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Albert J. Plueddemann and Robert Pinkel

Abstract

Estimation of spectral mean frequency (spectral first moment) by the variance technique is considered for a signal process contaminated by band limited, additive noise. It is shown that the covariance-based spectral mean estimator is biased for low signal-to-noise ratios if the noise bandwidth is not large compared to the signal bandwidth. The bias is towards the mean frequency of the noise spectrum, typically equivalent to the center of the frequency band passed by the receiver. This noise-biasing is potentially important in the processing of Doppler data from radars, sodars and sonars operating in a pulse-to-pulse incoherent mode. Biasing of the mean frequency estimator can be easily corrected if measurements of the noise covariance are available. In the absence of noise measurements, correction for biasing can still be accomplished by estimating the signal and noise bandwidths and introducing simple models for the signal and noise covariance functions. This technique allows estimation of noise covariance from measurements of signal-plus-noise covariance at more than one time lag. In addition, the models provide a means or predicting potential biasing problems in a generalized Doppler system.

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Robert Pinkel, Albert Plueddemann, and Robin Williams

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During 0ctober-November 1983, the Research Platform FLIP participated in the Mixed Layer Dynamics Experiment (MILDEX), off the coast of Southern California. Included among the equipment on board was an array of six Doppler sonars and a repeatedly profiling CTD. The sonars operate at frequencies between 67 and 80 kHz, with peak transmitted power of order 2 kW each. Four of the sonars were directed downward 53°, obtaining velocity profiles to depths in excess of 1100 m. The CTD was profiled to a depth of 320 m every 3 minutes. Approximately 6000 CTD profiles were obtained during MILDEX.

The MILDEX internal wavefield is slightly less energetic than the Garrett-Munk canonical standard, except in the near inertial frequency band. Here very low energy levels are seen. The semidiurnal baroclinic tide dominates the spectra of both horizontal and vertical velocity.

In this work, slant velocity estimates from back-to-back sonar beam are combined to form estimates of horizontal velocity and its vertical derivative, shear. These are compared with isopycnal vertical displacement and strain, derived from the CTD measurements over a 10-day period, in the depth range 200–300 m. Power spectra of shear, strain, and geocentric acceleration are presented, along with more customary spectral quantities. The shear and strain spectra of approximate &omega−3/2 form, with weak inertial and tidal peaks. Vertical coherences of horizontal and vertical velocity are also of similar form during the 10-day comparison period. There is little need to hypothesize the existence of an added class of motions to explain a disparity in the coherences. However, near the beginning and end of the cruise, when FLIP was being more rapidly advected through the water, the vertical coherence of horizontal velocity was significantly reduced relative to that of vertical velocity, particularly at high frequency. The ratios of clockwise to countclockwise horizontal velocity and shear variance are consistent with linear internal wave theory. Ratios of the vertical to horizontal velocity variance are also consistent, except in the tidal and twice tidal frequency bands. Here approximately four times as much vertical velocity variance is sun as would be predicted from the horizontal velocity measurements. This is found to be a “near field” effect associated with the reflection of the baroclinic tide from the sea surface. Scale vertical wavenumbers are defined from defined from the ratio of the strain to vertical displacement spectra, as well as shear to horizontal velocity spectra. These show characteristic vertical wavelengths of 300–500 m throughout the internal wave band, except at tidal and twice tidal frequencies, where the typical wavelengths are much longer (800 m) and at inertial and subinertial frequencies, where they are much shorter (∼200 m). Horizontal wavenumber scales can be derived from the ratios of strain to horizontal velocity and shear to vertical displacement. The derivation depends on the validity of linear shear-free internal wave theory in the WKB approximation. The two scales show an interesting pattern as a function of frequency, but agreement between them is poor.

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David A. Siegel and Albert J. Plueddemann

Abstract

Several popular techniques employed to remotely sense oceanic velocity fields utilize the Doppler shifts of backscattered radiation (such as sound or light) from suspended particles to estimate fluid velocities. Implicit in this use is the assumption that the motion of the particles and the fluid parcels about them is identical. Here, a simple dynamical model of a solid sphere in a unidirectional oscillating flow is used to evaluate the effects of differential particle motion on remotely sensed Doppler velocity estimates. The analysis indicates that typical oceanic particles will move with the fluid if their density is equal to the fluid's density or if the oscillation frequency (ω) is less than a critical frequency (ωc≡0.1νa −2; where ν is the kinematic viscosity of the fluid and a is the particle radius). For oscillation frequencies greater than ωc, the particle and flow velocities diverge significantly from each other. Particle motion will be amplified for particles less dense than the fluid and reduced for relatively heavy particles. The motions of particles and the fluid may have significant phase differences as well. Critical frequencies are estimated for some common oceanic particles enabling the performance of several Doppler velocity measurement techniques to be evaluated. The present results indicate that for some oceanographic applications the Doppler sensing of fluid velocities using particulate backscatter may be limited by the inability of the particles to follow the fluid motion. The model results suggest that it is possible to correct for the velocity differences between the particle and its fluid parcel if the size and relative density of the backscattering material is known. This strongly indicates that a greater emphasis must be placed on the characterization of the materials that are producing the backscattered signals.

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Michael A. Spall, Robert S. Pickart, Paula S. Fratantoni, and Albert J. Plueddemann
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Martin Flügge, Mostafa Bakhoday Paskyabi, Joachim Reuder, James B. Edson, and Albert J. Plueddemann

Abstract

Direct covariance flux (DCF) measurements taken from floating platforms are contaminated by wave-induced platform motions that need to be removed before computation of the turbulent fluxes. Several correction algorithms have been developed and successfully applied in earlier studies from research vessels and, most recently, by the use of moored buoys. The validation of those correction algorithms has so far been limited to short-duration comparisons against other floating platforms. Although these comparisons show in general a good agreement, there is still a lack of a rigorous validation of the method, required to understand the strengths and weaknesses of the existing motion-correction algorithms. This paper attempts to provide such a validation by a comparison of flux estimates from two DCF systems, one mounted on a moored buoy and one on the Air–Sea Interaction Tower (ASIT) at the Martha’s Vineyard Coastal Observatory, Massachusetts. The ASIT was specifically designed to minimize flow distortion over a wide range of wind directions from the open ocean for flux measurements. The flow measurements from the buoy system are corrected for wave-induced platform motions before computation of the turbulent heat and momentum fluxes. Flux estimates and cospectra of the corrected buoy data are found to be in very good agreement with those obtained from the ASIT. The comparison is also used to optimize the filter constants used in the motion-correction algorithm. The quantitative agreement between the buoy data and the ASIT demonstrates that the DCF method is applicable for turbulence measurements from small moving platforms, such as buoys.

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Michael Schlundt, J. Thomas Farrar, Sebastien P. Bigorre, Albert J. Plueddemann, and Robert A. Weller

Abstract

The comparison of equivalent neutral winds obtained from (i) four WHOI buoys in the subtropics and (ii) scatterometer estimates at those locations reveals a root-mean-square (RMS) difference of 0.56–0.76 m s−1. To investigate this RMS difference, different buoy wind error sources were examined. These buoys are particularly well suited to examine two important sources of buoy wind errors because 1) redundant anemometers and a comparison with numerical flow simulations allow us to quantitatively assess flow distortion errors, and 2) 1-min sampling at the buoys allows us to examine the sensitivity of buoy temporal sampling/averaging in the buoy–scatterometer comparisons. The interanemometer difference varies as a function of wind direction relative to the buoy wind vane and is consistent with the effects of flow distortion expected based on numerical flow simulations. Comparison between the anemometers and scatterometer winds supports the interpretation that the interanemometer disagreement, which can be up to 5% of the wind speed, is due to flow distortion. These insights motivate an empirical correction to the individual anemometer records and subsequent comparison with scatterometer estimates show good agreement.

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Tobias Kukulka, Albert J. Plueddemann, John H. Trowbridge, and Peter P. Sullivan

Abstract

Langmuir circulation (LC) is a turbulent upper-ocean process driven by wind and surface waves that contributes significantly to the transport of momentum, heat, and mass in the oceanic surface layer. The authors have previously performed a direct comparison of large-eddy simulations and observations of the upper-ocean response to a wind event with rapid mixed layer deepening. The evolution of simulated crosswind velocity variance and spatial scales, as well as mixed layer deepening, was only consistent with observations if LC effects are included in the model. Based on an analysis of these validated simulations, in this study the fundamental differences in mixing between purely shear-driven turbulence and turbulence with LC are identified. In the former case, turbulent kinetic energy (TKE) production due to shear instabilities is largest near the surface, gradually decreasing to zero near the base of the mixed layer. This stands in contrast to the LC case in which at middepth range TKE production can be dominated by Stokes drift shear. Furthermore, the Eulerian mean vertical shear peaks near the base of the mixed layer so that TKE production by mean shear flow is elevated there. LC transports horizontal momentum efficiently downward leading to an along-wind velocity jet below LC downwelling regions at the base of the mixed layer. Locally enhanced vertical shear instabilities as a result of this jet efficiently erode the thermocline. In turn, enhanced breaking internal waves inject cold deep water into the mixed layer, where LC currents transport temperature perturbation advectively. Thus, LC and locally generated shear instabilities work intimately together to facilitate strongly the mixed layer deepening process.

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Gregory P. Gerbi, John H. Trowbridge, Eugene A. Terray, Albert J. Plueddemann, and Tobias Kukulka

Abstract

Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.

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Michael A. Spall, Robert S. Pickart, Paula S. Fratantoni, and Albert J. Plueddemann

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The mean structure and time-dependent behavior of the shelfbreak jet along the southern Beaufort Sea, and its ability to transport properties into the basin interior via eddies are explored using high-resolution mooring data and an idealized numerical model. The analysis focuses on springtime, when weakly stratified winter-transformed Pacific water is being advected out of the Chukchi Sea. When winds are weak, the observed jet is bottom trapped with a low potential vorticity core and has maximum mean velocities of O(25 cm s−1) and an eastward transport of 0.42 Sv (1 Sv ≡ 106 m3 s−1). Despite the absence of winds, the current is highly time dependent, with relative vorticity and twisting vorticity often important components of the Ertel potential vorticity. An idealized primitive equation model forced by dense, weakly stratified waters flowing off a shelf produces a mean middepth boundary current similar in structure to that observed at the mooring site. The model boundary current is also highly variable, and produces numerous strong, small anticyclonic eddies that transport the shelf water into the basin interior. Analysis of the energy conversion terms in both the mooring data and the numerical model indicates that the eddies are formed via baroclinic instability of the boundary current. The structure of the eddies in the basin interior compares well with observations from drifting ice platforms. The results suggest that eddies shed from the shelfbreak jet contribute significantly to the offshore flux of heat, salt, and other properties, and are likely important for the ventilation of the halocline in the western Arctic Ocean. Interaction with an anticyclonic basin-scale circulation, meant to represent the Beaufort gyre, enhances the offshore transport of shelf water and results in a loss of mass transport from the shelfbreak jet.

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Gregory P. Gerbi, John H. Trowbridge, James B. Edson, Albert J. Plueddemann, Eugene A. Terray, and Janet J. Fredericks

Abstract

This study makes direct measurements of turbulent fluxes in the mixed layer in order to close heat and momentum budgets across the air–sea interface and to assess the ability of rigid-boundary turbulence models to predict mean vertical gradients beneath the ocean’s wavy surface. Observations were made at 20 Hz at nominal depths of 2.2 and 1.7 m in ∼16 m of water. A new method is developed to estimate the fluxes and the length scales of dominant flux-carrying eddies from cospectra at frequencies below the wave band. The results are compared to independent estimates of those quantities, with good agreement between the two sets of estimates. The observed temperature gradients were smaller than predicted by standard rigid-boundary closure models, consistent with the suggestion that wave breaking and Langmuir circulation increase turbulent diffusivity in the upper ocean. Similarly, the Monin–Obukhov stability function ϕh was smaller in the authors’ measurements than the stability functions used in rigid-boundary applications of the Monin–Obukhov similarity theory. The dominant horizontal length scales of flux-carrying turbulent eddies were found to be consistent with observations in the bottom boundary layer of the atmosphere and from laboratory experiments in three ways: 1) in statically unstable conditions, the eddy sizes scaled linearly with distance to the boundary; 2) in statically stable conditions, length scales decreased with increasing downward buoyancy flux; and 3) downwind length scales were larger than crosswind length scales.

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