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A Method of Separating Linear Internal Wave and Vortical Mode Energies Using Shipboard ADCP Velocity Measurements.

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Title: A Method of Separating Linear Internal Wave and Vortical Mode Energies Using Shipboard ADCP Velocity Measurements.
Authors: VLADOIU, ANDA1 avladoiu@apl.uw.edu, LIEN, REN-CHIEH1
Source: Journal of Atmospheric & Oceanic Technology. Jan2026, Vol. 43 Issue 1, p61-75. 15p.
Subjects: Internal waves, Acoustic Doppler current profiler, Potential energy, Helmholtz equation, Kinetic energy, Rotational flow, Oceanography
Abstract: We present a method to quantify total, horizontal kinetic and available potential energies of linear internal waves (IWs) and vortical mode (VM) using only two-dimensional (2D) (depth, along-track distance) measurements of horizontal velocity, such as those commonly taken by oceanic shipboard ADCP (SADCP). Previous IW and VM energy decomposition methods (Bühler et al., and their extensions) require both velocity and buoyancy measurements. Applying Helmholtz decomposition, 2D horizontal kinetic energy wavenumber (kx, kz) spectra are projected onto divergent Kdiv and rotational Krot components. IWtotal energy spectrum is EIW 5 2Kdiv. VM total energy is EVM 5 1/Bu[(1 1 Bu)Krot 2 Kdiv], where Bu 5 (N2k2 h)/(f 2k2z) is Burger number with N and f the buoyancy and inertial frequencies, kh the horizontal wavenumber magnitude, and kz the vertical wavenumber. IW and VM horizontal kinetic energy (K) and available potential energy (P) can be inferred from EVM and EIW as functions of Bu. The proposed method, derived directly from IW and VM theoretical polarization relations, is demonstrated using two sets of velocity and density data. The EVM derived by this new method agrees with results computed using the 2014 and 2017 Bühler et al. methods at Bu; O(1) and within a factor of; 2-3 elsewhere, confirming that IW and VM energy can be separated using only velocity data. At Bu, O(0.1), EVM is dominated by PVM, with KVM/PVM 5 Bu, and using K alone to extract EVM through the proposed method is challenging due to inherent uncertainty in spectral measurements. This method could be applied to global SADCP datasets to separate upper-ocean IW and VM energy contributions in different dynamical regions at horizontal scales O(100) m-O(100) km and vertical scales O(10)-O(100) m. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Atmospheric & Oceanic Technology is the property of American Meteorological Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: A Method of Separating Linear Internal Wave and Vortical Mode Energies Using Shipboard ADCP Velocity Measurements.
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  Data: <searchLink fieldCode="AR" term="%22VLADOIU%2C+ANDA%22">VLADOIU, ANDA</searchLink><relatesTo>1</relatesTo><i> avladoiu@apl.uw.edu</i><br /><searchLink fieldCode="AR" term="%22LIEN%2C+REN-CHIEH%22">LIEN, REN-CHIEH</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Atmospheric+%26+Oceanic+Technology%22">Journal of Atmospheric & Oceanic Technology</searchLink>. Jan2026, Vol. 43 Issue 1, p61-75. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Internal+waves%22">Internal waves</searchLink><br /><searchLink fieldCode="DE" term="%22Acoustic+Doppler+current+profiler%22">Acoustic Doppler current profiler</searchLink><br /><searchLink fieldCode="DE" term="%22Potential+energy%22">Potential energy</searchLink><br /><searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Kinetic+energy%22">Kinetic energy</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+flow%22">Rotational flow</searchLink><br /><searchLink fieldCode="DE" term="%22Oceanography%22">Oceanography</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We present a method to quantify total, horizontal kinetic and available potential energies of linear internal waves (IWs) and vortical mode (VM) using only two-dimensional (2D) (depth, along-track distance) measurements of horizontal velocity, such as those commonly taken by oceanic shipboard ADCP (SADCP). Previous IW and VM energy decomposition methods (Bühler et al., and their extensions) require both velocity and buoyancy measurements. Applying Helmholtz decomposition, 2D horizontal kinetic energy wavenumber (kx, kz) spectra are projected onto divergent Kdiv and rotational Krot components. IWtotal energy spectrum is EIW 5 2Kdiv. VM total energy is EVM 5 1/Bu[(1 1 Bu)Krot 2 Kdiv], where Bu 5 (N2k2 h)/(f 2k2z) is Burger number with N and f the buoyancy and inertial frequencies, kh the horizontal wavenumber magnitude, and kz the vertical wavenumber. IW and VM horizontal kinetic energy (K) and available potential energy (P) can be inferred from EVM and EIW as functions of Bu. The proposed method, derived directly from IW and VM theoretical polarization relations, is demonstrated using two sets of velocity and density data. The EVM derived by this new method agrees with results computed using the 2014 and 2017 Bühler et al. methods at Bu; O(1) and within a factor of; 2-3 elsewhere, confirming that IW and VM energy can be separated using only velocity data. At Bu, O(0.1), EVM is dominated by PVM, with KVM/PVM 5 Bu, and using K alone to extract EVM through the proposed method is challenging due to inherent uncertainty in spectral measurements. This method could be applied to global SADCP datasets to separate upper-ocean IW and VM energy contributions in different dynamical regions at horizontal scales O(100) m-O(100) km and vertical scales O(10)-O(100) m. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Atmospheric & Oceanic Technology is the property of American Meteorological Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1175/JTECH-D-25-0076.1
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 61
    Subjects:
      – SubjectFull: Internal waves
        Type: general
      – SubjectFull: Acoustic Doppler current profiler
        Type: general
      – SubjectFull: Potential energy
        Type: general
      – SubjectFull: Helmholtz equation
        Type: general
      – SubjectFull: Kinetic energy
        Type: general
      – SubjectFull: Rotational flow
        Type: general
      – SubjectFull: Oceanography
        Type: general
    Titles:
      – TitleFull: A Method of Separating Linear Internal Wave and Vortical Mode Energies Using Shipboard ADCP Velocity Measurements.
        Type: main
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            NameFull: VLADOIU, ANDA
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            NameFull: LIEN, REN-CHIEH
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            – D: 01
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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              Value: 43
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            – TitleFull: Journal of Atmospheric & Oceanic Technology
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