Abstract
Assigning a physical interpretation to turbulent fluctuations beneath waves is complex because eddies are advected by unsteady wave orbital motion. Here, the kinematic effects of wave orbital motion on turbulent fluctuations at a fixed location were investigated using model turbulence spatial spectra (κ spectra) together with a general form of the frozen turbulence approximation. Model autospectra and cospectra included an inertial subrange, a rolloff at energy-containing scales (L = 2π/κ0), and a dissipation range. Turbulence was advected by a background flow composed of waves (rms orbital velocity σw, peak frequency ωw, and spectral width Δωw) propagating parallel to a current uc. Expressions were derived for turbulence frequency spectra (ω spectra), and parameters were varied across ranges typical in the coastal ocean. Except close to the wave band, the ω-spectrum shape collapses with two dimensionless parameters, a velocity ratio σw/uc, and a time-scale ratio ucκ0/ωw, which can be used to diagnose the effects of wave advection on turbulence spectra. As σw/uc increases, less variance and covariance appear at low frequencies (ω < ucκ0) and more appear at high frequencies (ω > ucκ0). If σw/uc > 2, wave advection must be taken into account when estimating turbulence length scales and integral quantities (e.g., Reynolds stress) from the low-frequency portion of spectra. The offset of the −5/3 region due to waves is unaffected by the rolloff or dissipation range; therefore, previously proposed methods for estimating dissipation rate from wave-affected −5/3 spectra are robust. Although idealized, the results inform the interpretation of turbulence ω spectra beneath waves and guide the estimation of turbulence properties from those spectra.
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