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

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.

Turbulence from Breaking Surface Waves at a River Mouth

“…The key simplification is the assumption that the TKE dissipation rate is a 1D field with a robust average in time. A more realistic approach would evaluate the effect on the velocity field [as was done in Lumley and Terray (1983) and Rosman and Gerbi (2017)], rather than directly on the higher statistical moments of the velocity field (i.e., the TKE dissipation rate). Such a description would require knowledge of how the velocity field statistics vary with depth a priori.…”

Observational Evidence of Surface Wave‐Generated Strong Ocean Turbulence

“…Using this method, the turbulence characteristics in the surf zone were studied (Feddersen, , ). Rosman and Gerbi () confirmed that the method for the estimation of the TKE dissipation rate proposed by Feddersen et al () is robust.…”

Current and turbulence measurements at the FINO1 offshore wind energy site: analysis using 5-beam ADCPs

“…In order to check the kinematic effects of wave advection on the estimated RSs using Eq. 26, we use analytical shapes for the turbulence (co)spectra in the framework of the kinematic model proposed by Lumley and Terray (1983) and extended by Rosman and Gerbi (2017).…”