Oceanic Microstructure Research Articles

Observations of Broadband Acoustic Backscattering From Nonlinear Internal Waves: Assessing the Contribution From Microstructure

In this paper, measurements of high-frequency broadband (160-590 kHz) acoustic backscattering from surface trapped nonlinear internal waves of depression are presented. These waves are ideal for assessing the contribution from oceanic microstructure to scattering as they are intensely turbulent. Almost coincident direct microstructure measurements were performed and zooplankton community structure was characterized using depth-resolved net sampling techniques. The contribution to scattering from microstructure can be difficult to distinguish from the contribution to scattering from zooplankton using a single narrowband frequency as microstructure and zooplankton are often colocated and can have similar scattering levels over a range of frequencies. Yet their spectra are distinct over a sufficiently broad frequency range, allowing broadband backscattering measurements to reduce the ambiguities typically associated with the interpretation of narrowband measurements. In addition, pulse compression signal processing techniques result in very high-resolution images, allowing physical processes that are otherwise hard to resolve to be imaged, such as Kelvin-Helmholtz shear instabilities. In this study, high-resolution acoustic observations of multiple nonlinear internal waves are presented and regions with distinct scattering spectra are identified. Spectra that decrease in level across the available frequency band were highly correlated to regions of intense turbulence and high stratification, and to Kevin-Helmholtz shear instabilities in particular. Spectra that increase in level across the available frequency band were consistent with scattering dominated by small zooplankton. Simple inversions for relevant microstructure parameters are presented. Limitations of, and improvements to, the broadband system and techniques utilized in this study are discussed.

Measurements of acoustic scattering from zooplankton and oceanic microstructure using a broadband echosounder

Abstract Lavery, A. C., Chu, D., and Moum, J. N. 2010. Measurements of acoustic scattering from zooplankton and oceanic microstructure using a broadband echosounder. – ICES Journal of Marine Science, 67: 379–394. In principle, measurements of high-frequency acoustic scattering from oceanic microstructure and zooplankton across a broad range of frequencies can reduce the ambiguities typically associated with the interpretation of acoustic scattering at a single frequency or a limited number of discrete narrowband frequencies. With this motivation, a high-frequency broadband scattering system has been developed for investigating zooplankton and microstructure, involving custom modifications of a commercially available system, with almost complete acoustic coverage spanning the frequency range 150–600 kHz. This frequency range spans the Rayleigh-to-geometric scattering transition for some zooplankton, as well as the diffusive roll-off in the spectrum for scattering from turbulent temperature microstructure. The system has been used to measure scattering from zooplankton and microstructure in regions of non-linear internal waves. The broadband capabilities of the system provide a continuous frequency response of the scattering over a wide frequency band, and improved range resolution and signal-to-noise ratios through pulse-compression signal-processing techniques. System specifications and calibration procedures are outlined and the system performance is assessed. The results point to the utility of high-frequency broadband scattering techniques in the detection, classification, and under certain circumstances, quantification of zooplankton and microstructure.

On the use of broadband acoustic scattering techniques for observing physical and biological scattering features in the ocean.

Broadband acoustic scattering techniques, and associated signal processing techniques, are emerging as a powerful tool for the remote sensing of physical and biological scattering features in the ocean. These techniques allow (1) the frequency spectrum of oceanic scatterers to be measured, thereby resulting in enhanced classification and quantification potential relative to more traditional single‐frequency scattering techniques, and (2) increased spatial resolution resulting in high‐resolution images of oceanic scattering features, obtained through use of pulse compression signal processing techniques that exploit the broadband content of the signal. In this presentation, broadband processing techniques are discussed and results from laboratory and field measurements of broadband acoustic scattering from both physical and biological scatterers, spanning the frequency range from 100–600 kHz, are presented. Controlled laboratory broadband scattering measurements allow coherent ping‐to‐ping analysis to be performed as well as individual scattering features to be determined. The laboratory approaches are then expanded into the field to investigate physical and biological scattering features in the ocean on relevant temporal and spatial scales. Examples of broadband field measurements are presented from recent field experiments, and include scattering from nonlinear internal waves, zooplankton, turbulent oceanic microstructure, salinity microstructure in rivers, and bubbles.

Observations of wind-driven deepening of the surface mixing layer in the Tsushima strait

A detailed description of wind-driven deepening of the mixing layer in the Tsushima strait is given by combining current data from the acoustic Doppler current profiler (ADCP) attached to a satellite-tracked surface drifter, with microstructure data from the Turbulence Ocean Microstructure Acquisition Profiler (TurboMAP) deployed from a ship following the surface drifter. By collecting data in a Lagrangian manner we attempted to minimize the effect of horizontal advection. The dissipation rate of turbulent kinetic energy (TKE), ɛ, was measured directly using the TurboMAP, whereas the production rate of TKE, P, was estimated from horizontal velocities obtained using the ADCP based on the one-dimensional linear equation of motion. The TKE budget in the mixing layer is examined by applying the integrated TKE equation to the observed data. The sum of the temporal change of potential energy, shear production, dissipation, TKE flux, and the surface buoyancy flux terms changes dramatically with time, indicating the importance of the temporal change of TKE in the deepening process on a time scale shorter than one day, which is neglected in widely used bulk mixedlayer models.

Acoustic scattering from double‐diffusive microstructure

Laboratory measurements of high‐frequency broadband acoustic backscattering (200‐600 kHz) from the diffusive regime of double‐diffusive microstructure have been performed. This type of microstructure, which was characterized using direct microstructure and optical shadowgraph techniques, is identified by sharp density and sound speed interfaces separating well‐mixed layers. Acoustic backscattering measurements were performed for a range of physical parameters controlling the double‐diffusive microstructure. The echoes have been analyzed in both the frequency domain, providing information on the spectral response of the scattering, and in the time domain, using pulse compression techniques. High levels of variability were observed, associated with interface oscillations and turbulent plumes, with many echoes showing significant spectral structure. Acoustic estimates of interface thickness, obtained for the echoes with exactly two peaks in the compressed pulse output, were in good agreement with estimates based on direct microstructure and optical shadowgraph measurements. Predictions based on a one‐dimensional weak‐scattering model that includes the actual density and sound speed profiles agree reasonably with the measured scattering. A remote‐sensing tool for mapping oceanic microstructure, such as high‐frequency broadband acoustic scattering, could lead to a better understanding of the extent and evolution of double‐diffusive layering, and to the importance of double diffusion to oceanic mixing.

Acoustic scattering from double-diffusive microstructure

Laboratory measurements of high-frequency broadband acoustic backscattering (200-600 kHz) from the diffusive regime of double-diffusive microstructure have been performed. This type of microstructure, which was characterized using direct microstructure and optical shadowgraph techniques, is identified by sharp density and sound speed interfaces separating well-mixed layers. Vertical acoustic backscattering measurements were performed for a range of physical parameters controlling the double-diffusive microstructure. The echoes have been analyzed in both the frequency domain, providing information on the spectral response of the scattering, and in the time domain, using pulse compression techniques. High levels of variability were observed, associated with interface oscillations and turbulent plumes, with many echoes showing significant spectral structure. Acoustic estimates of interface thickness (1-3 cm), obtained for the echoes with exactly two peaks in the compressed pulse output, were in good agreement with estimates based on direct microstructure and optical shadowgraph measurements. Predictions based on a one-dimensional weak-scattering model that includes the actual density and sound speed profiles agree reasonably with the measured scattering. A remote-sensing tool for mapping oceanic microstructure, such as high-frequency broadband acoustic scattering, could lead to a better understanding of the extent and evolution of double-diffusive layering, and to the importance of double diffusion to oceanic mixing.

High-frequency broadband (150–600 kHz) acoustic backscattering from oceanic microstructure and zooplankton in the presence of internal solitary waves

As one of the founders of acoustical oceanography, Hank Medwin has directly or indirectly influenced the careers of many scientists. Throughout his illustrious and prolific career, Hank Medwin was passionate about using and developing acoustic techniques to study the ocean and, in particular, to study the physical processes of the ocean interior, a passion shared by the authors. In this spirit, the authors present highlights of an experiment in which a high-frequency broadband (150–600 kHz) acoustic backscattering system was used to investigate the scattering of sound from oceanic microstructure and zooplankton throughout the evolution, from generation to dissipation, of internal solitary waves. The broadband spectrum of the scattered returns is used to differentiate between regions in which the scattering is dominated by zooplankton versus microstructure. Interpretation of the measured scattering relies heavily on a fundamental understanding of scattering processes as well as on direct measurements of microstructure and biology.

Sheared turbulence in a weakly stratified upper ocean

Microstructure, ADCP and CTD profiles taken in the North Atlantic along 53°N under moderate and high winds showed that the median of log-normally distributed kinetic energy dissipation rate ε within the upper mixing layer is 1.5×10 −7 W/kg and the layer depth, on the average, is ∼40 m. Assuming that mixing efficiency γ is a constant ( γ = 0.2 ), the following scaling is proposed for the normalized eddy diffusivity: K ^ b = K b / κ u * z = ( 1 + Ri / R i cr ) - p P r tr - 1 , where K b = γ ε / N 2 , N 2 is the squared buoyancy frequency, u * the surface friction velocity, Ri the local Richardson number, P r tr = 1 + Ri / R i β the turbulent Prandtl number, p = 1 or 2/3, Ri cr=0.1 and Ri β =0.1 or 0.05. The power-law function with p = 1 relates the asymptotes of K b( Ri) to the buoyancy scale L N ∼ ( ε / N 3 ) 1 / 2 at Ri⪢ Ri cr and to the shear scale L Sh ∼ ( ε / Sh 3 ) 1 / 2 at Ri⪡ Ri cr. If p = 2 / 3 , the lengthscale L R = ( ε / N 2 Sh ) 1 / 2 replaces L N in spectra of ocean microstructure than due to the influence of local shear. This mixing regime corresponds to intermediate Richardson numbers (∼0.25< Ri<∼2). Alternatively, if γ is not a constant, but an increasing function of Ri for 0< Ri<1, then K ^ b ( Ri ) shows a very weak dependence on Ri for Ri<0.25. Numerical experiments using a one-dimensional q 2− ε model with different K b parameterizations indicate that the measured mixed-layer depth agrees well with model results when the diffusivity is parameterized with an Ri-dependent γ (the GISS model approach). The modeled dissipation profiles, however, resembled microstructure measurements better if γ is treated as a constant and the proposed formula for K ^ b ( Ri ) is used.

High-frequency acoustic volume scattering from zooplankton and moving oceanic microstructure

It is well accepted that high-frequency acoustic scattering techniques can be used to perform rapid, synoptic surveys of fish and zooplankton over relevant spatial and temporal scales. However, the use of these remote sensing techniques to probe small scale physical processes, such as oceanic microstructure, has not been fully accepted, or exploited. Yet there is a growing body of evidence in the form of both laboratory and field measurements suggesting that their use is feasible. Discrimination of scattering from microstructure versus zooplankton, which span similar spatial scales, is typically a limiting factor. Currently, acoustic discrimination of turbulence from zooplankton relies on either source of scattering being dominant as well as on the availability and accuracy of scattering models. A model for scattering from oceanic microstructure that includes fluctuations in the density and sound speed is presented. The effects on scattering from a layer of microstructure with a mean fluid velocity are discussed. Backscattering predictions are made based on data collected in Hudson Canyon with a tethered free-falling high-resolution vertical microstructure profiler, and compared to two-frequency acoustic data (120 and 420 kHz). The contribution to scattering from zooplankton is also estimated from nearby depth-resolved net tows together with zooplankton scattering models.

High-frequency acoustic scattering from turbulent oceanic microstructure: the importance of density fluctuations.

Acoustic scattering techniques provide a unique and powerful tool to remotely investigate the physical properties of the ocean interior over large spatial and temporal scales. With high-frequency acoustic scattering it is possible to probe physical processes that occur at the microstructure scale, spanning submillimeter to centimeter scale processes. An acoustic scattering model for turbulent oceanic microstructure is presented in which the current theory, which only accounts for fluctuations in the sound speed, has been extended to include fluctuations in the density as well. The inclusion of density fluctuations results in an expression for the scattering cross section per unit volume, sigma(v), that is explicitly dependent on the scattering angle. By relating the variability in the density and sound speed to random fluctuations in oceanic temperature and salinity, sigma(v) has been expressed in terms of the temperature and salinity wave number spectra, and the temperature-salinity co-spectrum. A Batchelor spectrum for temperature and salinity, which depends on parameters such as the dissipation rates of turbulent kinetic energy and temperature variance, has been used to evaluate sigma(v). Two models for the temperature-salinity co-spectrum have also been used. The predictions indicate that fluctuations in the density could be as important in determining backscattering as fluctuations in the sound speed. Using data obtained in the ocean with a high resolution vertical microstructure profiler, it is predicted that scattering from oceanic microstructure can be as strong as scattering from zooplankton.

Turbulence and fossil turbulence in oceans and lakes

Turbulence is defined as an eddy-like state of fluid motion where the intertial-vortex forces of the eddies are larger than any of the other forces that tend to damp the eddies out. Energy cascades of irrotational flows from large scales to small are non-turbulent, even if they supply energy to turbulence. Turbulent flows are rotational and cascade from small scales to large, with feedback. Viscous forces limit the smallest turbulent eddy size to the Kolmogorov scale. In stratified fluids, buoyancy forces limit large vertical overturns to the Ozmidov scale and convert the largest turbulent eddies into a unique class of saturated, non-propagating, internal waves, termed fossil-vorticity-turbulence. These waves have the same energy but different properties and spectral forms than the original turbulence patch. The Gibson (1980, 1986) theory of fossil turbulence applies universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as its growth is constrained and fossilized by buoyancy forces. Quantitative hydrodynamic-phase-diagrams (HPDs) from the theory are used to classify microstructure patches according to their hydrodynamic states. When analyzed in HPD space, previously published oceanic datasets showed their dominant microstructure patches are fossilized at large scales in all layers. Laboratory and field measurements suggested phytoplankton species with different swimming abilities adjust their growth strategies by pattern recognition of turbulence-fossil-turbulence dissipation and persistence times that predict survival-relevant surface layer sea changes. New data collected near a Honolulu waste-water outfall showed the small-to-large evolution of oceanic turbulence microstructure from active to fossil states, and revealed the ability of fossil-density-tubulence patches to absorb, and vertically radiate, internal wave energy, information, and enhanced turbulent-mixing-rates toward the sea surface so that the submerged waste-field could be detected from a space satellite (Bondur and Filatov, 2003).

Oceanic Velocity Microstructure Measurements in the 20th Century

The science of ocean turbulence was started more than 50 years ago by a small research group using a surplus mine-sweeping paravane to measure the velocity and temperature fluctuations in the ocean. The field has grown considerably and measurements are now conducted by researchers in many countries. A wide variety of sophisticated instrument systems are used to profile horizontally and vertically through the marine environment. Here we review the historical development of velocity micro-structure profiles over the past four decades and summarize the basic requirements for successful measurements. We highlight critical technological developments and glance briefly at some of the scientific discoveries made with these instruments.

Abyssal Mixing in the Brazil Basin*

One of the major objectives of the Deep Basin Experiment, a component of the World Ocean Circulation Experiment, was to quantify the intensity and spatial distribution of deep vertical mixing within the Brazil Basin. In this study, basin-averaged estimates of deep vertical mixing rates are calculated using two independent methodologies and datasets: 1) vertical fluxes are derived from large-scale temperature and density budgets using direct measurements of deep flow through passages connecting the Brazil Basin to surrounding basins and a comprehensive hydrographic dataset within the basin interior and 2) vertical mixing rates are estimated from finescale bathymetry and hydrographic data using a functional relationship between turbulent dissipation and bathymetric roughness, deduced from localized measurements of ocean microstructure obtained during the Deep Basin Experiment. The space‐time mean estimates of vertical mixing diffusivities across representative surfaces within the Antarctic Bottom Water layer fell in the range ; 1‐5(3 1024 m2 s 21) and were indistinguishable k from each other within the estimation uncertainties. The mixing rates inferred from potential temperature budgets update, and are consistent with, earlier estimates that were based on less data. Mixing rates inferred from budgets bounded by neutral surfaces are not significantly different from the former. This implies that lateral eddy fluxes along isopycnals are not important in the potential temperature budgets, at least within the large estimation uncertainties. Unresolved processes, such as cabbeling and low frequency variability, which complicate inference of mixing from large-scale budgets, have been considered. The agreement between diffusivity estimates based on a modeled relationship between bathymetric roughness and turbulent dissipation, with those inferred from large-scale budgets, provides independent confirmation that the mixing rates have been accurately quantified.

Quantification of stratospheric mixing from turbulence microstructure measurements

In the stratosphere, turbulence is confined within shallow, localised patches. The resulting vertical mixing of tracers is highly intermittent and difficult to quantify. Here a new technique is employed to estimate from high‐resolution, lower stratospheric mid‐latitude balloon data a well‐defined vertical diffusivity associated with this mixing. The technique, which is based on a stochastic model of the distribution of turbulent patches, emphasises the dependence of the diffusivity on the typical patch lifetime. Assuming a lifetime of a few hours, the diffusivity is found to be in the range 0.01–0.02m²s−1. This value is an order of magnitude smaller than those previously derived from radar measurements. The potential of the technique for the analysis of ocean microstructure measurements is noted.

Laboratory and ocean studies of phytoplankton response to fossil turbulence

Abstract Two classes of phytoplankton; dinoflagellates, which can swim, and diatoms, which cannot, apparently respond to turbulence and its enhanced persistence time through stratified fossil turbulence, but in opposite ways. Threshold levels of viscous dissipation rates for growth inhibition e GI and minimum duration times T GI for dinoflagellates have been quantified by laboratory tests and compared with observed negative dinoflagellate population response to ocean surface waves. Positive diatom population response to waves has been observed and quantified by laboratory studies. Both populations have the same but weaker response to winds. A model based on the observations and Gibson's fossil turbulence theory [Gibson, C.H., 1980. Fossil temperature, salinity, and vorticity turbulence in the ocean. In: Nihoul, J. (Ed.), Elsevier, Amsterdam, pp. 221–257; Gibson, C.H., 1986. Internal waves, fossil turbulence, and composite ocean microstructure spectra. J. Fluid Mech. 168, 89–117.] suggests that phytoplankton species may have evolved by means of turbulence and fossil turbulence pattern recognition that optimize their survival based on swimming ability in evolving surface layer sea states where an impending change of surface sea state from strongly stratified to mixed is signaled by persistent patches of stratified fossil vorticity turbulence with large e that can only be produced by breaking surface waves on a strongly stratified surface layer.

Oceanic Microstructure Measurements by BAKLAN and GRIF

The authors describe instruments and their calibration techniques developed at the Atlantic Branch of the P. P. Shizshov Institute of Oceanology, Russian Academy of Sciences and used for microstructure measurements by Russian oceanographers during the last decade. The vertical profiler BAKLAN and the towing body GRIF carried among other sensors a new microconductivity capillary probe with spectral resolution O(100 cpm). This sensor was used to calculate the scalar dissipation rate x with noise level of 3 3 10210 K2 s21. The kinetic energy dissipation rate « was measured by an airfoil-type sensor with a noise level less than 8 3 10210 Wk g 21. Results of the measurements are illustrated by the data obtained near the California coast and in the western equatorial Pacific. A parameterization of equatorial turbulence in terms of turbulent diffusivities and the gradient Richardson numbers is considered. A relationship between horizontal patchiness of conductivity microstructure in the coastal zone and local thermohaline fronts was detected.

Fossil turbulence revisited

A theory of fossil turbulence presented in the 11th Liege Colloquium on Marine Turbulence is ‘revisited’ in the 29th Liege Colloquium ‘Marine Turbulence Revisited’. The Gibson [Gibson, C.H., 1980. Fossil temperature, salinity, and vorticity turbulence in the ocean. : Nihoul, J. (Ed.), Marine Turbulence. Elsevier, Amsterdam, pp. 221–257] theory applied universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as it is constrained and fossilized by buoyancy forces. Towed oceanic microstructure measurements of Schedvin (1979) confirmed the predicted universal constants. Universal constants, spectra, hydrodynamic phase diagrams (HPDs) and other predictions of the theory have been reconfirmed by a wide variety of field and laboratory observations. A T (turbulent activity coefficient) vs. C (Cox number) HPDs classify microstructure patches as active, active-fossil, and fossil turbulence. So do Froude–Reynolds number Fr/Fr o vs. Re/Re F plots. Both HPDs show most oceanic microstructure patches are fossilized. The oceanic microstructure community has not yet adopted the fossil turbulence paradigm, for reasons that include a variety of misconceptions about stratified turbulence and turbulent mixing. Confusion of fossilized microstructure with turbulent microstructure leads to vast underestimates of average dissipation rates of kinetic energy ε and scalar variance χ, and therefore vast underestimates of vertical fluxes in most ocean layers. Fossil turbulence theory has many applications; for example, in marine biology, laboratory and field measurements suggest phytoplankton species with different swimming abilities adjust their growth strategies differently by pattern recognition of several days of turbulence–fossil–turbulence dissipation and persistence times above threshold values, signaling a developing surface layer sea change. In cosmology, self-gravitational structure masses are interpreted as fossils of primordial hydrodynamic states.

Spatial Variability of Turbulent Mixing in the Abyssal Ocean

Ocean microstructure data show that turbulent mixing in the deep Brazil Basin of the South Atlantic Ocean is weak at all depths above smooth abyssal plains and the South American Continental Rise. The diapycnal diffusivity there was estimated to be less than or approximately equal to 0.1 x 10(-4) meters squared per second. In contrast, mixing rates are large throughout the water column above the rough Mid-Atlantic Ridge, and the diffusivity deduced for the bottom-most 150 meters exceeds 5 x 10(-4) meters squared per second. Such patterns in vertical mixing imply that abyssal circulations have complex spatial structures that are linked to the underlying bathymetry.

Once again: once again—tidal friction

Topex/Poseidon (T/P) altimetry has reopened the problem of how tidal dissipation is to be allocated. There is now general agreement of a M 2 dissipation by 2.5 Terawatts (1 TW = 10 12 W), based on four quite separate astronomic observational programs. Allowing for the bodily tide dissipation of 0.1 TW leaves 2.4 TW for ocean dissipation. The traditional disposal sites since Jeffreys (1920) have been in the turbulent bottom boundary layer (BBL) of marginal seas, and the modern estimate of about 2.1 TW is in this tradition (but the distribution among the shallow seas has changed radically from time to time). Independent estimates of energy flux into the marginal seas are not in good agreement with the BBL estimates. T/P altimetry has contributed to the tidal problem in two important ways. The assimilation of global altimetry into Laplace tidal solutions has led to accurate representations of the global tides, as evidenced by the very close agreement between the astronomic measurements and the computed 2.4 TW working of the Moon on the global ocean. Second, the detection by Ray and Mitchum (1996) of small surface manifestation of internal tides radiating away from the Hawaiian chain has led to global estimates of 0.2 to 0.4 TW of conversion of surface tides to internal tides. Measurements of ocean microstructure yields 0.2 TW of global dissipation by pelagic turbulence (away from topography). We propose that pelagic turbulence is maintained by topographic scattering of barotropic into baroclinic tidal energy, via internal tides and internal waves. Previous estimates by Baines (1974); Baines, (1982)) of this conversion along 150,000 km of continental coastlines gave a negligible 0.02 TW; evidently the important conversion takes place along mid-ocean ridges. The maintenance of the abyssal global stratification requires a much larger expenditure of power. 2 TW versus 0.2 TW. This is usually attributed to wind forcing. If tidal power is to play a significant role here, then the BBL estimates need to be reduced. The challenge is to estimate dissipation from the energy flux divergence in the T/P adjusted tidal models, without prior assumptions concerning the dissipation processes.

Diascalar flux and the rate of fluid mixing

We define the rate at which a scalar θ mixes in a fluid flow in terms of the flux of θ across isoscalar surfaces. This flux θd is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state θ(t,z*.) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (∂/∂z*)θd.This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn–Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.