Turbulent mixing process in the Lombok Strait

Turbulent mixing process in the Lombok Strait was evaluated from density inversions in CTD (Conductivity Temperature Depth) profiles obtained from the INSTANT (International Nusantara Stratification and Transport) recovery cruise, June 14-19th 2005. The quality of the detected-overturn regions has been improved by applying wavelet denoising to CTD signals. The Thorpe analysis shows that many overturn regions less than 7 m were detected in throughout the water column of the Lombok Strait. Based on linear relationship between Thorpe Scale and Ozmidov Scale, the turbulent kinetic energy dissipation rate ε was estimated about 10−12−10−6 W kg−1 and density of eddy diffusivity Kρ (10−6−10−2 m2s −1). A relatively high of Kρ Ø (10−2 m2s −1) was found at the southern part of the strait, near the sill which obstruct the Indonesian Thoughflow into the Indian Ocean. The dipped and rebounded isopycnal surfaces of σθ= 25.5–26.5 near the sill and the presence of strong shear at the same depth of the interval solitary wave (150 to 250 m) indicate that strong turbulence in this layer was driven by shear instability associated with breaking internal waves.

Inhibited vertical mixing and seasonal persistence of a thin cyanobacterial layer in a stratified lake

Harmful blooms of the filamentous cyanobacteria Planktothrix rubescens have become common in many lakes as they have recovered from eutrophication over the last decades. These cyanobacteria, capable of regulating their vertical position, often flourish at the thermocline to form a deep chlorophyll maximum. In Lake Zurich (Switzerland), they accumulate during stratified season (May–October) as a persistent metalimnetic thin layer (~2 m wide). This study investigated the role of turbulent mixing in springtime layer formation, its persistence over the summer, and its breakdown in autumn. We characterised seasonal variation of turbulence in Lake Zurich with four surveys conducted in April, July and October of 2018 and September of 2019. Surveys included microstructure profiles and high-resolution mooring measurements. In July and October, the thin layer occurred within a strong thermocline ($$N \gtrsim 0.05$$ N ≳ 0.05 s$$^{-1}$$ - 1 ) and withstood significant turbulence, observed as turbulent kinetic energy dissipation rates ($$\varepsilon \approx 10^{-8}$$ ε ≈ 10 - 8 W kg$$^{-1}$$ - 1 ). Vertical turbulent overturns –monitored by the Thorpe scale– went mostly undetected and on average fell below those estimated by the Ozmidov scale ($$L_O \approx 1$$ L O ≈ 1 cm). Consistently, vertical diffusivity was close to molecular values, indicating negligible turbulent fluxes. This reduced metalimnetic mixing explains the persistence of the thin layer, which disappears with the deepening of the surface mixed layer in autumn. Bi-weekly temperature profiles in 2018 and a nighttime microstructure sampling in September 2019 showed that nighttime convection serves as the main mechanism driving the breakdown of the cyanobacterial layer in autumn. These results highlight the importance of light winds and convective mixing in the seasonal cycling of P. rubescens communities within a strongly stratified medium-sized lake.

Heat Transport through Diurnal Warm Layers

Penetration of solar radiation in the upper few meters of the ocean creates a near-surface, stratified diurnal warm layer. Wind stress accelerates a diurnal jet in this layer. Turbulence generated at the diurnal thermocline, where the shear of the diurnal jet is concentrated, redistributes heat downward via mixing. New measurements of temperature and turbulence from fast thermistors on a surface-following platform depict the details of this sequence in both time and depth. Temporally, the sequence at a fixed depth follows a counterclockwise path in logϵ–logN parameter space. This path also captures the evolution of buoyancy Reynolds number (a proxy for the anisotropy of the turbulence) and Ozmidov scale (a proxy for the outer vertical length scale of turbulence in the absence of the free surface). Vertically, the solar heat flux always leads to heating of fluid parcels in the upper few meters, whereas the turbulent heat flux divergence changes sign across the depth of maximum vertical temperature gradient, cooling fluid parcels above and heating fluid parcels below. In general, our measurements of fluid parcel heating or cooling rates of order 0.1°C h−1 are consistent with our estimates of heat flux divergence. In weak winds (<2 m s−1), sea surface temperature (SST) is controlled by the depth-dependent absorption of solar radiation. In stronger winds, turbulent mixing controls SST.

Direct Numerical Simulation Guidance for Thorpe Analysis to Obtain Quantitatively Reliable Turbulence Parameters

Thorpe analysis has been used to study turbulence in the atmosphere and ocean. It is clear that Thorpe analysis applied to individual soundings cannot be expected to give quantitatively reliable measurements of turbulence parameters because of the instantaneous nature of the measurement. A critical aspect of this analysis is the assumption of the linear relationship C = LO/LT between the Thorpe scale LT, derived from the sounding measurements, and the Ozmidov scale LO. It is the determination of LO that enables determination of the dissipation rate of turbulence kinetic energy ε. Single atmospheric and oceanic soundings cannot indicate either the source of turbulence or the stage of its evolution; different values of C are expected for different turbulence sources and stages of the turbulence evolution and thus cannot be expected to yield quantitatively reliable turbulence parameters from individual profiles. The variation of C with the stage of turbulence evolution is illustrated for direct numerical simulation (DNS) results for gravity wave breaking. Results from a DNS model of multiscale initiation and evolution of turbulence with a Reynolds number Re (which is defined using the vertical wavelength of the primary gravity wave and background buoyancy period as length and time scales, respectively) of 100 000 are sampled as in sounding of the atmosphere and ocean, and various averaging of the sounding results indicates a convergence to a well-defined value of C, indicating that applying Thorpe analysis to atmospheric or oceanic soundings and averaging over a number of profiles gives more reliable turbulence determinations. The same averaging study is also carried out when the DNS-modeled turbulence is dominated by turbulence growing from the initial instabilities, when the turbulence is fully developed, when the modeled turbulence is decaying, and when the turbulence is in a still-later decaying stage. These individual cases converge to well defined values of C, but these values of C show a large variation resulting from the different stages of turbulence evolution. This study gives guidance as to the accuracy of Thorpe analysis of turbulence as a function of the number of profiles being averaged. It also suggests that the values of C in different environments likely depend on the dominant turbulence initiation mechanisms and on the Reynolds number of the environment.

Decaying turbulence in a stratified fluid of high Prandtl number

Decaying turbulence in a density-stratified fluid with a Prandtl number up to $Pr=70$ is investigated by direct numerical simulation. In turbulent flow with a Prandtl number larger than unity, it is well known that the passive scalar fluctuations cascade to scales smaller than the Kolmogorov scale, and show the $k^{-1}$ spectrum in the viscous–convective range, down to the Batchelor scale. In decaying stratified turbulence, the same phenomenon is initially observed for the buoyant scalar of high $Pr~(=70)$, until the Ozmidov scale becomes small and the buoyancy becomes effective even at the Kolmogorov scale. After that moment, however, the velocity components near the Kolmogorov scale begin to show strong anisotropy dominated by the vertically sheared horizontal flow, which reduces the vertical scale of density fluctuations. An analysis similar to that of Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) indeed shows that the vertically sheared horizontal flow reduces the vertical scale of density fluctuations, without changing the horizontal scale.

Turbulent length scales in a fast-flowing, weakly stratified, strait: Cook Strait, New Zealand

There remains much to be learned about the full range of turbulent motions in the ocean. Here we consider turbulence and overturn scales in the relatively shallow, weakly stratified, fast-flowing tidal flows of Cook Strait, New Zealand. With flow speeds reaching 3 m s−1 in a water column of ∼300 m depth the location is heuristically known to be highly turbulent. Dissipation rates of turbulent kinetic energy ε, along with the Thorpe scale, LT, are described. Thorpe scales, often as much as one-quarter of the water depth, are compared with dissipation rates and background flow speed. Turbulent energy dissipation rates ε are modest but high for oceans, around 5×10-5 W kg−1. Comparison of the buoyancy-limit Ozmidov scale LOz suggest the Cook Strait data lie for the majority of the time in the LOz > LT regime, but not universally. Also, comparison of direct and LT-based estimates of ε exhibit reasonable similarity.

Mixing efficiency in large-eddy simulations of stratified turbulence

The irreversible mixing efficiency is studied using large-eddy simulations (LES) of stratified turbulence, where three different subgrid-scale (SGS) parameterizations are employed. For comparison, direct numerical simulations (DNS) and hyperviscosity simulations are also performed. In the regime of stratified turbulence where $Fr_{v}\sim 1$, the irreversible mixing efficiency $\unicode[STIX]{x1D6FE}_{i}$ in LES scales like $1/(1+2Pr_{t})$, where $Fr_{v}$ and $Pr_{t}$ are the vertical Froude number and turbulent Prandtl number, respectively. Assuming a unit scaling coefficient and $Pr_{t}=1$, $\unicode[STIX]{x1D6FE}_{i}$ goes to a constant value $1/3$, in agreement with DNS results. In addition, our results show that the irreversible mixing efficiency in LES, while consistent with this prediction, depends on SGS parameterizations and the grid spacing $\unicode[STIX]{x1D6E5}$. Overall, the LES approach can reproduce mixing efficiency results similar to those from the DNS approach if $\unicode[STIX]{x1D6E5}\lesssim L_{o}$, where $L_{o}$ is the Ozmidov scale. In this situation, the computational costs of numerical simulations are significantly reduced because LES runs require much smaller computational resources in comparison with expensive DNS runs.

Turbulent Length Scales in a Fast-flowing, Weakly Stratified, Strait: Cook Strait, New Zealand

There remains much to be learned about the full range of turbulent motions in the ocean. Here we consider turbulence and overturn scales in the relatively shallow, weakly stratified, fast-flowing tidal flows of Cook Strait, New Zealand. With flow speeds reaching 3 m s−1 in a water column of ~ 300 m depth the location is heuristically known to be highly turbulent. Dissipation rates of turbulent kinetic energy ε along with the Thorpe scale, LT, are described. Thorpe scales, often as much as one quarter of the water depth, are compared with dissipation rates and background flow speed. Turbulent energy dissipation rates ε are modest but high for oceans, around 5 × 10–5 W kg−1. Comparison of the buoyancy-limit Ozmidov scale LOz suggest the Cook Strait data lie for the majority of the time in the LOz > LT regime, but not universally. Also, comparison of direct and LT -based estimates of ε exhibit reasonable similarity.

TURBULENT MIXING PROCESSES IN LABANI CHANNEL, THE MAKASSAR STRAIT

<p><em>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 (L_T) 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 </em><em>10^-11- 10^-5Wkg^-1 and </em><em>density eddy diffusivity K_ρ</em><em>(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 K_ρ (O = 10^-3 – 10^-2 m²s^-1). It reveals that turbulent mixing has an important role on determining ITF water mass character. </em></p><p><strong><em>Keywoods</em></strong><em>: turbulent mixing, wavelet denoising, overturn region, Thorpe method, Labani Channel, Makassar Srait.</em></p>

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.