Shear Probes Research Articles

Multiscale rheology from bulk to nano using a quartz tuning fork-atomic force microscope.

Rheological characteristics exhibit significant variations at nanoscale confinement or near interfaces, compared to bulk rheological properties. To bridge the gap between nano- and bulk-scale rheology, allowing for a better and holistic understanding of rheology, developing a single experimental platform that provides rheological measurements across different scales, from nano to bulk, is desirable. Here, we present the novel methodology for multiscale rheology using a highly sensitive atomic force microscope based on a quartz tuning fork (QTF) force sensor. We employ microscale and nanoscale shear probes attached to the QTF, oscillating parallel to a substrate surface for rheological measurements as a function of the tip-substrate distance with sub-nanometer resolution. Silicone oils with viscosities ranging from 5 cSt to 10 000 cSt are used as calibration samples, and we have successfully derived the bulk rheological moduli. Furthermore, an increase in modulus is observed within the regime of tribo-nanorheology at distances less than 50nm from the surface. Through such multiscale measurements, it is confirmed that this increase is due to the formation of a layered structure of silicone oil polymers on the solid surface. These results provide a comprehensive understanding of the tribo-rheological properties of complex fluids across different scales.

ATOMIX benchmark datasets for dissipation rate measurements using shear probes

Turbulent mixing in the ocean, lakes and reservoirs facilitates the transport of momentum, heat, nutrients, and other passive tracers. Turbulent fluxes are proportional to the rate of turbulent kinetic energy dissipation per unit mass, ε. A common method for ε measurements is using microstructure profilers with shear probes. Such measurements are now widespread, and a non-expert practitioner will benefit from best practice guidelines and benchmark datasets. As a part of the Scientific Committee on Oceanographic Research (SCOR) working group on “Analysing ocean turbulence observations to quantify mixing” (ATOMIX), we compiled a collection of five benchmark data of ε from measurements of turbulence shear using shear probes. The datasets are processed using the ATOMIX recommendations for best practices documented separately. Here, we describe and validate the datasets. The benchmark collection is from different types of instruments and covers a wide range of environmental conditions. These datasets serve to guide the users to test their ε estimation methods and quality-assurance metrics, and to standardize their data for archiving.

Multi-Frequency Noise Reduction Method for Underwater Radiated Noise of Autonomous Underwater Vehicles

The multi-frequency noisy vibration of an autonomous underwater vehicle (AUV) is a significant factor affecting the performance of shear probes mounted on the head of AUVs. Many efforts have been made to suppress mechanical radiation noise; however, conventional noise reduction methods have their limitations, such as mode mixing. In order to extract thorough information from the aliasing modes and achieve multi-frequency mode targeted correction, a multi-frequency noise reduction method is proposed, based on secondary decomposition and the multi-mode coherence correction algorithm. Weak impulses in aliasing shear mode are enhanced, and mixing frequencies are isolated for thorough decomposition. Noisy mechanical vibrations in the shear modes are eliminated with the use of the acceleration modes along the identical central frequency series. The denoised modes are used to reconstruct the cleaned shear signal, and the updated spectra are aligned with the standard Nasmyth spectrum. Compared with the raw profiles, the variation in the dissipation rate estimated from the corrected shear is reduced by more than an order of magnitude.

Best practices recommendations for estimating dissipation rates from shear probes

As a part of the Scientific Committee on Oceanographic Research (SCOR) Working Group #160 “Analyzing ocean turbulence observations to quantify mixing” (ATOMIX), we have developed recommendations on best practices for estimating the rate of dissipation of kinetic energy, ε, from measurements of turbulence shear using shear probes. The recommendations provided here are platform-independent and cover the conceivable range of dissipation rates in the ocean, seas, and other natural waters. They are applicable to commonly deployed platforms that include vertical profilers, fixed and moored instruments, towed profilers, submarines, self-propelled ocean gliders, and other autonomous underwater vehicles. The procedure for preparing the shear data for spectral estimation is discussed in detail, as are the quality control metrics that should accompany each estimate of ε. The methods are illustrated using a high-quality ‘benchmark’ dataset, while potential pitfalls are demonstrated with a second dataset containing common faults.

Flippin’ χSOLO, an Upper-Ocean Autonomous Turbulence-Profiling Float

Abstract A new autonomous turbulence profiling float has been designed, built, and tested in field trials off Oregon. Flippin’ χSOLO (FχS) employs a SOLO-II buoyancy engine that not only changes but also shifts ballast to move the center of mass to positions on either side of the center of buoyancy, thus causing FχS to flip. FχS is outfitted with a full suite of turbulence sensors—two shear probes, two fast thermistors, and pitot tube, as well as a pressure sensor and three-axis linear accelerometers. FχS descends and ascends with turbulence sensors leading, thereby permitting measurement through the sea surface. The turbulence sensors are housed antipodal from communication antennas so as to eliminate flow disturbance. By flipping at the sea surface, antennas are exposed for communications. The mission of FχS is to provide intensive profiling measurements of the upper ocean from 240 m and through the sea surface, particularly during periods of extreme surface forcing. While surfaced, accelerometers provide estimates of wave height spectra and significant wave height. From 3.5 day field trials, here we evaluate (i) the statistics from two FχS units and our established shipboard profiler, Chameleon, and (ii) FχS-based wave statistics by comparison to a nearby NOAA wave buoy. Significance Statement The oceanographic fleet of Argo autonomous profilers yields important data that define the state of the ocean’s interior. Continued deployments over time define the evolution of the ocean’s interior. A significant next step will be to include turbulence measurements on these profilers, leading to estimates of thermodynamic mixing rates that predict future states of the ocean’s interior. An autonomous turbulence profiler that employs the buoyancy engine, mission logic, and remote communication of one particular Argo float is described herein. The Flippin’ χSOLO is an upper-ocean profiler tasked with rapid and continuous profiling of the upper ocean during weather conditions that preclude shipboard profiling and that includes the upper 10 m that is missed by shipboard turbulence profilers.

A turbulence data reduction scheme for autonomous and expendable profiling floats

Abstract. Autonomous and expendable profiling-float arrays such as those deployed in the Argo Program require the transmission of reliable data from remote sites. However, existing satellite data transfer rates preclude complete transmission of rapidly sampled turbulence measurements. It is therefore necessary to reduce turbulence data on board. Here we propose a scheme for onboard data reduction and test it with existing turbulence data obtained with a modified SOLO-II profiling float. First, voltage spectra are derived from shear probe and fast-thermistor signals. Then, we focus on a fixed-frequency band that we know to be unaffected by vibrations and that approximately corresponds to a wavenumber band of 5–25 cpm. Over the fixed-frequency band, we make simple power law fits that – after calibration and correction in post-processing – yield values for the turbulent kinetic energy dissipation rate ϵ and thermal-variance dissipation rate χ. With roughly 1 m vertical segments, this scheme reduces the necessary data transfer volume 300-fold to approximately 2.5 kB for every 100 m of a profile (when profiling at 0.2 m s−1). As a test, we apply our scheme to a dataset comprising 650 profiles and compare its output to that from our standard turbulence-processing algorithm. For ϵ, values from the two approaches agree within a factor of 2 87 % of the time; for χ, they agree 78 % of the time. These levels of agreement are greater than or comparable to that between the ϵ and χ values derived from two shear probes and two fast thermistors, respectively, on the same profiler.

High-Sensitivity MEMS Shear Probe for Autonomous Profiling Observation of Marine Turbulence

Autonomous profiling observation of full-depth marine turbulence is very important for ocean research. Anisotropic turbulence near the boundary layer needs to be observed well. However, there is lack of high-spatial-resolution and high-sensitivity methods to fulfill vector turbulence observation. Hence, a highly sensitive bullet-headed MEMS shear probe for observing ocean vector turbulence is developed in this manuscript. The sensing mechanism, design and fabrication are demonstrated in detail. In order to meet the bandwidth requirements for observing ocean turbulence, we perform wet-mode simulations of probe structure to achieve an eigenfrequency of 490 Hz. Through sensitivity calibration experiments, it achieves a sensitivity of 4.84 × 10−2 V·m·s2/kg, which is much higher than those of shear probes reported previously. In addition, the vector test validates that the probe can measure ocean vector turbulence. The results show that the proposed probe is promising in autonomous profiling observation of marine turbulence.

The Statistics of Oceanic Turbulence Measurements. Part II: Shear Spectra and a New Spectral Model

Abstract This manuscript provides (i) the statistical uncertainty of a shear spectrum and (ii) a new universal shear spectrum, and (iii) shows how these are combined to quantify the quality of a shear spectrum. The data from four collocated shear probes, described in Part I, are used to estimate the spectra of shear, Ψ(k), for wavenumbers k ≥ 2 cpm, from data lengths of 1.0 to 50.5 m, using Fourier transform (FT) segments of 0.5 m length. The differences of the logarithm of pairs of simultaneous shear spectra are stationary, distributed normally, independent of the rate of dissipation, and only weakly dependent on wavenumber. The variance of the logarithm of an individual spectrum, , equals one-half of the variance of these differences and is , where Nf is the number of FT segments used to estimate the spectrum. This term σlnΨ provides the statistical basis for constructing the confidence interval of the logarithm of a spectrum, and thus, the spectrum itself. A universal spectrum of turbulence shear is derived from the nondimensionalization of 14 600 spectra estimated from 5 m segments of data. This spectrum differs from the Nasmyth spectrum and from the spectrum of Panchev and Kesich by 8% near its peak, and is approximated to within 1% by a new analytic equation. The difference between the logarithms of a measured and a universal spectrum, together with the confidence interval of a spectrum, provides the statistical basis for quantifying the quality of a measured shear (and velocity) spectrum, and the quality of a dissipation estimate that is derived from the spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a spectrum of turbulent shear or velocity that is derived from a finite number of discrete Fourier transform segments, and they can be used to quantify the quality of a spectrum.

The Statistics of Oceanic Turbulence Measurements. Part I: Shear Variance and Dissipation Rates

Abstract An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy ϵ at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂w/∂x while the other measures ∂υ/∂x, where w and υ are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using (and similarly for the υ component), for averaging lengths, L ranging from 1 to 104 Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of between pairs of probes are stationary, zero mean, and distributed normally for averaging lengths of L = ∼30 to 104 Kolmogorov lengths. The variance of the differences, , scales as L−7/9, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10−10 to ∼10−5 W kg−1. The variance decreases more slowly than L−1 because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an ϵ estimate such as the 95% interval . This result also applies to the traditional ϵ estimates that are made by way of spectral integration, after L is adjusted for the truncation of the shear spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.

Galaxy blending effects in deep imaging cosmic shear probes of cosmology

ABSTRACT Upcoming deep imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time will be confronted with challenges that come with increased depth. One of the leading systematic errors in deep surveys is the blending of objects due to higher surface density in the more crowded images; a considerable fraction of the galaxies which we hope to use for cosmology analyses will overlap each other on the observed sky. In order to investigate these challenges, we emulate blending in a mock catalogue consisting of galaxies at a depth equivalent to 1.3 yr of the full 10-yr Rubin Observatory that includes effects due to weak lensing, ground-based seeing, and the uncertainties due to extraction of catalogues from imaging data. The emulated catalogue indicates that approximately 12 per cent of the observed galaxies are ‘unrecognized’ blends that contain two or more objects but are detected as one. Using the positions and shears of half a billion distant galaxies, we compute shear–shear correlation functions after selecting tomographic samples in terms of both spectroscopic and photometric redshift bins. We examine the sensitivity of the cosmological parameter estimation to unrecognized blending employing both jackknife and analytical Gaussian covariance estimators. An ∼0.025 decrease in the derived structure growth parameter S8 = σ8(Ωm/0.3)0.5 is seen due to unrecognized blending in both tomographies with a slight additional bias for the photo-z-based tomography. This bias is greater than the 2σ statistical error in measuring S8.

An Empirical Evaluation of Turbulence Closure Models in the Coastal Ocean

AbstractA comprehensive in situ data set was obtained for the purpose of testing upper ocean turbulence models. The data set was collected in 38 m deep water over the North Carolina shelf. Available time series of surface meteorological forcing, including waves, winds, and heat fluxes, as well as underwater profiles of temperature, salinity, and horizontal velocity, were found suitable for constraining and testing numerical models in realistic environmental scenarios of the coastal ocean. The Navy Coastal Ocean Model was tested in a vertical 1‐D mode with a suite of previously incorporated subgrid turbulence closure models. Modeled output of turbulent quantities, such as the turbulent kinetic energy and its dissipation rate, were evaluated against comparable turbulence observations from a bottom mounted acoustic velocity profiler and a glider mounted turbulent shear probe. The results demonstrate a steady incremental skill increase among available turbulence closure models over several decades of their development, however the correlation with observed turbulence remains weak. The analysis of remaining model errors identified a need to add wave‐dependence to the air‐sea momentum flux formulation to account for waves that are out of balance or misaligned with the wind.

Technical note: Turbulence measurements from a light autonomous underwater vehicle

Abstract. A self-contained turbulence instrument from Rockland Scientific was installed on a light autonomous underwater vehicle (AUV) from OceanScan Marine Systems and Technology Lda. We report on the data quality and discuss limitations of dissipation estimated from two shear probes during a deployment in the Barents Sea in February 2021. The AUV mission lasted for 5 h, operating at a typical horizontal speed of 1.1 m s−1. The AUV was programmed to find and cross the maximum along-path thermal gradient at 10, 20 and 30 m depths along 4 km transects. Although the AUV vibrations contaminate the shear probe records, the noise is mitigated by removing vibration-induced components from shear spectra using the accelerometer signal measured in multiple directions. Dissipation rate estimates in the observed transects varied in the range 1×10-8 and 6×10-6 W kg−1, with the values from the two orthogonal probes typically in agreement to within a factor of 2. Dissipation estimates from the AUV show good agreement with nearby vertical microstructure profiles obtained from the ship during the transects, indicating that the turbulence measurements from the AUV are reliable for this relatively turbulent environment. However, the lowest reliable dissipation rates are limited to 5×10-8 W kg−1, making this setup unfit for use in quiescent environments.

Design and Motion Performance Analysis of Turbulent AUV Measuring Platform.

The use of a multi-functional autonomous underwater vehicle (AUV) as a platform for making turbulence measurements in the ocean is developed. The layout optimization of the turbulence package and platform motion performance are limitation problems in turbulent AUV design. In this study, the computational fluid dynamics (CFD) method has been used to determine the optimized layout position and distance of the shear probe integrated into an AUV. When placed 0.8 D ahead of the AUV nose along the axis, the shear probe is not influenced by flow distortion and can contact the water body first. To analyze the motion of the turbulence AUV, the dynamic model of turbulence AUV for planar flight is obtained. Then, the mathematical equations of speed and angle of attack under steady-state motion have also been obtained. By calculating the hydrodynamic coefficients of the turbulence AUV and given system parameters, the simulation analysis has been conducted. The simulation results demonstrated that the speed of turbulent AUV is 0.5–1 m/s, and the maximum angle of attack is less than 6.5°, which meets the observation requirements of the shear probe. In addition, turbulence AUV conducted a series of sea-trials in the northern South China Sea to illustrate the validity of the design and measurement. Two continuous profiles (1000 m) with a horizontal distance of 10 km were completed, and numerous high-quality spatiotemporal turbulence data were obtained. These profiles demonstrate the superior flight performance of turbulence AUV. Analysis shows that the measured data are of high quality, with the shear spectra being in very good agreement with the Nasmyth spectrum. Dissipation rates are consistent with background shear. When shear velocity is weak, the measurement of dissipation rate is 10−10 W Kg−1. All indications are that the turbulence AUV is suitable for long-term, contiguous ocean microstructure measurements, which will provide data needed to understand the temporal and spatial variability of the turbulent processes in the oceans.

A New Cross-Platform Instrument for Microstructure Turbulence Measurements

This study developed a new cross-platform instrument for microstructure turbulence measurement (CPMTM) and evaluated its performance. The CPMTM is designed as an “all-in-one” payload that can be easily integrated with a variety of marine instrumentation platforms. The sensors in the CPMTM include two shear probes, a fast-response temperature probe, and an accelerometer for monitoring vibrations. In addition, a custom-designed flexible connection vibration-damping device is used to isolate platform vibrations. To validate the CPMTM performance, a direct comparison was carried out with a reference acoustic Doppler velocimeter in a controlled flume for four background turbulence levels. The results of the comparison show that the velocity spectra measured by the CPMTM and ADV w components are in agreement, which demonstrates the ability of the CPMTM to acquire accurate turbulence data. Furthermore, the CPMTM was integrated into the long-range Sea-Whale 2000 AUV and tested in the northern South China Sea in September 2020. The data collected by the CPMTM show that the measured shear spectrum of the noise reduction agrees well with the empirical Nasmyth spectrum. Turbulent kinetic energy dissipation rates as low as 7 × 10−10 W kg−1 can be resolved. Laboratory and field experiments illustrate that the CPMTM has an extraordinarily low noise level and is validated for turbulence measurements.

Moored Turbulence Measurements using Pulse-Coherent Doppler Sonar

AbstractUpper-ocean turbulence is central to the exchanges of heat, momentum, and gasses across the air/sea interface, and therefore plays a large role in weather and climate. Current understanding of upper-ocean mixing is lacking, often leading models to misrepresent mixed-layer depths and sea surface temperature. In part, progress has been limited due to the difficulty of measuring turbulence from fixed moorings which can simultaneously measure surface fluxes and upper-ocean stratification over long time periods. Here we introduce a direct wavenumber method for measuring Turbulent Kinetic Energy (TKE) dissipation rates, ϵ, from long-enduring moorings using pulse-coherent ADCPs. We discuss optimal programming of the ADCPs, a robust mechanical design for use on a mooring to maximize data return, and data processing techniques including phase-ambiguity unwrapping, spectral analysis, and a correction for instrument response. The method was used in the Salinity Processes Upper-ocean Regional Study (SPURS) to collect two year-long data sets. We find the mooring-derived TKE dissipation rates compare favorably to estimates made nearby from a microstructure shear probe mounted to a glider during its two separate two-week missions for (10−8) ≤ ϵ ≤ (10−5) m2 s−3. Periods of disagreement between turbulence estimates from the two platforms coincide with differences in vertical temperature profiles, which may indicate that barrier layers can substantially modulate upper-ocean turbulence over horizontal scales of 1-10 km. We also find that dissipation estimates from two different moorings at 12.5 m, and at 7 m are in agreement with the surface buoyancy flux during periods of strong nighttime convection, consistent with classic boundary layer theory.

A novel two-dimensional high SNR MEMS shear stress sensor for ocean turbulence

Ocean turbulence observation is essentially important to the study of microscopic structure and macroscopic motion. The shear probe sensor is one of the effective ways for turbulence measurement. However, most of the shear probe sensors sensitive in a single direction and the observation of turbulence is short of directivity characteristics. In this work, a ciliated two-dimensional MEMS shear stress sensor with high signal to noise ratio is designed for ocean turbulence measurement. The MEMS sensor is composed of four silicon beams with varistors and a bionic cilium. To evaluate the performance of the sensor, comparisons with a PNS shear probe (PNS06) are made in a calibration water tank. The results reveal that the MEMS sensor performs similarly to the PNS shear probe in the same experimental condition and has high signal to noise ratio. Additionally, the MEMS sensor is highly sensitive to flow direction. The MEMS sensor is found to work well under the hydrostatic pressure of 40 MPa, which make it suitable for deep ocean turbulence measurements.

Best Practices for Comparing Ocean Turbulence Measurements across Spatiotemporal Scales

AbstractThe turbulent energy dissipation rate in the ocean can be measured by using rapidly sampling microstructure shear probes, or by applying a finescale parameterization to coarser-resolution density and/or shear profiles. The two techniques require measurements that are on different spatiotemporal scales and generate dissipation rate estimates that also differ in spatiotemporal scale. Since the distribution of the measured energy dissipation rate is closer to lognormal than normal and fluctuates with the strength of the turbulence, averaging the two approaches on equivalent spatiotemporal scales is critical for accurately comparing the two methods. Here, microstructure data from the 1997 Brazil Basin Tracer Release Experiment (BBTRE) is used to demonstrate that comparing averages of the dissipation rate on different spatiotemporal scales can generate spurious discrepancies of up to a factor of order 10 in regions of strong turbulence and smaller biases of up to a factor of 2 in the presence of weaker turbulence.

Modular, Flexible, Low-Cost Microstructure Measurements: The Epsilometer

AbstractThe Epsilometer (“epsi”) is a small (7 cm diameter × 30 cm long), low-power (0.15 W), and extremely modular microstructure package measuring thermal and kinetic energy dissipation rates, χ and ε. Both the shear probes and FP07 temperature sensors are fabricated in house following techniques developed by Michael Gregg at the Applied Physics Laboratory/University of Washington (APL/UW). Sampling eight channels (two shear, two temperature, three-axis accelerometer, and a spare for future sensors) at 24 bit precision and 325 Hz, the system can be deployed in standalone mode (battery power and recording to microSD cards) for deployment on autonomous vehicles, wave powered profilers, or it can be used with dropping body termed the “epsi-fish” for profiling from boats, autonomous surface craft or ships with electric fishing reels or other simple winches. The epsi-fish can also be used in real-time mode with the Scripps “fast CTD” winch for fully streaming, altimeter-equipped, line-powered, rapid-repeating, near-bottom shipboard profiles to 2200 m. Because this winch has a 25 ft (~7.6 m) boom deployable outboard from the ship, contamination by ship wake is reduced one to two orders of magnitude in the upper 10–15 m. The noise floor of ε profiles from the epsi-fish is ~10−10 W kg−1. This paper describes the fabrication, electronics, and characteristics of the system, and documents its performance compared to its predecessor, the APL/UW Modular Microstructure Profiler (MMP).

Estimate of turbulent energy dissipation rate using free-fall and CTD-attached fast-response thermistors in weak ocean turbulence

The measurement of turbulence is necessary to quantify the vertical, diapycnal transport of heat, water and substances influencing climate, nutrient supply and marine ecosystems. As specialist instrumentation and ship-time are required to conduct microstructure measurements to quantify turbulence intensity, there is a need for more inexpensive and easy measurement methods. This study demonstrated that the turbulent energy dissipation rate, ε, estimated from fast-response thermistors Fastip Probe model 07 (FP07) with the depth-average of a > 10 m depth interval well agreed with those from current shear probes to a range of 10–11 W/kg (m2s−3) in the two casts of the most accurate and stable free-fall vertical microstructure profiler, VMP6000 in the Oyashio water. This range cannot be measured with velocity shear probes equipped in smaller profilers in which the lower limit of ε > O (10–10) W/kg. These results extend turbulence measurements using the FP07 to 10–11 W/kg. They may be especially useful for turbulence observations in deep oceans where ε is generally weak (< 10–10 W/kg). As FP07 are much less sensitive to instrument vibrations than current shear and may be attached to various observational platforms such as temperature-conductivity-depth (CTD) profilers and floats. The CTD-attached FP07 observations near the VMP6000 profiles demonstrated their capabilities in the ε range of 10–11–10–8 W/kg by data screening using a Wsd>0.1(W-0.3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}>0.1(W-0.3)$$\\end{document} criterion (1 s mean lowering rate W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W$$\\end{document} m/s and its standard deviation Wsd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}$$\\end{document}) under rough conditions where the cast-mean Wsd>\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}>$$\\end{document} 0.07 m/s and the standard deviation of Wsd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${W}_{\\mathrm{sd}}$$\\end{document} in each cast σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document} >0.05 m/s.

A wavelet-entropy based segmentation of turbulence measurements from a moored shear probe near the wavy sea surface

In this study, we explore the applicability of a wavelet-entropy based segmentation technique in reduction of motion-induced contaminations in time-domain from subsurface turbulence measurements made by a moving shear probe. After the quality screening of data, the Shannon entropy procedure is combined with a time-dependent adaptive wavelet thresholding method to split each 60-s long shear segment into a number of motion-reduced subblocks. The wavelet-entropy strategy leads to preventing the false detection effect caused by applying either wavelet de-noising or Shannon entropy alone for conditions where the turbulence (strongly) overlap with scales induced by waves or platform motions. The longest stationary subblock, with a size greater than 16-s, is then used to extract the Turbulent Kinetic Energy (TKE) dissipation rate, varepsilon. Efficiency of the proposed method is verified by comparing with varepsilon measurements made by a nearby free-falling microstructure profiler. While the quality of observations is constrained by a number of factors such as sensors’ angle of attack, and the wave kinematical and dynamical effects, results demonstrate significant improvements, by approximately a factor of 5–10, compared with varepsilon measurements from each 60-s segment using the Goodman et al. [13] method. Furthermore, the magnitudes of the motion-corrected varepsilon using the proposed method is largely consistent with the scaling suggested by Terray et al. [30].