Thorpe Scale Research Articles

Deep circulation driven by strong vertical mixing in the Timor Basin

The importance of deep mixing in driving the deep part of the overturning circulation has been a long debated question at the global scale. Our observations provide an illustration of this process at the Timor Basin scale of ∼1000 km. Long-term averaged moored velocity data at the Timor western sill suggest that a deep circulation is present in the Timor Basin. An inflow transport of ∼0.15 Sv is observed between 1600 m and the bottom at 1890 m. Since the basin is closed on its eastern side below 1250 m depth, a return flow must be generated above 1600 m with a ∼0.15 Sv outflow. The vertical turbulent diffusivity is inferred from a heat and transport balance at the basin scale and from Thorpe scale analysis. Basin averaged vertical diffusivity is as large as 1 × 10−3 m2 s−1. Observations are compared with regional low-resolution numerical simulations, and the deep observed circulation is only recovered when a strong vertical diffusivity resulting from the parameterization of internal tidal mixing is considered. Furthermore, the deep vertical mixing appears to be strongly dependent on the choice of the internal tide mixing parameterization and also on the prescribed value of the mixing efficiency.

TURBULENT MIXING PROCESSES IN LABANI CHANNEL, THE MAKASSAR STRAIT

Study on turbulent mixing processes in Labani Channel, the Makassar Strait, was conducted by using the INSTANT (International Nusantara Stratification And Transport) program dataset, in Juli 2005. The turbulent mixing process was evaluated using Thorpe method, where the overturning eddies were revealed by density inversions in CTD (Conductivity Temperature Depth) profiles. All individual identified-overturn regions was validated by the GK’s test (Galbraith and Kelly test) where at first noise on CTD signals had been removed by applying wavelet denoising. A large number of overturn regions with Thorpe scale (LT) less than 0.5 m were detected in the thermocline layer of Makassar Strait. Based on linear relationship between Thorpe and Ozmidov scale, order of magnitude of the turbulent energy kinetic dissipation rate in Labani Channel was estimated about 10-11- 10-5Wkg-1 and density eddy diffusivity Kρ(10-6 – 10-2) m2/s . The strong of turbulen mixing was found at the layer of NPSW at 150 m depth and NPIW at 300 m depth, indicated by high values of Kρ (O = 10-3 – 10-2 m2s-1). It reveals that turbulent mixing has an important role on determining ITF water mass character. Keywoods: turbulent mixing, wavelet denoising, overturn region, Thorpe method, Labani Channel, Makassar Srait.

Trains of large Kelvin‐Helmholtz billows observed in the Kuroshio above a seamount

AbstractTrains of large Kelvin‐Helmholtz (KH) billows within the Kuroshio current at ~230 m depth off southeastern Taiwan and above a seamount were observed by shipboard instruments. The trains of large KH billows were present in a strong shear band along the 0.55 m s−1 isotach within the Kuroshio core; they are presumably produced by flow interactions with the rapidly changing topography. Each individual billow, resembling a cat's eye, had a horizontal length scale of 200 m, a vertical scale of 100 m, and a timescale of 7 min, near the local buoyancy frequency. Overturns were observed frequently in the billow cores and the upper eyelids. The turbulent kinetic energy dissipation rates estimated using the Thorpe scale had an average value of O(10−4) W kg−1 and a maximum value of O(10−3) W kg−1. The turbulence mixing induced by the KH billows may exchange Kuroshio water with the surrounding water masses.

Deep ventilation in the Okinawa Trough induced by Kerama Gap overflow

AbstractNear‐bottom water flowing over the Kerama Gap's sills is thought to ventilate the deep water below ∼1100 m depth in the Okinawa Trough and then upwell with 5–10 years residence time. The present study follows up on this phenomenon, using comprehensive profile data of temperature, salinity, dissolved oxygen, currents and turbulence obtained by intensive shipboard observations performed in June 2013 and June 2014 in the region. Strong near‐bottom subtidal flow with speeds exceeding 0.5 m s−1 was observed within a layer of about 100 m thickness over the western side of the peak of the main sill. Temperature and salinity sections along the Kerama Gap indicated some depressions and overturns of the deep water downstream of the strong overflow, suggesting the existence of breaking internal gravity waves and hydraulic jumps. Associated vertical diffusivities, estimated using the Thorpe scale and the buoyancy frequency, were three to four orders of magnitude larger than typical values observed in the thermocline of the open ocean (∼10−5 m2 s−1). The dissolved oxygen section also indicated strong vertical mixing and associated upwelling with the entrainment of the near‐bottom overflow water into the lower thermocline beneath the Kuroshio in the Okinawa Trough. The present study not only supports the previous conceptual model but also provides new evidence that the Okinawa Trough is an upwelling location where nutrient rich Philippine Sea intermediate water is sucked up into the lower thermocline below the Kuroshio.

Study of the overturning length scales at the Spanish planetary boundary layer

Abstract. The focus of this paper is to analyse the behaviour of the maximum Thorpe displacement (dT)max and the Thorpe scale LT at the atmospheric boundary layer (ABL), extending previous research with new data and improving our studies related to the novel use of the Thorpe method applied to ABL. The maximum Thorpe displacements vary between −900 and 950 m for the different field campaigns. The Thorpe scale LT ranges between 0.2 and 680 m for the different data sets which cover different stratified mixing conditions (turbulence shear-driven and convective regions). We analyse the relationship between (dT)max and the Thorpe scale LT and we deduce that they verify a power law. We also deduce that there is a difference in exponents of the power laws for convective conditions and shear-driven conditions. These different power laws could identify overturns created under different mechanisms.

Estimates of the temperature flux–temperature gradient relation above a sea floor

The relation between the flux of temperature (or buoyancy), the vertical temperature gradient and the height above the bottom is investigated in an oceanographic context, using high-resolution temperature measurements. The model for the evolution of a stratified layer by Balmforth et al. (J. Fluid Mech., vol. 355, 1998, pp. 329–358) is reviewed and adapted to the case of a turbulent flow above a wall. Model predictions are compared with the average observational estimates of the flux, exploiting a flux estimation method proposed by Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193). This estimation method enables the disentanglement of the dependence of the average flux on the height above the bottom and on the background temperature gradient. The classical N-shaped flux–gradient relation is found in the observations. The model and the observations show similar qualitative behaviour, despite the strong simplifications used in the model. The results shed light on the modulation of the temperature flux by the presence of the boundary, and support the idea of a turbulent flux following a mixing-length argument in a stratified flow. Furthermore, the results support the use of Thorpe scales close to a boundary, if sufficient averaging is performed, suggesting that the Thorpe scales are affected by the boundary in a similar way to the mixing length.

Observation of summertime upwelling off the eastern and northeastern coasts of Hainan Island, China

Using cruise observations and reanalysis data, this study analyzes the effects of wind, freshwater, and turbulent mixing on the two upwellings: one is off the eastern coast of Hainan Island (HEU) and the other is off the northeastern coast of Hainan Island (HNEU). During the cruise in 2009, the HNEU occurred with southwesterly to southeasterly wind. The relative large values of turbulent kinetic energy dissipation rate and diffusivity estimated from the Thorpe scale indicate that the upwelling water is further uplifted to the surface by strong turbulent mixing in the HNEU region. But the HEU was not observed under the southeasterly wind. During the cruise in 2012, the HNEU disappeared in the upper layer with freshwater covered and southeasterly wind, while the apparent HEU only accompanied with southwesterly wind. To obtain the general characteristics, we define three types of upwelling patterns, i.e., the intensified HEU, the intensified HNEU, and both HEU and HNEU in one day, using the reanalysis data. The composites of sea surface temperature (SST), wind, and precipitate for each upwelling pattern identify that the HNEU is associated with the prevailing southeasterly wind and can be limited in the lower layer when it is covered by freshwater. But the HEU is mainly driven by southwesterly wind but is not remarkably affected by freshwater.

Physical and optical properties of phytoplankton-rich layers in a coastal fjord: a step toward prediction and strategic sampling of plankton patchiness

Dense aggregations of phytoplankton in layers or patches alter the optical and physical properties of the water column and result in significant hetero- geneity in trophic and demographic rates of local plank- ton populations. Determining the factors driving patch formation, persistence, intensity, and dissipation is key to understanding the ramifications of plankton patchi- ness in marine systems. Regression and multi-parametric statistical analyses were used to identify the physical and optical properties associated with 71 phytoplank- ton-rich layers (PRLs) identified from 158 CTD profiles collected between 2008 and 2010 in East Sound, Wash- ington, USA. Generalized additive models (GAMs) were used to explore water column properties associated with and characterizing PRLs. Patch presence was associated with increasing water column stability represented by the Brunt-Vaisala frequency (N 2 ), Thorpe scale (Lt), and turbulent energy dissipation rate (e). A predictive re- gression identified patch presence with 100% accuracy when log10(N 2 ) = �1 and 70% of the cases when log10(e) = �3. A GAM of passively measured variables, which did not include fluorescence, was able to model patch inten- sity with considerable agreement (R 2 = 0.58), and the fit was improved by including fluorescence (R 2 = 0.69). Flu- orescence alone was an insufficient predictor of PRLs, due in part to the influence of non-photochemical quenching (NPQ) in surface waters and the wide range of fluorescence intensities observed. The results show that a multi-parametric approach was necessary to char- acterize phytoplankton patches and that physical struc- ture, resulting in steep gradients in bio-optical proper- ties, hold greater predictive power than bio-optical properties alone. Integration of these analytical ap- proaches will aid theoretical studies of phytoplankton patchiness but also improve sampling strategies in the field that utilize autonomous, in situ instrumentation.

Numerical Modeling of Multiscale Dynamics at a High Reynolds Number: Instabilities, Turbulence, and an Assessment of Ozmidov and Thorpe Scales

Abstract A high–Reynolds number direct numerical simulation (DNS) is employed to explore the instability and turbulence dynamics accompanying an idealized multiscale flow that approximates such environments observed throughout the atmosphere. The DNS describes the superposition of a stable gravity wave (GW) and a stable, oscillatory, finescale shear flow that together yield significant wave–wave interactions, GW breaking, Kelvin–Helmholtz instabilities (KHI), fluid intrusions, and turbulence. Larger-scale GW breaking and KHI events account for the strongest turbulence intensities, with intrusions competing with KHI and GW breaking at smaller spatial scales and later times. These dynamics drive a series of sheet-and-layer structures in the velocity, stability, and dissipation fields that persist for many buoyancy periods. Measures of local turbulence intensities include energy dissipation rates, Ozmidov and Thorpe scales (LO and LT, respectively), and a buoyancy Reynolds number sufficient to ensure sustained, strong turbulence events. These exhibit significant variability between and within instability events of different types. The Ozmidov and Thorpe scales for individual events are employed to assess variations of their ratio, C = LO/LT, with time. The value of C is highly variable with event type and time but typically increases with time because significant fluid overturning most often precedes turbulence. The value of C determined for the entire domain varies from 0 prior to instability to approximately 2 or larger at late times, with minima (maxima) prior to (following) significant instability and turbulence events. This appears to preclude an assumption that C is constant in stratified flows, except perhaps as an event average that may depend on event type.

An examination of double‐diffusive processes in a mesoscale eddy in the Arctic Ocean

AbstractTemperature and salinity measurements of an Atlantic Water mesoscale eddy in the Arctic Ocean's Canada Basin are analyzed to understand the effects of velocity shear on a range of double‐diffusive processes. Double‐diffusive structures in and around the eddy are examined through the transition from low shear (outside the eddy and within its solid body core) to high geostrophic shear zones at the eddy flanks. The geostrophic Richardson number takes large values where a double‐diffusive staircase is observed and lowest values at the eddy flanks where geostrophic velocity is largest and a well‐formed staircase is not present. A Thorpe scale analysis is used to estimate turbulent diffusivities in the flank regions. Double‐diffusive and turbulent heat, salt, and buoyancy fluxes from the eddy are computed, and used to infer that the eddy decays on time scales of around 4–9 years. Fluxes highlight that Atlantic Water heat within the eddy can be fluxed downward into deeper water layers by means of both double‐diffusive and turbulent mixing. Estimated lateral variations in vertical fluxes across the eddy allow for speculation that double diffusion speeds up the eddy decay, having important implications for the transfer of Atlantic Water heat in the Arctic Ocean.

Biases in Thorpe-Scale Estimates of Turbulence Dissipation. Part II: Energetics Arguments and Turbulence Simulations

AbstractThis paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the available potential energy of the mean flow to drive mixing. In shear-driven flows, the rms of the Thorpe displacement, known as the Thorpe scale is shown to be equivalent to the turbulent component of the displacement. In this case, the Thorpe scale approximates the Ozmidov scale, or, which is the same, the Thorpe scale is the appropriate scale to diagnose mixing and dissipation. However, when mixing is driven by the available potential energy of the mean flow (convective-driven mixing), this study shows that the Thorpe scale is (much) larger than the Ozmidov scale. Using the rms of the Thorpe displacement overestimates dissipation and mixing, since the amount of turbulent available potential energy (measured by the turbulent displacement) is only a fraction of the total available potential energy (measured by the Thorpe scale). Corrective measures are discussed that can be used to diagnose mixing from knowledge of the Thorpe displacement. In a companion paper, Mater et al. analyze field data and show that the Thorpe scale can indeed be much larger than the Ozmidov scale.

A simple approach for estimating the refractive index structure parameter (Cn²) profile in the atmosphere.

Utilizing the so-called Thorpe scale as a measure of the turbulence outer scale, we propose a physically-based approach for the estimation of Cn2 profiles in the lower atmosphere. This approach only requires coarse-resolution temperature profiles (a.k.a., soundings) as input, yet it has the intrinsic ability to capture layers of high optical turbulence. The prowess of this computationally inexpensive approach is demonstrated by validations against observational data from a field campaign over Mauna Kea, Hawaii.

Instabilities in nonlinear internal waves on the Washington continental shelf

Previous studies have identified two primary mechanisms (shear instability and convective instability) by which nonlinear internal waves (NLIWs) induce mixing on continental shelves. To determine the relative importance of these and their dependence on background flow conditions, we examine a much longer (6 month) data set from a moored ADCP/thermistor chain with 2 m vertical spacing in which over 600 NLIWs are detected. Turbulent properties of the 318 waves with detectable overturning instabilities are documented using Thorpe scales. The 130 waves detected while an ADCP was functioning are classified based on a Froude number criterion (Fr = uc, where u is velocity in the wave propagation direction, c is the wave phase speed). Of these, 108 waves are identified as shear-instability (Type I; Fr 1). Composites are constructed by averaging in a wave coordinate frame over all waves in each category, showing the mean spatial structure of dissipation and other wave quantities. Turbulence is highest at the sheared interface for Type I waves and throughout the wave core for Type II waves. No relationship between wave instability mechanisms and wave/background parameters such as wave steepness, stratification, or mean flow is found, except that unstable waves tend to be more energetic, demonstrating a need to better understand wave propagation and breaking in complex and variable coastal oceanographic background flows.

동해 남서부 해역의 대륙사면에서 Thorpe 규모(scale)를 이용한 연직 난류 확산계수 추정

Thorpe scale analysis was performed using two sets of 25-hour-long hourly CTD data. Raw density profiles collected on the continental slope of the southwestern East Sea were post-processed to reduce instrument noises and measurement errors. Density inversions were detected by applying the overturn ratio test proposed by Gargett and Garner (2008). The value of <TEX>$K_z$</TEX> below the main thermocline estimated with the Osborn parameterization was <TEX>$5.3{\times}10^{-4}(1.1{\times}10^{-4})m^2s^{-1}$</TEX> and that with the Shih parameterization was <TEX>$5.9{\times}10^{-5}(2.4{\times}10^{-5})m^2s^{-1}$</TEX>during the spring (neap) tidal period. This result suggests that internal tides can enhance vertical mixing in the observation region.

Pathways, Volume Transport, and Mixing of Abyssal Water in the Samoan Passage

AbstractThe flow of dense water through the Samoan Passage accounts for the major part of the bottom water renewal in the North Pacific and is thus an important element of the Pacific meridional overturning circulation. A recent set of highly resolved measurements used CTD/LADCP, a microstructure profiler, and moorings to constrain the complex pathways and variability of the abyssal flow. Volume transport estimates for the dense northward current at several sections across the passage, calculated using direct velocity measurements from LADCPs, range from 3.9 × 106 to 6.0 × 106 ± 1 × 106 m3 s−1. The deep channel to the east and shallower pathways to the west carried about equal amounts of this volume transport, with the densest water flowing along the main eastern channel. Turbulent dissipation rates estimated from Thorpe scales and direct microstructure agree to within a factor of 2 and provide a region-averaged value of O(10−8) W kg−1 for layers colder than 0.8°C. Associated diapycnal diffusivities and downward turbulent heat fluxes are about 5 × 10−3 m2 s−1 and O(10) W m−2, respectively. However, heat budgets suggest heat fluxes 2–6 times greater. In the vicinity of one of the major sills of the passage, highly resolved Thorpe-inferred diffusivity and heat flux were over 10 times larger than the region-averaged values, suggesting the mismatch is likely due to undersampled mixing hotspots.

Using an ADCP to Estimate Turbulent Kinetic Energy Dissipation Rate in Sheltered Coastal Waters

AbstractTurbulent microstructure and acoustic Doppler current profiler (ADCP) data were collected near Tacoma Narrows in Puget Sound, Washington. Over 100 coincident microstructure profiles have been compared to ADCP estimates of turbulent kinetic energy dissipation rate (ϵ). ADCP dissipation rates were calculated using the large-eddy method with theoretically determined corrections for sensor noise on rms velocity and integral-scale calculations. This work is an extension of Ann Gargett’s approach, which used a narrowband ADCP in regions with intense turbulence and strong vertical velocities. Here, a broadband ADCP is used to measure weaker turbulence and achieve greater horizontal and vertical resolution relative to the narrowband ADCP. Estimates of ϵ from the Modular Microstructure Profiler (MMP) and broadband ADCP show good quantitative agreement over nearly three decades of dissipation rate, 3 × 10−8–10−5 m2 s−3. This technique is most readily applied when the turbulent velocity is greater than the ADCP velocity uncertainty (σ) and the ADCP cell size is within a factor of 2 of the Thorpe scale. The 600-kHz broadband ADCP used in this experiment yielded a noise floor of 3 mm s−1 for 3-m vertical bins and 2-m along-track average (≈four pings), which resulted in turbulence levels measureable with the ADCP as weak as 3 × 10−8 m2 s−3. The value and trade-off of changing the ADCP cell size, which reduces noise but also changes the ratio of the Thorpe scale to the cell size, are discussed as well.

Validation of Thorpe-scale-derived vertical diffusivities against microstructure measurements in the Kerguelen region

Abstract. The Thorpe scale is an energy-containing vertical overturning scale of large eddies associated with shear-generated turbulence. This study investigates indirect estimates of vertical diffusivities from the Thorpe scale method in the polar front region east of the Kerguelen Islands based on fine-scale density profiles gathered during the 2011 KEOPS2 (KErguelen Ocean and Plateau compared Study 2) cruise. These diffusivities are validated in comparison with diffusivities estimated from the turbulence dissipation rate directly measured via a TurboMAP (Turbulence ocean Microstructure Acquisition Profiler) microstructure profiler. The results are sensitive to the choice of the diffusivity parameterization and the overturn ratio Ro, and the optimal results have been obtained from the parameterization by Shih et al. (2005) and the Ro = 0.25 criterion, rather than the parameterization by Osborn (1980) and the Ro = 0.2 criterion originally suggested by Gargett and Garner (2008). The Thorpe-scale-derived diffusivities in the KEOPS2 region show a high degree of spatial variability, ranging from a canonical value of O(10−5) m2 s−1 in the Winter Water layer and in the area immediately north of the polar front to a high value of O(10−4) m2 s−1 in the seasonal thermocline between the surface mixed layer and the Winter Water. The latter high diffusivities are found especially over the shallow plateau southeast of the Kerguelen Islands and along the polar front that is attached to the escarpment northeast of the islands. The interaction of strong frontal flow with prominent bottom topography likely causes the observed elevated mixing rates.

Comparison of Ellison and Thorpe scales from Eulerian ocean temperature observations

AbstractOcean turbulence dissipation rate is estimated either by means of microstructure shear measurements, or by adiabatically reordering vertical profiles of density. The latter technique leads to the estimate of the Thorpe scale, which in turn can be used to obtain average turbulence dissipation rate by comparing the Thorpe scale to the Ozmidov scale. In both cases, the turbulence dissipation rate can be estimated using single vertical profiles from shipborne instrumentation. We present here an alternative method to estimate the length scale of overturns by using the Ellison length scale. The Ellison scale is estimated from temperature variance just beyond the internal wave band, measured by moored instruments. We apply the method to high resolution temperature data from two moorings deployed at different locations around the Josephine seamount (North Eastern Atlantic Ocean), in a region of bottom‐intensified turbulence. The variance of the temperature time series just above the internal wave frequency band is well correlated with the Thorpe scale. The method is based on the time‐frequency decomposition of variance called “maximum overlap discrete wavelet transform.” The results show that the Ellison length scale can be a viable alternative to the Thorpe scale for indirectly estimating turbulence dissipation rate from moored instruments in the ocean if time resolution is sufficiently high. We suggest that fine structure contaminated temperature measurements can provide reliable information on turbulence intensity.

Anisotropic turbulence and Rossby waves in an easterly jet: An experimental study

AbstractA westward propagating jet is investigated experimentally. The focus is on complex interaction between anisotropic turbulence with inverse energy cascade and Rossby waves. The energy spectrum is highly anisotropic. To diagnose turbulence characteristics, we explore the analogy between turbulent overturns in stably stratified and quasi‐geostrophic flows and develop a novel method based upon the monotonizing of potential vorticity (PV). The RMS displacement from the monotonic PV profile yields a length scale, LM, analogous to the Thorpe's scale used in flows with stable stratification. As the Thorpe scale is proportional to the Ozmidov scale, the scale LM is proportional to the scale Lβ at which the time scales of turbulent overturns and Rossby waves are approximately equal. The relationship between LM and Lβ is established here for the first time. The method of PV monotonizing offers a simple and powerful tool for diagnosing geophysical and planetary macroturbulence.

Double-diffusive layering and mixing in Patagonian fjords

Double-diffusive layering was quantified for the first time in the Chilean Patagonian fjords region (41.5–56°S). Approximately 600 temperature and salinity profiles collected during 1995–2012 were used to study water masses, quantify diffusive layering and compute the vertical diffusivity of heat. Development of “diffusive-layering” or simply “layering” was favored by relatively fresh–cold waters overlying salty–warm waters. Fresh waters are frequently derived from glacial melting that influences the fjord either directly or through rivers. Salty waters are associated with Modified Subantarctic (MSAAW) and Subantarctic Water (SAAW). Double-diffusive convection occurred as layering in 40% of the year-round data and as salt fingering in <1% of the time. The most vigorous layering, was found at depths between 20 and 70m, as quantified by (a) Turner angles, (b) density ratios, and (c) heat diffusivity (with maximum values of 5×10−5m2s−1). Diffusive-layering events presented a meridional gradient with less layering within the 41–47°S northern region, relative to the southern region between 47° and 56°S. Layering occupied, on average, 27% and 56% of the water column in the northern and southern regions, respectively. Thermohaline staircases were detected with microprofile measurements in Martinez and Baker channels (48°S), showing homogeneous layers (2–4m thick) below the pycnocline (10–40m). Also in this area, increased vertical mixing coincided with the increased layering events. High values of Thorpe scale (LT∼7m), dissipation rate of TKE (ε=10−5–10−3Wkg−1) and diapycnal eddy diffusivity (Kρ=10−6–10−3m−2s−1) were associated with diffusive layering. Implications of these results are that diffusive layering should be taken into account, together with other mixing processes such as shear instabilities and wind-driven flows, in biological and geochemical studies.