Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves

Abstract

Field measurements of wave orbital velocities and pressure, collected in the lower part of the water column in 7 m depth with a three-component acoustic Doppler current meter and a co-located pressure transducer, are compared to the second-order theory for weakly nonlinear surface gravity waves in arbitrary water depth (Hasselmann 1962). Pressure and velocity spectra and cross-spectra are in excellent agreement with (linear) free wave transfer functions, even at (and higher than) twice the spectral peak frequency where nonlinearities (forced secondary waves) are expected to be important. Theoretical predictions show that although secondary waves sometimes contribute a significant fraction of the energy observed at double swell and sea frequencies, their effect on velocity-pressure transfer functions is small. However, forced waves are more apparent in deviations from Gaussian statistics. Good agreement between observed and predicted third-order statistics shows that Hasselmann's weakly nonlinear theory accurately describes the secondary pressure and orbital velocity (both horizontal and vertical components) field at double swell and sea frequencies, even for moderately large (0(0.1–0.2)) values of the nonlinear perturbation parameter. Only with near-breaking swell and relatively strong nonlinearities (perturbation parameter ≈ 0.22), do the observed third-order statistics diverge significantly from Hasselmann's theory.

Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth

“…This assumption, which implies a frictionless interior ocean, is well supported by the observed weak attenuation of swells propagating across ocean basins (Ardhuin et al 2009) and local comparisons of the observed wave orbital motion with second order wave theory (e.g. Herbers et al 1992). Vorticity effects can be important in the vicinity of the surface and bottom boundary layers (e.g.…”

Observing Directional Properties of Ocean Swell with an Acoustic Doppler Current Profiler (ADCP)

“…However, in practice, this capability is compromised by the small horizontal aperture of the array and high noise levels of the ADCP velocity measurements. Highresolution estimation techniques that attempt to fit an exact or near-exact solution to (10) are known to be extremely sensitive to errors in the observations (especially for wavelengths that are long compared with the array footprint), typically resulting in estimates of S(u) with wildly spurious structures (see Herbers and Guza 1990 for further discussion and examples).…”

“…The first-generation, so-called narrowband ADCPs relied on pulse-to-pulse incoherent processing, resulting in noise levels that were too high to resolve high-frequency wind waves and swell, and thus these instruments were used primarily to observe mean current profiles based on long averaging intervals. On the other hand, pulse-to-pulse coherent systems (Lhermitte and Serafin 1984) with very low noise levels can provide accurate measurements of the wave orbital flow field (e.g., Herbers et al 1991Herbers et al , 1992 but suffer from a rangevelocity ambiguity that is undesirable for long-range current profiling applications. The second-generation of so-called broadband ADCPs combines features of incoherent and coherent sonars to reduce noise levels while maintaining the full-range profiling capability (Brumley et al 1991).…”

“…High-resolution estimation techniques that yield an exact or approximate fit to array cross-spectra are known to be sensitive to measurement errors, often resulting in spurious structure in the directional spectrum estimates (e.g., Long and Hasselmann 1979;Pawka 1983;Herbers and Guza 1990). In addition to the high noise level of the velocity measurements, the ADCP sampling (in upwardlooking configuration) is sparse near the surface and may not adequately resolve the high-frequency wave motion that is confined to the upper part of the water column.…”

“…This technique was chosen over more sophisticated inverse methods, because for many applications knowing the mean propagation direction and spreading of the dominant wave systems is often sufficient and inverse model estimates with more degrees of freedom obtained from these inherently noisy datasets often contain spurious features that require cautious interpretation. The method presented here allows for a direct evaluation of the best-fit solution by sweeping through the parameter space, thus avoiding the iterative approach that is needed to solve the nonlinear inverse problem (e.g., Long and Hasselmann 1979;Pawka 1983;Herbers and Guza 1990). The accuracy of the ADCP directional spectrum estimates is evaluated in section 4 through comparison with independent estimates from a surface-following buoy.…”