Measurements Of Dissipation Rate Research Articles

Turbulent diapycnal fluxes as a pilot Essential Ocean Variable

We contend that ocean turbulent fluxes should be included in the list of Essential Ocean Variables (EOVs) created by the Global Ocean Observing System. This list aims to identify variables that are essential to observe to inform policy and maintain a healthy and resilient ocean. Diapycnal turbulent fluxes quantify the rates of exchange of tracers (such as temperature, salinity, density or nutrients, all of which are already EOVs) across a density layer. Measuring them is necessary to close the tracer concentration budgets of these quantities. Measuring turbulent fluxes of buoyancy (Jb), heat (Jq), salinity (JS) or any other tracer requires either synchronous microscale (a few centimeters) measurements of both the vector velocity and the scalar (e.g., temperature) to produce time series of the highly correlated perturbations of the two variables, or microscale measurements of turbulent dissipation rates of kinetic energy (ϵ) and of thermal/salinity/tracer variance (χ), from which fluxes can be derived. Unlike isopycnal turbulent fluxes, which are dominated by the mesoscale (tens of kilometers), microscale diapycnal fluxes cannot be derived as the product of existing EOVs, but rather require observations at the appropriate scales. The instrumentation, standardization of measurement practices, and data coordination of turbulence observations have advanced greatly in the past decade and are becoming increasingly robust. With more routine measurements, we can begin to unravel the relationships between physical mixing processes and ecosystem health. In addition to laying out the scientific relevance of the turbulent diapycnal fluxes, this review also compiles the current developments steering the community toward such routine measurements, strengthening the case for registering the turbulent diapycnal fluxes as an pilot Essential Ocean Variable.

Turbulent Mixing During Late Summer in the Ice–Ocean Boundary Layer in the Central Arctic Ocean: Results From the MOSAiC Expedition

AbstractWe examined mixing processes within the ice–ocean boundary layer (IOBL) close to the geographic North Pole, with an emphasis on wind‐driven sea ice drift. Observations were conducted from late August to late September 2020, during the final leg of the international Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition. Measurements of ice motion, and profiles of currents, hydrography, and microstructure turbulence were conducted. The multifarious direct observations of sea ice and the upper ocean were used to quantify the transport of momentum, heat, and salt in the IOBL. The ice drift was mostly characterized by the inertial oscillation at a semi‐diurnal frequency, which forced an inertial current in the mixed layer. Observation‐derived heat and salinity fluxes at the ice–ocean interface suggest early termination of basal melting and transitioning to refreezing, resulting from a rise in the freezing point temperature by the presence of freshened near‐surface water. Based on the friction velocity, the measured dissipation rate (ε) of turbulent energy can be approximated as 1.4–1.7 times of the “Law of the Wall” criterion. We also observed a spiraling Ekman flow and find its vertical extent in line with the estimate from ε‐based diffusivity. Following passage of a storm, the enhanced oscillatory motions of the ice drift caused trapping of the near‐inertial waves (NIWs) that exclusively propagated through the base of the weakly stratified mixed layer. We accounted Holmboe instabilities and NIWs for the observed distinct peak of the dissipation rate near the bottom of the mixed layer.

Bio-Physical Controls on Wave Transformation in Coastal Reed Beds: Insights From the Razelm-Sinoe Lagoon System, Romania

Coastal wetlands are dynamic bio-physical systems in which vegetation affects the movement of water and sediment, which in turn build and maintain the landform and ecosystem. Wetlands are an effective buffer against coastal erosion and flooding, enhance water quality and human health and wellbeing. Numerous field and laboratory experiments have quantified the reduction of waves by coastal ecosystems. Numerical models, however, are only able to capture observed reduction in wave energy when calibration coefficients are obtained by comparison with measured dissipation rates. A deeper understanding of how wave attenuation varies over time, with local flow conditions and ecosystem properties, is still lacking and should be acquired from a greater range of ecosystem types and geographical settings. Few studies have observed the detailed seasonal variations in how coastal wetlands function as wave buffers and how such seasonal variations might be explained. Equally, few studies have focused on the effect of coastal reed beds on wave dynamics. This study addresses both: i) seasonal variability in wave dissipation through reed vegetation and ii) intricate connections between reed vegetation and the physical context (meteorological and topographical) that might explain such variability. We present observations of wind generated wave transformation through two Phragmites australis reed beds in the Razelm-Sinoe Lagoon System, Danube Delta, Romania. We find that seasonal changes in vegetation density and biomass, as well as meteorological conditions, affect observed wave conditions within the first few meters of the reed beds. Our results also show a preferential reduction of higher frequency waves, irrespective of reed stem diameter or density and suggest the potential importance of seasonal vegetation debris to observed wave dissipation. Such complex and non-linear biogeomorphic effects on wave dissipation are not currently well understood or captured in the parameterisation of vegetation-induced wave dissipation. Our study highlights the importance of an accurate and temporally granular quantification of nearshore bathymetry, wetland topography, and vegetation to fully understand, model, and manage bio-physical interactions in coastal wetlands. More specifically, our results point towards the need for spatially and temporally explicit wave decay functions in emergent reed vegetation. This is particularly critical where the accurate evaluation of the flood and erosion risk contribution of any wetland is required as part of nature-based coastal protection solutions.

Variable Physical Drivers of Near‐Surface Turbulence in a Regulated River

AbstractInland waters, such as lakes, reservoirs and rivers, are important sources of climate forcing trace gases. A key parameter that regulates the gas exchange between water and the atmosphere is the gas transfer velocity, which itself is controlled by near‐surface turbulence in the water. While in lakes and reservoirs, near‐surface turbulence is mainly driven by atmospheric forcing, in shallow rivers and streams it is generated by bottom friction of gravity‐forced flow. Large rivers represent a transition between these two cases. Near‐surface turbulence has rarely been measured in rivers and the drivers of turbulence have not been quantified. We analyzed continuous measurements of flow velocity and quantified turbulence as the rate of dissipation of turbulent kinetic energy over the ice‐free season in a large regulated river in Northern Finland. Measured dissipation rates agreed with predictions from bulk parameters, including mean flow velocity, wind speed, surface heat flux, and with a one‐dimensional numerical turbulence model. Values ranged from to . Atmospheric forcing or gravity was the dominant driver of near‐surface turbulence for similar fraction of the time. Large variability in near‐surface dissipation rate occurred at diel time scales, when the flow velocity was strongly affected by downstream dam operation. By combining scaling relations for boundary‐layer turbulence at the river bed and at the air‐water interface, we derived a simple model for estimating the relative contributions of wind speed and bottom friction of river flow as a function of depth.

Observations of Eddy-Modulated Turbulent Mixing in the Southern Bay of Bengal

AbstractLong-term measurements of turbulent kinetic-energy dissipation rate (ε), and turbulent temperature-variance dissipation rate (χT) in the thermocline, along with currents, temperature, and salinity were made at two subsurface moorings in the southern Bay of Bengal (BoB). This is a part of a major international program, conducted between July 2018 and June 2019, for investigating the role of the BoB on the monsoon intraseasonal oscillations. One mooring was located on the typical path of the Southwest Monsoon Current (SMC), and the other was in a region where the Sri Lanka Dome is typically found during the summer monsoon. Microstructure and finescale estimates of vertical diffusivity revealed the long-term subthermocline mixing patterns in the southern BoB. Enhanced turbulence and large eddy diffusivities were observed within the SMC during the passage of a subsurface-intensified anticyclonic eddy. During this time, background shear and strain appeared to influence high-frequency motions such as near-inertial waves and internal tides, leading to increased mixing. Near the Sri Lanka Dome, enhanced dissipation occurred at the margins of the cyclonic feature. Turbulent mixing was enhanced with the passage of Rossby waves and eddies. During these events, values of χT exceeding 10−4 °C2 s−1 were recorded concurrently with ε values exceeding 10−5 W kg −1. Inferred diffusivity peaked well above background values of 10−6 m2 s−1, leading to an annually-averaged diffusivity near 10−4 m2 s−1. Turbulence appeared low throughout much of the deployment period. Most of the mixing occurred in spurts during isolated events.

Investigation of bubble-particle attachment, detachment and collection efficiencies in a mechanical flotation cell

The paper presents the effect of impeller speed and superficial gas velocity on bubble-particle attachment, detachment and collection efficiencies using pure quartz particles in a mechanical flotation cell. Detachment and collection efficiencies in different parts of cell were calculated by local turbulent energy dissipation rate measurements using high speed stereoscopic particle image velocimetry technique. In addition to high detachment efficiency, low attachment efficiency is also one of the reasons for low collection efficiency for coarse particles. The flotation rate constant increased with an increase in superficial gas velocity. However, the effect of superficial gas velocity on collection efficiency was negligible. This means that any effect of superficial gas velocity on flotation rate constant was due to changes in the number of bubbles and collision frequency. The flotation rate constant, collision frequency, and the number of bubbles increased with increasing impeller speed. However, collection efficiency decreased with increasing impeller speed.

The role of turbulence and internal waves in the structure and evolution of a near-field river plume

Abstract. An along-channel momentum budget is quantified in the near-field plume region of a controlled river flow entering Doubtful Sound, New Zealand. Observations include highly resolved density, velocity and turbulence, enabling a momentum budget to be constructed over a control volume. Estimates of internal stress (τ) were made from direct measurements of turbulence dissipation rates (ϵ) using vertical microstructure profiles. High flow speeds of the surface plume over 2 m s−1 and strong stratification (N2∼10-1 s−2) resulted in enhanced turbulence dissipation rates (ϵ>10-3 W kg−1) and internal stress (τ>10-2 m2 s−2) at the base of the surface layer. Internal waves were observed propagating along the base of the plume, potentially released subsequent to a hydraulic jump in the initial 1 km downstream of the plume discharge point. The momentum flux divergence of these internal waves suggests that almost 15 % of the total plume momentum can be transported out of the system by wave radiation, therefore playing a crucial role in the redistribution of momentum within the near-field plume. Observations illustrate that the evolution of the momentum budget components vary between the distinct surface plume layer and the turbulent, shear-stratified interfacial layer. Within the surface plume, a momentum balance was achieved. The dynamical balance demonstrates that the deceleration of the plume, driven by along-channel advection, is controlled by turbulence stress from the plume discharge point to as far as 3 km downstream. In the interfacial layer, however, the momentum equation was dominated by the turbulence stress term and the balance was not closed. The redistribution of momentum within the shear-stratified layer by internal wave radiation and other hydraulic features could account for the discrepancy in the budget.

Chemical Signaling in the Turbulent Ocean—Hide and Seek at the Kolmogorov Scale

Chemical cues and signals mediate resource acquisition, mate finding, and the assessment of predation risk in marine plankton. Here, we use the chemical properties of the first identified chemical cues from zooplankton together with in situ measurements of turbulent dissipation rates to calculate the effect of turbulence on the distribution of cues behind swimmers as well as steady state background concentrations in surrounding water. We further show that common zooplankton (copepods) appears to optimize mate finding by aggregating at the surface in calm conditions when turbulence do not prevent trail following. This near surface environment is characterized by anisotropic turbulence and we show, using direct numerical simulations, that chemical cues distribute more in the horizontal plane than vertically in these conditions. Zooplankton may consequently benefit from adopting specific search strategies near the surface as well as in strong stratification where similar flow fields develop. Steady state concentrations, where exudation is balanced by degradation develops in a time scale of ~5 h. We conclude that the trails behind millimeter-sized copepods can be detected in naturally occurring turbulence below the wind mixed surface layer or in the absence of strong wind. The trails, however, shorten dramatically at high turbulent dissipation rates, above ~10−3 cm2 s−3 (10−7 W kg−1)

Mixing Rates and Bottom Drag in Bering Strait

AbstractThree shipboard survey lines were occupied in Bering Strait during autumn of 2015, where high-resolution measurements of temperature, salinity, velocity, and turbulent dissipation rates were collected. These first-reported turbulence measurements in Bering Strait show that dissipation rates here are high even during calm winds. High turbulence in the strait has important implications for the modification of water properties during transit from the Pacific Ocean to the Arctic Ocean. Measured diffusivities averaging 2 × 10−2 m2 s−1 are capable of causing watermass property changes of 0.1°C and 0.1 psu during the ~1–2-day transit through the narrowest part of the strait. We estimate friction velocity using both the dissipation and profile methods and find a bottom drag coefficient of 2.3 (±0.4) × 10−3. This result is smaller than values typically used to estimate bottom stress in the region and may improve predictions of transport variability through Bering Strait.

Measurements of Enhanced Near-Surface Turbulence under Windrows

AbstractObservations of waves, winds, turbulence, and the geometry and circulation of windrows were made in a shallow bay in the winter of 2018 outside of Rimouski, Québec. Water velocities measured from a forward-looking pulse-coherent ADCP mounted on a small zodiac show spanwise (cross-windrow) convergence, streamwise (downwind) velocity enhancement, and downwelling in the windrows, consistent with the view that windrows are the result of counterrotating pairs of wind-aligned vortices. The spacing of windrows, measured with acoustic backscatter and with surface imagery, was measured to be approximately twice the water depth, which suggests an aspect ratio of 1. The magnitude and vertical distribution of turbulence measured from the ADCP are consistent with a previous scaling and observations of near-surface turbulence under breaking waves, with dissipation rates larger and decaying faster vertically than what is expected from a shear-driven boundary layer. Measurements of dissipation rate are partitioned to within, and outside of the windrow convergence zones, and measurements inside the convergence zones are found to be nearly an order of magnitude larger than those outside with similar vertical structure. A ratio of time scales suggests that turbulence likely dissipates before it can be advected horizontally into convergences, but the advection of wave energy into convergences may elevate the surface flux of TKE and could explain the elevated turbulence in the windrows. These results add to a limited number of conflicting observations of turbulence variability due to windrows, which may modify gas flux, and heat and momentum transport in the surface boundary layer.

Formation and decay of eddy currents generated by crossed surface waves

The mass-transport induced by crossed surface waves consists of the Stokes and Euler contributions which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and it is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass-transport theoretically and experimentally and demonstrate that both contributions have different time scales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution evolves faster, feeling the additional damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film presented on the fluid surface with the compression modulus being the only non-zero rheological parameter of the film. Then the Euler contribution into the mass-transport becomes parametrically larger and the evolution of the Stokes contribution becomes parametrically faster. The parameter is the same in both cases and it is equal to the quality factor of surfaces waves, which is modified by the presence of a surface film. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

Kink Instability: Evolution and Energy Dissipation in Relativistic Force-free Nonrotating Jets

Abstract We study the evolution of kink instability in a force-free, nonrotating plasma column of high magnetization. The main dissipation mechanism is identified as reconnection of magnetic field lines with various intersection angles, driven by the compression of the growing kink lobes. We measure dissipation rates dU Bϕ /dt ≈ −0.1U Bϕ /τ, where τ is the linear growth time of the kink instability. This value is consistent with the expansion velocity of the kink mode, which drives the reconnection. The relaxed state is close to a force-free Taylor state. We constrain the energy of that state using considerations from linear stability analysis. Our results are important for understanding magnetic field dissipation in various extreme astrophysical objects, most notably in relativistic jets. We outline the evolution of the kink instability in such jets and derive constraints on the conditions that allow for the kink instability to grow in these systems.

Breaking waves in deep water: measurements and modeling of energy dissipation

In the presence of strong winds, ocean surface waves dissipate significant amounts of energy by breaking. Here, breaking rates and wave-following turbulent dissipation rate measurements are compared with numerical WAVEWATCH III estimates of bulk energy dissipation rate. At high winds, the measurements suggest that turbulent dissipation becomes saturated; however, the modeled bulk dissipation continues to increase as a cubic function of wind speed. Similarly, the mean square slope (i.e., the steepness) of the measured waves becomes saturated, while the modeled mean squared slope grows linearly with wind speed. Only a weak relation is observed between breaker fraction and wind speed, possibly because these metrics do not capture the scale (e.g., crest length) of the breakers. Finally, the model skill for basic parameters such as significant wave height is shown to be sensitive to the dissipation rate, indicating that the model skill may be compromised under energetic conditions.

Turbulence at the periphery of Sri Lanka dome

Measurements of kinetic energy dissipation rate ε and other oceanographic variables (temperature, salinity, density, and current profiles) were conducted at 20 stations along a 90 nautical mile section at the southwestern periphery of Sri Lanka Dome (SLD), which is a mesoscale cyclonic eddy that usually appears in Bay of Bengal to the east of Sri Lanka during summer monsoons. The broad aim was to document and interpret the structure of flow and turbulence in SLD and quantify turbulent mixing therein using parametric studies. A tendency of upward doming (upwelling) of the pycnocline toward the SLD center is observed, leading to substantial shallowing of the mixed layer therein, with the mixed layer depth decreasing from ~40 m outside the SLD to ~10–15 m inside the cyclonic eddy. The cumulative distribution of ε in the SLD pycnocline (below 40 m depth) is well approximated by the Burr probability distribution. A high level of ε in the pycnocline was observed at the inner periphery of SLD, concurrent with low values of gradient Richardson numberRi. A parameterization for eddy diffusivity in the SLD pycnocline as a function of Ri is suggested.

Investigation of bubble-particle interactions in a mechanical flotation cell, part 1: Collision frequencies and efficiencies

In this study the influence of impeller speed and superficial gas velocity on hydrodynamic parameters, bubble-particle collision frequency and efficiency using pure quartz particles of different sizes in an aerated Denver flotation cell was investigated. Collision frequency in different parts of cell was calculated by local turbulent energy dissipation rate measurements. Collision efficiency due to gravitational, inertial, interceptional and turbulence mechanism was determined. The overall collision efficiency (Ec) was also investigated. The results showed that the bubble-particle frequencies for different particle sizes in the turbulent zone were 10–12 times higher than in the quiescent zone. Under various hydrodynamic conditions, minimum and maximum values of Ec were observed for −38 µm and −300 + 212 µm particles, respectively. The turbulence mechanism was the main collision mechanism for fine particles. The collision efficiency of coarse particles was mainly influenced by gravitational, inertial and interceptional mechanisms.

Eastern Arctic Ocean Diapycnal Heat Fluxes through Large Double-Diffusive Steps

AbstractThe diffusive layering (DL) form of double-diffusive convection cools the Atlantic Water (AW) as it circulates around the Arctic Ocean. Large DL steps, with heights of homogeneous layers often greater than 10 m, have been found above the AW core in the Eurasian Basin (EB) of the eastern Arctic. Within these DL staircases, heat and salt fluxes are determined by the mechanisms for vertical transport through the high-gradient regions (HGRs) between the homogeneous layers. These HGRs can be thick (up to 5 m and more) and are frequently complex, being composed of multiple small steps or continuous stratification. Microstructure data collected in the EB in 2007 and 2008 are used to estimate heat fluxes through large steps in three ways: using the measured dissipation rate in the large homogeneous layers; utilizing empirical flux laws based on the density ratio and temperature step across HGRs after scaling to account for the presence of multiple small DL interfaces within each HGR; and averaging estimates of heat fluxes computed separately for individual small interfaces (as laminar conductive fluxes), small convective layers (via dissipation rates within small DL layers), and turbulent patches (using dissipation rate and buoyancy) within each HGR. Diapycnal heat fluxes through HGRs evaluated by each method agree with each other and range from ~2 to ~8 W m−2, with an average flux of ~3–4 W m−2. These large fluxes confirm a critical role for the DL instability in cooling and thickening the AW layer as it circulates around the eastern Arctic Ocean.

Turbulent mixing and heat fluxes under lake ice: the role of seiche oscillations

Abstract. We performed a field study on mixing and vertical heat transport under the ice cover of an Arctic lake. Mixing intensities were estimated from small-scale oscillations of water temperature and turbulent kinetic energy dissipation rates derived from current velocity fluctuations. Well-developed turbulent conditions prevailed in the stably stratified interfacial layer separating the ice base from the warmer deep waters. The source of turbulent mixing was identified as whole-lake (barotropic) oscillations of the water body driven by strong wind events over the ice surface. We derive a scaling of ice–water heat flux based on dissipative Kolmogorov scales and successfully tested against measured dissipation rates and under-ice temperature gradients. The results discard the conventional assumption of nearly conductive heat transport within the stratified under-ice layer and suggest contribution of the basal heat flux into the melt of ice cover is higher than commonly assumed. Decline of the seasonal ice cover in the Arctic is currently gaining recognition as a major indicator of climate change. The heat transfer at the ice–water interface remains the least studied among the mechanisms governing the growth and melting of seasonal ice. The outcomes of the study find application in the heat budget of seasonal ice on inland and coastal waters.

Studies of Turbulence Dissipation in the Taurus Molecular Cloud with Core Velocity Dispersion

Abstract Turbulence dissipation is an important process affecting the energy balance in molecular clouds, the birth place of stars. Previously, the rate of turbulence dissipation is often estimated with semi-analytic formulae from simulation. Recently, we developed a data analysis technique called core velocity dispersion, which, for the first time, provides direct measurements of the turbulence dissipation rate in Taurus, a star-forming cloud. The thus measured dissipation rate of is similar to those from dimensional analysis, and is also consistent with the previous energy injection rate based on molecular outflows and bubbles.

Comparison of in situ microstructure measurements to different turbulence closure schemes in a 3-D numerical ocean circulation model

In situ measurements of kinetic energy dissipation rate ε and estimates of eddy viscosity KZ from the Gulf of Lion (NW Mediterranean Sea) are used to assess the ability of k−ɛ and k−ℓ closure schemes to predict microscale turbulence in a 3-D numerical ocean circulation model. Two different surface boundary conditions are considered in order to investigate their influence on each closure schemes’ performance. The effect of two types of stability functions and optical schemes on the k−ɛ scheme is also explored. Overall, the 3-D model predictions are much closer to the in situ data in the surface mixed layer as opposed to below it. Above the mixed layer depth, we identify one model’s configuration that outperforms all the other ones. Such a configuration employs a k−ɛ scheme with Canuto A stability functions, surface boundary conditions parameterizing wave breaking and an appropriate photosynthetically available radiation attenuation length. Below the mixed layer depth, reliability is limited by the model’s resolution and the specification of a hard threshold on the minimum turbulent kinetic energy.

Mixture-fraction imaging at 1 kHz using femtosecond laser-induced fluorescence of krypton.

Femtosecond, two-photon-absorption laser-induced-fluorescence (TALIF) imaging measurements of krypton (Kr) are demonstrated to study mixing in gaseous flows. A measurement approach is presented in which observed Kr TALIF signals are 7times stronger than the current state-of-the-art methodology. Fluorescence emission is compared for different gas pressures and excitation wavelengths, and the strongest fluorescence signals were observed when the excitation wavelength was tuned to 212.56nm. Using this optimized excitation scheme, 1-kHz, single-laser-shot visualizations of unsteady flows and two-dimensional measurements of mixture fraction and scalar dissipation rate of a Kr-seeded jet are demonstrated.