Interpreting Fixed-Location Observations of Turbulence Advected by Waves: Insights from Spectral Models

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 = 2 π / κ 0 ), and a dissipation range. Turbulence was advected by a background flow composed of waves (rms orbital velocity σ w , peak frequency ω w , and spectral width Δ ω w ) propagating parallel to a current u c . 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 σ w / u c , and a time-scale ratio u c κ 0 / ω w , which can be used to diagnose the effects of wave advection on turbulence spectra. As σ w / u c increases, less variance and covariance appear at low frequencies ( ω < u c κ 0 ) and more appear at high frequencies ( ω > u c κ 0 ). If σ w / u c > 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.