Rotation of the velocity measurements: Difference between revisions

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To estimate <math>\varepsilon</math> from all the different velocity components, the measurements must be rotated into the main direction of the flow. In some instances, the instrument's [[frame of reference]]  may be aligned with the direction of flow, which is ideal to account for the varying levels of [[Velocity inertial subrange model#anisotropy|anisotropy]]  amongst components <ref name="Gargett.etal1984">{{Cite journal
|authors= A. E. Gargett, T. R. Osborn, and P.W. Nasmyth
|journal_or_publisher= J. Fluid. Mech.
|paper_or_booktitle=  Local isotropy and the decay of turbulence in a stratified fluid
|year= 1984
|doi=10.1017/S0022112084001592
}}</ref><ref name="Bluteau.etal2011">{{Cite journal
|authors= C.E. Bluteau, N.L. Jones, and G. Ivey
|journal_or_publisher=  Limnol. Oceanogr.: Methods
|paper_or_booktitle= Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows
|year= 2011
|doi=10:4319/lom.2011.9.302
}}</ref>. If this isn't the case, then the velocities' measurement frame must be rotated into that of the flow, which we refer to as the analysis frame of reference.


The velocities are measured in either the instrument's coordinate system (XYZ), beam coordinates, or more rarely in the earth's coordinate system (ENU=east, north and up). When estimating <math>\varepsilon</math>, measured velocities are often rotated in the flow's frame of reference since  [[Velocity inertial subrange model|inertial subrange model]] differs between the velocity components, and the effects of [[Anisotropic turbulence|anisotropy]] are more pronounced in the transverse and vertical direction. When the vertical velocities are too heavily impacted by [[Anisotropic turbulence|anisotropy]], the longitudinal direction may be used to derive <math>\varepsilon</math>.  In these instances, the longitudinal velocity must  align with the mean flow direction, which may require rotating the measurements into a new frame of reference i.e., the analysis frame of reference.
= Methods used for rotating into the analysis frame of reference=


* Using time-averaged velocities in each segment
* Principal component analysis


In some setups, the instrument's x-axis is already aligned with the general direction of the mean flow. This is particularly desirable when planning on calculating turbulent shear stresses via covariances as correlated noise may ensue when rotating the measurements into a new frame of reference ({{FontColor|fg=red|text=Insert reference}}). For some shallow systems, it's possible to align an instrument's x-axis with the direction of the flow (see Fig 1b). Alternatively, the entire dataset  may be rotated using the velocities' principal components over the entire timeseries. For instance, the Tidal Slough example (Fig 1a) flows generally along the channel's length except at the turn of the tide. In other datasets, like the Tidal Shelf, it's necessary to rotate each segment into the flow's direction.


==Recommendations==
{{FontColor|fg=white|bg=red|text=We will update when our final recommendation is set in stone. Also, comment about large vertical velocities on sloped bottoms... The page is too wordy}}


[[File:Frame of reference adv.png|800px|frame|Fig 1. Examples of measured velocities from two ADVs highlighting that their x-axis may be un-aligned with the flow's. The blue dots and lines that represent the principal axes are for a 5-min subset of the entire timeseries shown in red. The left example (a) is from the shelf break in ~190 m of water, while the right example (b) is from a tidally-influenced slough (a few meters deep). The statistics in each panel were estimated for the entire timeseries, and highlights that the flow's frame of reference is much more variable in the Tidal shelf example (a) than the Tidal Slough (b). Another key difference is that in the slough example (b), the instrument's x-axis was oriented along the length of the channel, and thus in the general direction of the flow. This is the ideal set-up for turbulence measurements from acoustic-Doppler velocity-meters.]]
If one intends on using only the vertical velocity component to estimate <math>\varepsilon</math>, then the rotation of the velocity measurements into a new frame of reference may be skipped. The analysis frame of reference is thus the same as the measurement frame provided one direction is aligned with gravity.


= Methods to rotate=
{{FontColor|fg=white|bg=red|text=If not, then which strategy is best ? I think all are OK}}
==References==
<references />
 
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Return to [[Preparing quality-controlled velocities]]

Latest revision as of 18:54, 5 July 2022


To estimate [math]\displaystyle{ \varepsilon }[/math] from all the different velocity components, the measurements must be rotated into the main direction of the flow. In some instances, the instrument's frame of reference may be aligned with the direction of flow, which is ideal to account for the varying levels of anisotropy amongst components [1][2]. If this isn't the case, then the velocities' measurement frame must be rotated into that of the flow, which we refer to as the analysis frame of reference.

Methods used for rotating into the analysis frame of reference

  • Using time-averaged velocities in each segment
  • Principal component analysis


Recommendations

We will update when our final recommendation is set in stone. Also, comment about large vertical velocities on sloped bottoms... The page is too wordy

If one intends on using only the vertical velocity component to estimate [math]\displaystyle{ \varepsilon }[/math], then the rotation of the velocity measurements into a new frame of reference may be skipped. The analysis frame of reference is thus the same as the measurement frame provided one direction is aligned with gravity.

If not, then which strategy is best ? I think all are OK

References

  1. ↑ A. E. Gargett, T. R. Osborn and and P.W. Nasmyth. 1984. Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid. Mech.. doi:10.1017/S0022112084001592
  2. ↑ C.E. Bluteau, N.L. Jones and and G. Ivey. 2011. Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows. Limnol. Oceanogr.: Methods. doi:10:4319/lom.2011.9.302

Return to Preparing quality-controlled velocities

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