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 (kappa 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 pi/kappa(0)), and a dissipation range. Turbulence was advected by a background flow composed of waves (rms orbital velocity sigma(w), peak frequency omega(w), and spectral width Delta omega(w)) propagating parallel to a current u(c). Expressions were derived for turbulence frequency spectra (omega spectra), and parameters were varied across ranges typical in the coastal ocean. Except close to the wave band, the v-spectrum shape collapses with two dimensionless parameters, a velocity ratio sigma(w)/u(c), and a time-scale ratio u(c)kappa(0)/omega(w), which can be used to diagnose the effects of wave advection on turbulence spectra. As sw/uc increases, less variance and covariance appear at low frequencies (omega < u(c)kappa(0)) and more appear at high frequencies (omega > u(c)kappa(0)). If sigma(w)/u(c) > 2, wave advectionmust 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 omega spectra beneath waves and guide the estimation of turbulence properties from those spectra.