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Hartmut Peters

Abstract

Spatial variations of vertical turbulent mixing along a stretch of the Hudson River estuary are examined with focus on the vicinity of a “hydraulic control point” at the George Washington Bridge at which the cross section narrows and the thalweg takes a bend. Richardson numbers are lowered and mixing is enhanced downstream of this “modest” morphological feature, qualitatively following predictions based on hydraulic theory by Chant and Wilson. The enhancement in the viscous dissipation rate ε is only a modest factor of 2–3, however, extending over 2 km along the river. Upon averaging over tidal and fortnightly cycles and multiple cruises, streamwise variations of ε along the probed 15-km stretch of the estuary are surprisingly small, given that individual depth averages of ε across the halocline vary by over three orders of magnitude. The principal result is that the observed part of the Hudson River showed strong broadly distributed mixing everywhere, with little local concentration.

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Hartmut Peters
and
Reinoud Bokhorst

Abstract

Turbulent mixing in the water column was observed with a microstructure profiler in the Hudson River estuary during two cruises in summer and fall 1995. The focus is on the estimation of turbulent salt flux and turbulent stress from measured viscous dissipation rates (ε), and on the tidal and fortnightly variability of these fluxes. In estimating eddy viscosity (K m ) and eddy diffusivity (K ρ ), the authors follow measurement/modeling techniques of Busch and Osborn, while prescribing a variable flux Richardson number (R f ) dependent upon the gradient Richardson number (Ri). It is argued that a steady-state production–dissipation balance holds in the turbulent kinetic energy budget.

All turbulence characteristics varied strongly over semidiurnal tidal cycles and over the fortnightly cycle. Subject to complications arising from nontidal flows, the “strongest” mixing occurred during flood on neap tides, and during ebb on spring tides. In the lower part of the water column during floods and spring ebb K m and K ρ reached maxima of 1–5 (×10−2 m2 s−1) and decreased roughly exponentially with increasing height by 1–3 decades. The smallest eddy coefficients occurred in the halocline during neap tide with K m ≈ 10−4 m2 s−1 and K ρ ≈ 10−5 m2 s−1. Mostly, the internal turbulent stress (τ y ) was close to 0 in the upper third of the water column and approached the bottom shear stress with decreasing height. Neap ebb had small |τ y | even close to the bottom in response to stable stratification. During spring ebb, in contrast, τ y decayed approximately linearly from the bottom shear stress to 0 at the surface. The largest turbulent salt flux (J S ) of 8–10 (×10−4 kg m−2 s−1) occurred through much of the water column during spring ebbs. Most floods also had significant J S , while neap ebbs showed small J S . Among the estimated turbulence characteristics, J S is subject to the most pronounced systematic uncertainty owing to lack of knowledge of the variation of R f as a function of Ri.

The stress profiles and the turbulent salt flux estimated from the microstructure profiling are compatible with independent estimates based on moored observations of currents, density, and pressure analyzed by Geyer et al. in terms of the integral momentum and salt balances of the estuary. The role of turbulent mixing within the observed flow is qualitatively that envisioned in the early concepts of Pritchard from the 1950s.

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Helmut Baumert
and
Hartmut Peters

Abstract

A new simple two-equation turbulence closure is constructed by hypothesizing that there is an extra energy sink in the turbulent kinetic energy (k) equation representing the transfer of energy from k to internal waves and other nonturbulent motions. This sink neither contributes to the buoyancy flux nor to dissipation, the nonturbulent mode being treated as inviscid. The extra sink is proportional to the squared ratio between the turbulent time scale τk/ε, with turbulent dissipation rate ε, and the buoyancy period T = 2π/N. With a focus on high–Reynolds number, spatially homogeneous, stably stratified shear flow away from boundaries, the turbulence is described by equations for a master length scale Lk 3/2/ε and the master time scale τ. It is assumed that the onset of the collapse of turbulence into nonturbulence occurs at τ = T. The new theory is almost free of empirical parameters and compares well with laboratory and numerical experiments. Most remarkable is that the model predicts the turbulent Prandtl number, which is generally σ = σ 0/[1 − (τ/T)2], with σ 0 = 1/2, and hence is not a unique function of mean flow variables. Only in structural equilibrium ( τ̇ = 0) is the Prandtl number a unique function of the gradient Richardson number R g : σ = σ 0/(1 − 2R g ). These forms of the Prandtl number function immediately determine the flux Richardson number R f = R g /σ. Steady state occurs at R s g = 1/4 with R f = 1/4, and within structural equilibrium the collapse of turbulence is complete at R g = 1/2.

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Hartmut Peters
and
Helmut Baumert
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Hartmut Peters
and
Reinoud Bokhorst

Abstract

Variations of turbulent mixing in the water column and in the benthic boundary layer were observed with a microstructure profiler in the Hudson River estuary during two cruises in summer and fall of 1995. Variability patterns of stratification, shear, Richardson number (Ri), and turbulent dissipation rates (ϵ) were similar to those of earlier observations, with strong turbulence in the weakly stratified bottom layer, weak turbulence in the halocline during neap tides, and low Ri and high ϵ spanning the water column during spring ebbs. Depth-integrated turbulent dissipation rates ∫ ρϵ dz approximately equaled the work done by the tidal pressure gradient force adjusted for the change in tidal kinetic energy. Alternatively, a suitable scaling for ∫ ρϵ dz is also provided by the product of bottom shear stress and depth-average velocity τ b υ , a relationship that fails at slack tide, however. At heights above bottom of z ≲ 0.3 m, and again excepting slack tides, observed ϵ were highly correlated with a law-of-the-wall dissipation rate ϵ b = u 3 /(κz). Ratios ϵ/ϵ b were close to 1. Here, the friction velocity is u∗, and von Kármán’s constant is κ. Most profiles of the normalized dissipation rate ϵ/ϵ b showed a weak increase with z in the lowest 1.5 m, a departure from law of the wall scaling attributed to stable stratification. Such deviations from the law of the wall were smallest during spring floods when the near-bottom stratification was weak or unstable. Turbulence in the stratified water column well above the bottom appeared to be locally generated by shear instability even though ϵ b and ϵ were correlated throughout the water column. During spring ebbs, ϵ exceeded ϵ b by almost an order of magnitude at z ≳ 2 m.

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Michael J. McPhaden
and
Hartmut Peters

Abstract

A diurnal cycle in temperature and vertical displacement variance has been observed in the stratified region below the surface mixed layer using moored time-series data at 0°, 140°W for there periods: November 1984, April 1987, and May–June 1987. The November 1984 and April 1987 periods coincided with the TROPIC HEAT and TROPIC HEAT-2 experiments, during which direct measurements of turbulent dissipation rates were made near the mooring site. In May–June 1987, a special set of moored time series were collected between 30-m and 61-m depth with 1-minute temporal resolution in addition to standard measurements at 15-minute resolution. The high-resolution data indicated the existence of a diurnal cycle in variance that was most pronounced at frequencies of 10–30 cph and that was coherent over the 31-m extent of the vertical array. It is likely that this diurnal cycle in variance was due in part to internal waves remotely generated at the base of the nighttime mixed layer and that the appearance of internal waves in the thermocline at frequencies higher than the local Väisälä frequency (about 2–7 cph) in May–June 1987 was due to Doppler shifting by the Equatorial Undercurrent. It is also likely that part of the observed diurnal cycle in variance was due to local shear instabilities in the Equatorial Undercurrent that may have been triggered by the diurnally modulated internal wave field. More coarsely resolved 15-minute moored time-series data from November 1984, April 1987, and May–June 1987 indicated the presence of a diurnal cycle after averaging over at least 30 days of data. Largest diurnal ranges in temperature and vertical displacement variance were typically observed in November 1984 when wind speed, zonal wind stress, and mean vertical shear were largest and when the mean gradient Richardson number was smallest. The diurnal cycle in turbulent dissipation rate had a larger amplitude in November 1984 than in April 1987, consistent with a dynamical connection between internal wave variability and turbulence in the equatorial thermocline.

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Hartmut Peters
and
William E. Johns
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Hartmut Peters
and
William E. Johns

Abstract

Turbulence in the Red Sea outflow plume in the western Gulf of Aden was observed with an upward-looking, five-beam, 600-kHz acoustic Doppler current profiler (ADCP). The “Bottom Lander” ADCP was deployed on the seafloor in two narrow, topographically confined outflow channels south of Bab el Mandeb for periods of 18–40 h at three locations at 376-, 496-, and 772-m depths. Two deployments were taken during the winter season of maximum outflow from the Red Sea and two in the summer season of minimum outflow. These short-term observations exhibit red velocity spectra with high-frequency fluctuations of typically a few centimeters per second RMS velocity during strong plume flow as well as strong subtidal variations. In one winter season event, the plume flow was reduced by a factor of 4 over an 18-h time span. In variance-preserving form, velocity spectra show a separation at frequencies of 0.3–3 cycles per hour between low-frequency and high-frequency signals. The latter show significant coherence between horizontal and vertical velocity components; hence they carried turbulent stress. Based on a comparison with velocity spectra from atmospheric mixed-layer observations, the authors argue that large variance at frequencies of the order of 1 cph was possibly associated with bottom-generated, upward-propagating internal waves. One coherent feature that matched such waves was observed directly. Higher frequencies correspond to turbulent motions of energy-carrying scales. The turbulent Reynolds stress at heights above the bottom between 4 and 30–40 m was computed for most of the ADCP observations. Near the bottom, the streamwise turbulent stress and the streamwise velocity followed a quadratic drag law with drag coefficients ranging from 0.002 to 0.008. There was also significant spanwise stress, hinting at the three-dimensional nature of the boundary layer flow. The time–height variations of the stress and its spectrum proved to be complex, one of its most striking features being angles of up to ∼40° between the direction of the stress and that of the low-frequency flow. The turbulent shear production and eddy viscosity were also examined. On the technical side, the paper discusses the role of the fifth, center-beam velocity measurements in correcting for instrument tilt along with the effect of beam spreading in the 30° Janus configuration of the “regular” four ADCP beams. Instrumental noise and detection limits for the stress are also established.

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Hartmut Peters
and
William E. Johns

Abstract

South of the Strait of Bab el Mandeb, saline Red Sea Water flows downslope into the Gulf of Aden mainly along the narrow 130-km-long “Northern Channel” (NC) and the shorter and wider “Southern Channel” (SC). In the NC, the Red Sea plume simultaneously exhibited weak entrainment into a 35–120-m-thick, weakly stratified bottom layer while a 35–285-m-thick interfacial layer above showed signs of vigorous mixing, overturns up to 30 m thick, and extensive zones of gradient Richardson numbers below 1/4. Turbulent overturning scales, or Thorpe scales, are extracted from regular CTD profiles and equated to Ozmidov scales. On this basis, interfacial mixing is quantified in terms of estimated turbulent dissipation rates, vertical turbulent salt flux, and interfacial stress. Even though these estimates are subject to significant uncertainty, they demonstrate the intensity of mixing during strong winter outflow in terms of eddy diffusivities Kρ on the order of 10−2 m2 s−1. The large Kρ occur in strong stratification such that vertical turbulent salt fluxes are also large. Along the NC, relative maxima of Kρ correspond to maxima in the bulk Froude number. Direct short-term measurements of the Reynolds stress just above the seafloor at two locations, one in the NC and one in the SC, allow comparisons of the bottom stress τb with the interfacial turbulent stress τi . The ratio τi /τb shows large scatter in a small sample, with maximum values on the order of 1. An outlines procedures of making and reducing lowered acoustic Doppler current profiler measurements optimized for observing descending plumes.

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John M. Toole
,
Hartmut Peters
, and
Michael C. Gregg

Abstract

A four and one-half day time series of upper-ocean shear and density observations was collected in the tropical Pacific Ocean in November 1984. The measurements were made on the equator at 139°50′W during a period when the equatorial undercurrent was well developed and 20–30 day period velocity fluctuations were prominent. Shear observations were collected with a ship-mounted acoustic-Doppler velocity profiler; density data were obtained from a loosely tethered microstructure instrument. The mean shear profile during the series strongly reflected the structure of the undercurrent; however, the meridional component contributed significantly to the magnitude of the total shear. The mean Richardson number was large near the undercurrent core, but fell to values less than 0.5 25 m above and below the core, and was below 0.25 in the upper 40 m for most of the sample period. Buoyancy frequency varied on a diurnal time scale in the upper 50 m owing to the solar heating cycle, but a compensating diurnal shear cycle was found only above 24 m. Consequently, the Richardson number varied diurnally in the depth range of 25–50 m. The shear and density fluctuations at depths greater than 50 m were not clearly connected to the diurnal near-surface features and exhibited no dominant periodicity. As has been seen in previous internal wave studies, the data below the diurnal surface layer exhibited a cutoff at Ri ∼ 0.25, perhaps indicative of shear mixing control of the Richardson number distribution.

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