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

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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 ( k x , k z ) spectra are projected onto divergent K div and rotational K rot components. IW total energy spectrum is E IW = 2 K div . VM total energy is E VM = 1/Bu[(1 + Bu) K rot − K div ], where is Burger number with N and f the buoyancy and inertial frequencies, k h the horizontal wavenumber magnitude, and k z the vertical wavenumber. IW and VM horizontal kinetic energy ( K ) and available potential energy ( P ) can be inferred from E VM and E IW 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 E VM 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), E VM is dominated by P VM , with K VM / P VM = Bu, and using K alone to extract E VM 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.

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