Temperature Variance Dissipation Rate Research Articles

Oceanic turbulence parameters recognition based on convolutional neural network

The distortion induced by ocean turbulence has a substantial impact on the propagation of light in water, posing challenges for applications including underwater wireless optical communications and submarine surveys. Obtaining accurate information about the properties of oceanic turbulence (OT), particularly the parameters describing OT, is crucial for addressing these challenges and enhancing the performance of such applications. In this paper, we propose a convolutional neural network (CNN) and validate its ability to recognize OT parameters. The physical quantities of oceanic turbulence collectively influence the formation and strength of turbulence. We recognize the dissipation rate of temperature variance χ T and the turbulent kinetic energy dissipation rate ɛ, taking into account various balance parameter ω, transmission distance z. Furthermore, in order to simultaneously recognize χ T and ɛ, we enhanced the existing network by modifying the output structure, resulting in a dual-output architecture that facilitates concurrent classification of both χ T and ɛ. Our method for classifying turbulence parameters will contribute to the field of underwater wireless optical communication and promote its further development.

Turbulent Diffusivity Profiles on the Shelf and Slope at the Southern Edge of the Canada Basin

AbstractVertical profiles of temperature microstructure at 95 stations were obtained over the Beaufort shelf and shelfbreak in the southern Canada Basin during a November 2018 research cruise. Two methods for estimating the dissipation rates of temperature variance and turbulent kinetic energy were compared using this data set. Both methods require fitting a theoretical spectrum to observed temperature gradient spectra, but differ in their assumptions. The two methods agree for calculations of the dissipation rate of temperature variance, but not for that of turbulent kinetic energy. After applying a rigorous data rejection framework, estimates of turbulent diffusivity and heat flux are made across different depth ranges. The turbulent diffusivity of temperature is typically enhanced by about one order of magnitude in profiles on the shelf compared to near the shelfbreak, and similarly near the shelfbreak compared to profiles with bottom depth >1,000 m. Depth bin means are shown to vary depending on the averaging method (geometric means tend to be smaller than arithmetic means and maximum likelihood estimates). The statistical distributions of heat flux within the surface, cold halocline, and Atlantic water layer change with depth. Heat fluxes are typically <1 Wm−2, but are greater than 50 Wm−2 in ∼8% of the overall data. These largest fluxes are located almost exclusively within the surface layer, where temperature gradients can be large.

Contribution of Thermohaline Staircases to Deep Water Mass Modifications in the Western Mediterranean Sea From Microstructure Observations

Recent observations from profiles of temperature and salinity in the Algerian Sea showed that salt finger mixing can significantly warm and salinify the deep waters within a period of 2 years, thereby contributing to the erosion of deep water properties formed during winter convection episodes. In this study, heat, salt, and buoyancy fluxes associated with thermohaline staircases are estimated using microstructure observations from four locations of the Western Mediterranean Sea: The Tyrrhenian Sea, the Algerian Sea, the Sardino-Balearic Sea, and the Ligurian Sea. Those fluxes are compared to the rare estimates found in the Mediterranean Sea. Microstructure data show that the temperature variance dissipation rate is one to three orders of magnitude larger in the strong steps that separate weakly stratified layers than in the layers, while the turbulent kinetic energy dissipation rate remains usually weak both in steps and layers. In the steps, the turbulent eddy diffusivity of salt is on average twice as large as that of temperature. The buoyancy flux ratio decreases with the density ratio. It is found that staircases induce a downward heat transfer rate of 46 to 103 × 109 W over the whole western basin, and a downward salt transfer rate of 4.5 to 10.3 × 103 kg s–1 between 1000 and 2000 m. This heat convergence is 2–5 times as large as the western Mediterranean geothermal heat flux in this depth range. Over the whole western basin, heat and salt convergences from salt-fingering staircases are 50% to 100% of those generated by mechanical mixing. Finally, it is found that heat and salt convergences from geothermal heating, salt-fingering and mechanical mixing can balance a deep water upwelling of 0.4 × 106 m3 s–1.

Analysis of the transmission characteristics of Hank-Bessel beam in anisotropic ocean turbulence

Based on the Rytov approximation theory, we analyze the cross-spectral density of Hankel-Bessel (HB) beams in anisotropic ocean turbulence. In this paper, we study the orbital angular momentum (OAM) mode detection probability, the crosstalk probability and the spiral phase spectrum of the HB beam, and establish the OAM mode detection probability model in anisotropic ocean turbulence. The results show that the detection probability of the emission mode is decreased and the spiral phase spectrum is expanded due to the ocean turbulence. Furthermore, with the increase of anisotropy factor, the influence of ocean turbulence on the detection probability of HB beam becomes smaller. Meanwhile, with the increase of the temperature variance dissipation rate and the equilibrium parameter, and the decrease of the dynamic energy dissipation rate, the influence of ocean turbulence on the orbital angular momentum transmission is increased.

Estimation of mean turbulent kinetic energy and temperature variance dissipation rates using a spectral chart method

A method aimed at estimating εk and εθ, respectively, the mean dissipation rates of turbulent kinetic energy k and half the temperature variance θ2/2, is developed for slightly heated turbulent flows of air. It is limited to a Prandtl number near unity and applicable to flows where temperature can be treated as a passive scalar. A significant advantage of the method is that εk and εθ can both be estimated from the measurement of a temperature frequency spectrum, Gθθ(f). The method relies on the collapse in the dissipative range of one-dimensional temperature spectra, ϕθ(k1η), when normalized with εθ, εk, and ν. This collapse ensues from a similarity analysis of scale-by-scale budgets of the second-order structure function for the temperature. A generic spectrum ϕθG(k1η), defined in the wavenumber range 0.07 ≤ k1η ≤ 0.7, is used to construct a spectral chart. The method has been tested in several flows and found to be reliable. In particular, it is tested on the axis of a slightly heated round jet, where εk and εθ can be estimated accurately via the budgets of k and θ2/2, and the agreement between these estimates and the spectral chart results is almost perfect.

Characteristics of temperature dissipation rate in a turbulent near wake

This work aims to provide in-depth understanding of the effects the quasi-periodical Kármán vortices produce on the temperature dissipation rate in a turbulent cylinder near wake. Measurements are made at x/d = 10, 20 and 40, where x is the streamwise distance from the cylinder axis and d is the cylinder diameter, with a Reynolds number of 2.5 × 103 based on d and the free-stream velocity. A multi-wire probe is deployed to measure simultaneously the fluctuating temperature and its gradient vector, at nominally the same spatial point in the plane of the mean shear. It is found that the coherent streamwise and spanwise temperature derivatives are similarly distributed with respect to the spanwise vortex, exhibiting twin peaks at the temperature fronts, while the coherent lateral component is linked to the rib-like structures. The temperature variance dissipation rate is found to be statistically independent of the temperature fluctuation when the Kármán vortex is so weak (say at x/d = 40) that the large-scale temperature front resulting from the vortex entrainment ceases to be present and the coherent strain rate at the saddle region is relatively small. In addition, the most effective turbulent mixing is found to take place around the temperature front near the wake centerline, which is in contrast to the conjecture by Hussain and Hayakawa (1987).

A Correlation for the Discontinuity of the Temperature Variance Dissipation Rate at the Fluid-Solid Interface in Turbulent Channel Flows

Discontinuity of the dissipation rate associated with the temperature variance at the fluid-solid interface is analyzed in a turbulent channel flow at a Reynolds number, based on the friction velocity of 395 and a Prandtl number of 0.71. The analysis is performed with a wall-resolved Large Eddy Simulation and the results are used to derive a regression for the dissipation rate discontinuity, which depends only on the fluid-solid thermal diffusivity and conductivity ratios. Wall-resolved Large Eddy Simulations at a higher Reynolds number and a higher Prandtl number are used to investigate the validity of two correlations derived from the regression for the selected thermal properties ratios. The present results are obtained with the open-source Computational Fluid Dynamics solver Code_Saturne, and use the fully conservative fluid-solid thermal coupling capability introduced by the authors in version 5.0.

Influence of oceanic turbulence on propagation of Airy vortex beam carrying orbital angular momentum

With Rytov approximation theory, we derive the analytic expression of detection probability of Airy vortex beam carrying orbital angular momentum (OAM) through an anisotropic weak oceanic turbulence. We investigate the influences of turbulence parameters and beam parameters on the propagation properties of Airy-OAM beam. The numerical simulation results show that the anisotropic oceanic turbulence with a lower dissipation rate of temperature variance, smaller ratio of temperature and salinity contributions to the refractive index spectrum, larger dissipation rate of kinetic energy per unit mass of fluid, bigger inner scale factor, higher anisotropic coefficient causes the larger detection probability of Airy-OAM beam. Moreover, the Airy-OAM beam with a smaller topological charge, larger main ring radius and longer wavelength, has strong resistance to oceanic turbulent interference. Additionally, the detection probability decreases with the increase of receiving aperture size. In comparison with Laguerre-Gaussian-OAM beam, Airy-OAM beam has more anti-interference to turbulence when its topological charge is larger than 5 due to its non-diffraction and self-healing characteristics. The results are useful for underwater optical communication link using Airy-OAM beam.

Polarimetric lidar measurements of aquatic turbulence - laboratory experiment.

Lidar is one of few remote sensing methods available to researchers to sense below the oceanic air-surface. We present polarimetric lidar measurements of turbulence in a laboratory generated turbulent flow. We found that the nearforward light depolarization characterized by the depolarization rate γ(z), varies with the turbulent flow parameter: χ(z)∊(z)1/4, where χ(z) and ∊(z) are the respective depth dependent, temperature variance, and turbulent kinetic energy dissipation rates. The presence of particles in the flow modifies the values of γ in such a way that the ratio γ(z)/α(z) becomes independent of the particle concentration and depends only on χ(z)∊(z)1/4. We posit that the mechanism of light depolarization in turbulent flow with particles is forward scattered light interaction between turbulent refractive index inhomogeneities and flow particles. Such interactions result so that the observed depolarization rate, γ(z), is much larger than expected from 'pure' turbulent flow. Our observations open up the fascinating possibility of using lidar for turbulence measurements of aquatic flows.

A Surface-Layer Study of the Transport and Dissipation of Turbulent Kinetic Energy and the Variances of Temperature, Humidity and CO $$_2$$ 2

We discuss scalar similarities and dissimilarities based on analysis of the dissipation terms in the variance budget equations, considering the turbulent kinetic energy and the variances of temperature, specific humidity and specific CO $$_2$$ content. For this purpose, 124 high-frequency sampled segments are selected from the Boundary Layer Late Afternoon and Sunset Turbulence experiment. The consequences of dissipation similarity in the variance transport are also discussed and quantified. The results show that, for the convective atmospheric surface layer, the non-dimensional dissipation terms can be expressed in the framework of Monin–Obukhov similarity theory and are independent of whether the variable is temperature or moisture. The scalar similarity in the dissipation term implies that the characteristic scales of the atmospheric surface layer can be estimated from the respective rate of variance dissipation, the characteristic scale of temperature, and the dissipation rate of temperature variance.

Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean.

Applying the angular spectrum theory, we derive the expression of a new Hermite-Gaussian (HG) vortex beam. Based on the new Hermite-Gaussian (HG) vortex beam, we establish the model of the received probability density of orbital angular momentum (OAM) modes of this beam propagating through a turbulent ocean of anisotropy. By numerical simulation, we investigate the influence of oceanic turbulence and beam parameters on the received probability density of signal OAM modes and crosstalk OAM modes of the HG vortex beam. The results show that the influence of oceanic turbulence of anisotropy on the received probability of signal OAM modes is smaller than isotropic oceanic turbulence under the same condition, and the effect of salinity fluctuation on the received probability of the signal OAM modes is larger than the effect of temperature fluctuation. In the strong dissipation of kinetic energy per unit mass of fluid and the weak dissipation rate of temperature variance, we can decrease the effects of turbulence on the received probability of signal OAM modes by selecting a long wavelength and a larger transverse size of the HG vortex beam in the source's plane. In long distance propagation, the HG vortex beam is superior to the Laguerre-Gaussian beam for resisting the destruction of oceanic turbulence.

Effects of oceanic turbulence on the propagation of four-petal Gaussian model beams

The evolution of average intensity for four-petal Gaussian model (FPGM) laser beams propagating through the oceanic turbulence is investigated. The analytical expressions of the average intensity at any receiver plane are derived based on the extended Huygens-Fresnel principle. Our results indicate that with the propagation distance increasing long enough in far field area, the initial profile of FPGM laser beams gradually disappears, and finally the profile converts into Gauss-like beam with several small petals. We also find that the spreading of the FPGM laser beam increases with the increasing of waist width of the Gaussian beam and equivalent temperature structure constant. The beam spreading decreases with the increasing of the dissipation rate of temperature variance and the inner scale of turbulence. The salinity fluctuation has a greater contribution to the spreading of the FPGM beam than that of the temperature fluctuation. Our results can be helpful for the design of the free space optical wireless communication and underwater imaging systems operating in oceanic environment.

Autonomous microstructure EM-APEX floats

Fast responding FP-07 thermistors have been incorporated on autonomous profiling EM-APEX floats to measure microscale ocean temperature fluctuations produced by turbulence. In this implementation, the FP-07 thermistor generates an electrical signal corresponding to ocean temperature fluctuations, which is conditioned by an analog circuit board, and digitized and recorded on a custom data acquisition and storage board. The raw and processed temperature observations are stored on a microSD card. Results from eight microstructure EM-APEX floats deployed in the Sargasso Sea are presented here. The slow profiling speed of EM-APEX floats enables them to resolve the higher wavenumber regime of the microscale temperature gradient spectrum, beyond the roll-off wavenumber. The temperature variance dissipation rate χ is computed directly by integrating the observed temperature gradient spectrum over the turbulence wavenumber region without the need to fit the observed temperature gradient spectrum to the empirical spectral form. The accuracy of χ estimated from microstructure EM-APEX floats is confirmed by the agreement, within a factor of 2, between the temperature diffusivity KT computed from our estimates of χ and estimates of diapcynal diffusivity computed from simultaneous tracer measurements. The observed temperature gradient spectra averaged over many realizations resemble the Batchelor spectral form, though individual spectra often do not fit the empirical prediction. Estimates of χ from different floats have similar temporal fluctuations and vertical profiles, further supporting measurement quality. Estimates of χ exhibit a lognormal distribution, as expected for statistically homogeneous isotropic turbulence. Turbulence measurements derived from FP-07 sensors on autonomous profiling floats are of comparable quality to those on conventional free-fall microstructure profilers.

A novel platform to study the effect of small-scale turbulent density fluctuations on underwater imaging in the ocean

Optical signal transmission is an important component of numerous underwater applications, including visibility and electro-optical (EO) communication. In addition to the well-studied effect of particle backscatter, underwater optical signal transmission can be limited by changes in the index of refraction (IOR) due to small-scale variations in temperature and salinity, sometimes called “optical turbulence”. These variations in IOR, which are associated with oceanic turbulence, can lead to the blurring of an underwater optical target, particularly at high spatial frequencies, thus reducing target detail. The 2011 Bahamas Optical Turbulence Experiment (BOTEX) was conducted to investigate this impact of turbulence on underwater optical signal transmission. Investigating naturally occurring “optical turbulence” requires a platform held at depth, capable of concurrent measurements of optical impairment by turbulence, which requires a significant optical path length, as well as associated physical and optical background conditions of the ambient environment. Our novel platform consisted of a high-speed camera and optical target mounted on a 5m-long frame, along with several Nortek Vector Acoustic Doppler Velocimeter (ADV) and PME Conductivity–Temperature (CT) probes, to estimate turbulent kinetic energy and temperature variance dissipation rates experienced by the frame. Data on the background turbulence was collected with a Rockland Oceanographic Vertical Microstructure Profiler, to aid in analysis and guide error estimates of the ADV/CT measurements. This study was the first effort attempting to collect turbulence measurements on a frame designed for the investigation of the effect of density microstructure variations on optical signal transmission in the open ocean. Our results highlight the numerous challenges associated with studying this phenomenon in the dynamic oceanic environment. Here, we present the interpretation of the high-resolution velocity and temperature measurements collected on the frame and discuss the associated difficulties. Despite the numerous challenges, the investigation of the effect of microstructure on underwater optics is needed for efforts aimed at mitigating the impact of “optical turbulence” on underwater EO signal transmission and may help advance optical methods to quantify oceanic microstructure.

Dissipation measurements using temperature microstructure from an underwater glider

Microstructure measurements of temperature and current shear are made using an autonomous underwater glider. The glider is equipped with fast-response thermistors and airfoil shear probes, providing measurements of dissipation rate of temperature variance, χ, and of turbulent kinetic energy, ε, respectively. Furthermore, by fitting the temperature gradient variance spectra to a theoretical model, an independent measurement of ε is obtained. Both Batchelor (εB) and Kraichnan (εK) theoretical forms are used. Shear probe measurements are reported elsewhere; here, the thermistor-derived εB and εK are compared to the shear probe results, demonstrating the possibility of dissipation measurements using gliders equipped with thermistors only. A total of 152 dive and climb profiles are used, collected during a one-week mission in the Faroe Bank Channel, sampling the turbulent dense overflow plume and the ambient water above. Measurement of ε with thermistors using a glider requires careful consideration of data quality. Data are screened for glider flight properties, measurement noise, and the quality of fits to the theoretical models. Resulting dissipation rates from the two independent methods compare well for dissipation rates below 2×10−7 W kg−1. For more energetic turbulence, thermistors underestimate dissipation rates significantly, caused primarily by increased uncertainty in the time response correction. Batchelor and Kraichnan spectral models give very similar results. Concurrent measurements of ε and χ are used to compute the dissipation flux coefficient Γ (or so-called apparent mixing efficiency). A wide range of values is found, with a mode value of Γ≈0.14, in agreement with previous studies. Gliders prove to be suitable platforms for ocean microstructure measurements, complementary to existing methods.

Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties

AbstractGeometrical confinement of turbulent Rayleigh–Bénard convection (RBC) in Cartesian geometries is found to reduce the local Bolgiano length scale in the centre of the cell $L_{B,centre}$ and can therefore be used to study cascade processes in the bulk of RBC. The dependence of $L_{B,centre}$ versus $\varGamma $ suggests a cut-off to the local $L_B$, which depends on the Prandtl number $Pr$ and is of the order of the cell’s smallest dimension. It is also observed that geometrical confinement changes the topology of the flow, causing the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate (averaged over the centre of the cell and normalized by their respective global averages) to exhibit a maximum at a certain $\varGamma $, which roughly coincides with the aspect ratio at which the viscous and thermal boundary layers of the two opposite lateral walls merge. As a result the mean heat flux through the core region also exhibits a maximum. Unlike in the cubic case, we find that geometrical confinement of the flow results in a local balance of the heat flux and the turbulent kinetic energy dissipation rate for $Pr= 4.38$ for all values of the Rayleigh number $Ra$ (up to $10^{10}$), while no balance is observed for $Pr= 0.7$. The need for very high bulk resolution to accurately resolve the gradients of the flow field at high $Ra$ is shown by analysing the second-order structure functions of the vertical velocity and temperature in the bulk of RBC. Under-resolution of the temperature field yields a large error in the dissipative range scaling, which is believed to be an effect of intermittently penetrating thermal plumes. The resolution contrast resulting from the requirement to resolve the thermal plumes and the homogeneous and isotropic background turbulence scales as $\delta _T / \langle \eta _k \rangle _{centre} \sim Ra^{0.1}$ and should therefore be taken into account when tackling very high $Ra$. In the case studied here, under-resolution can have a significant effect on the local heat flux through the centre of the cell.

DNS, LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.

Mixing process on the northeast coast of Hokkaido in summer

Direct measurements using a free-falling micro-profiler were conducted on the northeast coast of Hokkaido in the summer of 2007 to clarify the mixing process in the Soya Warm Current (SWC) region in terms of microstructure. The distribution of the Turner angle (Tu) showed that these regions have a high potential for double diffusive convection, but direct measurements of the turbulent dissipation rate (e) and dissipation of temperature variance (\( \chi_{T} \)) did not necessarily correspond to each other in the SWC region, especially in the offshore front of SWC and farther offshore. The mixing efficiency indicated that, even though the Turner angle (Tu) indicated a high potential for double diffusive convection, turbulent mixing was the main contributor to the mixing process in this region, and double-diffusive convection only contributed partially and sparsely, especially in the boundary off SWC water. The bottom mixed layer (BML) is known to thicken off the SWC. The vertical diffusivity coefficient was enhanced near the bottom (10−4–10−3 m2 s−1) off the SWC, and these results support that turbulence near the bottom off the SWC contributed to the thickening of the BML.

Microstructure measurements along a quasi‐meridional transect in the northeastern Atlantic Ocean

This study presents vertical profiles of turbulence parameters obtained in the upper 100 m of the northeastern Atlantic Ocean along a transect from tropical permanently stratified waters to subpolar seasonally stratified waters in July–August 2009. The focus is to fully characterize the vertical mixing along this transect for further studies related to phytoplankton and nutrient distributions. Derived values of temperature eddy diffusivity KT, of temperature variance dissipation rate χT, and of turbulent kinetic energy dissipation rate ε indicate a northward increase of turbulent mixing below the mixed layer. In the northern stations where the wind stress is sufficiently high, the vertical distributions of ε in the mixed layer follow the wind stress scaling. The related low wind‐scaling factors, and the low values of ε encountered at this cruise, are in agreement with a strongly stratified upper water column at midday in summer.

Mixing in the three-dimensional wake of an experimental modelled vehicle

Experimental results on tracer gas diffusion within the near wake of a simplified model car (Ahmed model with a rear slant angle of 25°) are presented. Pollutant emission is simulated using heated air injected through a small pipe at one side of the model base. Fine cold wire thermometry is used to measure instantaneous temperature excess and variance of temperature gradient in the near wake. Measurements of the three mean velocity components were made using a laser Doppler anemometers system. Characteristics of the mean and fluctuating temperature fields, time-averaged flow streamlines and scalar dissipation measurements are presented and discussed. The local mixing time scale is determined from the measured mean dissipation rate of temperature variance. Its value shows that micromixing is not a limiting phenomenon for chemical reactions in the near wake.