp01/02. Tracers are OK this time.
Exp0550.28n.a.0.2094Out of resonance, very weak flow.
Exp0650.56n.a.0.2094Out of resonance, very weak flow. Imges are missing from PCO2 (disk full, restart).
Exp0750.44n.a.0.2094Closer to resonance, apparently.
Exp0850.43n.a.0.2094Closer to resonance, apparently.
Exp0950.41n.a.0.2094Closer to resonance, apparently.
Exp103.750.4188n.a.0.2094Testing the effect of amplitude at resonance, I.
Exp11100.4188n.a.0.2094Testing the effect of amplitude at resonance, II.
Exp12200.4188n.a.0.2094Testing the effect of amplitude at resonance, III.
Exp13150.4188n.a.0.2094Testing the effect of amplitude at resonance, IV.
Exp147.50.4188n.a.0.2094Testing the effect of amplitude at resonance, V.
Exp152.50.41n.a.0.2094Testing the combined effect of amplitude and frequency.
Exp162.50.43n.a.0.2094Testing the combined effect of amplitude and frequency.
Exp175n.a.0.41880.2094Noise-like lid forcing.
Exp187.5n.a.0.41880.2094Noise-like lid forcing.
Exp192.5n.a.0.41880.2094Noise-like lid forcing ("laminar" amplitude).
Exp205n.a.0.41880.2094Noise-like lid forcing LONG run (3000 s), repetition.
Exp215n.a.0.840.2094Noise-like lid forcing, large $\gamma$, LONG run (3000 s).
Exp222.50.4188n.a.0.2094Stratified ($N=0.6$ rad/s), periodic.
Exp2350.4188n.a.0.2094Stratified ($N=0.6$ rad/s), periodic.
Exp2450.6n.a.0.2094Stratified ($N=0.6$ rad/s), periodic, $\omega\approx N$
PCO1 stopped at i=2599
PCO2 stopped at i=2603
Exp255n.a.0.41880.2094Stratified ($N=0.6$ rad/s), stochastic.
Exp2650.4-0.6 (ramp)n.a.0.2094Stratified ($N=0.6$ rad/s), periodic, temporally changing $\omega$. Long run (3000 s).
Exp27100.4-0.6 (ramp)n.a.0.2094Stratified ($N=0.6$ rad/s), periodic, temporally changing $\omega$. Long run (3000 s).
Exp285n.a.0.41880.2094Stratified ($N=0.6$ rad/s), stochastic, repetition. Long run (3000 s).
PCO2 stopped at i=5361 (instead of 6000)
Exp29100.6n.a.0.2094Stratified ($N=0.6$ rad/s), periodic, $\omega\approx N$.
Exp30200.6n.a.0.2094Stratified ($N=0.6$ rad/s), periodic at resonance, extremely large amplitude.
Exp315RAMP 0.3-1n.a.0.2094long run (6000s). PCO2 in two parts _1 (beginning), and _2 (end), PCO2 is missing from the middle
Exp325RAMP back. 1-0.3n.a.0.2094long run (6000s)
Exp3350.4188n.a.0.2094TOP VIEW, 1500s,(9 levels, 9 volumes, 100 image/level) $\omega=f$
Exp3450.8376n.a.0.2094TOP VIEW, 1500s, (9 levels, 9 volumes, 100 image/level), $\omega=2 f$
Exp3550.6282n.a.0.2094TOP VIEW, 1500s, (9 levels, 9 volumes, 100 image/level), $\omega=1.5 f$
Exp362.50.4188n.a.0.2094TOP VIEW, 3000s,(9 levels, 9 volumes, 100 image/level) $\omega=f$
Exp373.750.4188n.a.0.2094TOP VIEW, 3000s,(9 levels, 9 volumes, 100 image/level) $\omega=f$
Exp38100.4188n.a.0.2094TOP VIEW, 1500s,(9 levels, 9 volumes, 100 image/level) $\omega=f$
Exp39200.4188n.a.0.2094TOP VIEW, 1500s,(9 levels, 9 volumes, 100 image/level) $\omega=f$
Exp405n.a.0.41880.2094Extremely long, overnight NOISY experiment, top view.
Exp417.5n.a.n.a.0.20945h+1/2h relax, top view.
Exp422.50.4188n.a.0.209410h+1/2h relax,NOISY, top view.
Exp442.50.4188n.a.0.20943500s, top view.
Exp4550.4188n.a.0.20943500s, top view.
Exp465RAMP 0.3-1n.a.0.20946300s, top view.
Exp475RAMP back 1-0.3n.a.0.20946300s, top view.
Exp4850.4188n.a.0.209410h, NOISY, top view.

7 - Diary:

Tuesday, November 8th 2016

We conducted three preliminary experiments, to check the instrumentation and get a general impression of what is happening. We set the system to the resonance condition (i.e. oscillation frequency = 2*Omega), and we used vertical laser sheet at the middle of the tank for the PIV. We have two cameras pointing perpendicularly to the laser sheet. One with a 15 cm x 15 cm field of view, and another with a larger 35 cm x 35 cm field of view. The two fields of view overlap a bit.

(To compare: the thickness of the normal, stationary Ekman layer in the setup is about a few millimeters and the whole water depth D = 50 cm) We conducted these preliminary runs each of which lasted for 100 periods of the oscillation (i.e. 1500 s).

1st run (code: Exp01).: $\Omega$ = 2 RPM = 0.21 rad/s (corresponding to period $T$ = 30 s), forcing freq.: $\omega$ = $f$ = 0.42 rad/s. Velocity amplitude: $U_0$ = 5 cm/s, yielding $U(t) = U_0 \sin(\omega t)$. Here we could not really observe the top, because too many PIV tracers were dissolved in teh system and the view was "foggy".

2nd run (code: Exp02).: Same as above, a bit later. Now the situation was just the opposite - not enough tracers in the field of view, but the data can be used. However, we could detect a certain vibration of the camera (in the vertical direction mostly). This may be to the vibration of the camera mast itself. Later this has been fixed (as much as possible. Some vibration is of course unavoidable, but can be easily compensated later during the data processing.)

3rd run (code: Exp03).: We are not sure about the oscillating Ekman layers, but for a stationary Ekman layer (with the parameters of the setup) at $U_0$ = 5 cm/s the boundary layer would already be turbulent. So just to be sure that the effect is visible in a laminar Ekman layer as well, we did this third experiment with exactly the same parameters as above BUT with half the velocity amplitude: $U_0$ = 2.5 cm/s.

This time the distribution of the PIV tracers was perfect. What is visible (in all experiments) is that in a certain layer below the lid the flow moves in the same direction as the lid, but with a certain phase lag that seems to depend on the depth. There is a certain level below the lid (ca. 7-10 cm below) where the flow is already in counterphase with the lid. (Lid moves left, deep particles move right, and vice versa.) And there seems to be a level, separating the two regions, where the horizontal flow (in the laser plane) is minimum, around zero.

Wednesday, November 9th 2016

4th run (code: Exp04).: This was a repetition of Exp01/02. This time the PIV tracers were properly distributed.

5th run (code: Exp05).: We have decided to check the flow far from the resonance to obtain a baseline. Therefore this experiment was done at $\omega = 0.28$ rad/s, i.e. ca. 0.66$f$.

6th run (code: Exp06).: Still far from the resonance, but this time at a higher forcing frequency, i.e. $\omega = 0.56$ rad/s, i.e. ca. 1.33$f$. During this experiment there was a technical glitch. The disk that is meant tos atore the data for the wide-field camera (PCO2) has become full. The problem was solved by the end of the run, but still, a certain section is missing. Therefore, we have a "PCO2_beginning" folder alongside the regular "PCO2" folder here.

7th run (code: Exp07).: Zooming in to the resonance peak. $\omega = 0.44$ rad/s ($\approx 1.05 f$)

8th run (code: Exp08).: Zooming in to the resonance peak. $\omega = 0.43$ rad/s ($\approx 1.027 f$)

9th run (code: Exp09).: Zooming in to the resonance peak. $\omega = 0.41$ rad/s ($\approx 0.98 f$)

10th run (code: Exp10).: Checking amplitude-dependence. $U_0 = 3.75$ cm/s $\omega = 0.4188$ rad/s (resonance).

11th run (code: Exp11).: Checking amplitude-dependence. $U_0 = 10$ cm/s $\omega = 0.4188$ rad/s (resonance).

12th run (code: Exp12).: Checking amplitude-dependence. $U_0 = 20$ cm/s $\omega = 0.4188$ rad/s (resonance).

Monday, November 14th 2016

13th run (code: Exp13).: Checking amplitude-dependence. $U_0 = 15$ cm/s $\omega = 0.4188$ rad/s (resonance).

14th run (code: Exp14).: Checking amplitude-dependence. $U_0 = 7.5$ cm/s $\omega = 0.4188$ rad/s (resonance).

15th run (code: Exp15).: Checking amplitude- and frequency dependence, simultaneously. $U_0 = 2.5$ cm/s $\omega = 0.41$ rad/s ($\approx 0.98 f$).

16th run (code: Exp16).: Checking amplitude- and frequency dependence, simultaneously. $U_0 = 2.5$ cm/s $\omega = 0.43$ rad/s ($\approx 1.027 f$).

17th run (code: Exp17).: First run with "noisy" forcing. $U_0 = 5$ cm/s, $\gamma = f$.

Tuesday, November 15th 2016

18th run (code: Exp18).: Second run with "noisy" forcing. $U_0 = 7.5$ cm/s, $\gamma = f$.

19th run (code: Exp19).: Second run with "noisy" forcing. $U_0 = 2.5$ cm/s, $\gamma = f$.