scholarly journals Goldilocks mixing in oceanic shear-induced turbulent overturns

2021 ◽  
Vol 928 ◽  
Author(s):  
A. Mashayek ◽  
C.P. Caulfield ◽  
M.H. Alford
Keyword(s):  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Intermediate Phase ◽  
Turbulent Flux ◽  
Geographical Location ◽  
Small Scale ◽  
Supporting Evidence ◽  
Stratified Turbulence ◽  
Wide Range ◽  
Variable Flux

We present a new, simple and physically motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $\varGamma _{\mathcal {M}}= {\mathcal {M}}/\epsilon$ , i.e. the ratio of the irreversible rate ${\mathcal {M}}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy $\epsilon$ . Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, ‘hot’ growing phase, the intermediate energetically forced phase and the final ‘cold’ fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the ‘Goldilocks’ phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. The value of $\varGamma _{\mathcal {M}}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence ${\sim }0.2\text {--}0.25$ . Importantly, although buoyancy effects are still significant at leading order for the turbulent dynamics during this intermediate phase, the marginal balance in the flow ensures that the turbulent mixing of the (density) scalar is nevertheless effectively ‘locked’ to the turbulent mixing of momentum. We present supporting evidence for our parameterization through comparison with six oceanographic datasets that span various turbulence generation regimes and a wide range of geographical location and depth. Using these observations, we highlight the significance of parameterizing an inherently variable flux coefficient for capturing the turbulent flux associated with rare energetic, yet fundamentally shear-driven (and so not strongly stratified) overturns that make a disproportionate contribution to the total mixing. We also highlight the importance of representation of young turbulent patches in the parameterization for connecting the small scale physics to larger scale applications of mixing such as ocean circulation and tracer budgets. Shear-induced turbulence is therefore central to irreversible mixing in the world's oceans, apparently even close to the seafloor, and it is critically important to appreciate the inherent time dependence and evolution of mixing events: history matters to mixing.

scholarly journals Role of overturns in optimal mixing in stratified mixing layers

2017 ◽  
Vol 826 ◽  
pp. 522-552 ◽  
Author(s):  
A. Mashayek ◽  
C. P. Caulfield ◽  
W. R. Peltier
Keyword(s):  
Numerical Simulations ◽  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Isotropic Turbulence ◽  
Life Cycles ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Small Scale ◽  
Mean Flow

Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale $L_{O}$ compared to the so-called Thorpe overturning scale $L_{T}$ which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when $L_{T}\sim L_{O}$, the mixing is most active and efficient since stirring by the largest overturns becomes ‘optimal’ in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of $L_{O}/L_{T}\sim 1$ in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with $L_{T}-L_{O}$ data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes.

Laboratory Measurement of Entrainment and Mixing in Oceanic Overflows

2007 ◽  
Author(s):  
Jun Chen ◽  
Philippe Odier ◽  
Michael Rivera ◽  
Robert Ecke
Keyword(s):  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Thermohaline Circulation ◽  
Global Climate ◽  
Ambient Medium ◽  
Gravity Current ◽  
Small Scale ◽  
Inclined Plate ◽  
Denmark Strait ◽  
Series Of Experiments

The mixing and entrainment processes existing in oceanic overflows, e.g., Denmark Strait Overflow (DSO), affect the global thermohaline circulation. Owing to limited spatial resolution in global climate prediction simulations, the small-scale dynamics of oceanic mixing must be properly modeled. A series of experiments are performed in an Oceanic Overflow Facility to study the mixing and entrainment of a gravity current along an inclined plate, flowing into a steady ambient medium. At small values of the Richardson number, the shear dominates the stabilizing effect of the stratification and the flow at the interface of the current becomes unstable, resulting in turbulent mixing. In addition, the level of turbulence is enhanced by an active grid device. Using PIV and PLIF to measure, respectively, the velocity and density fields, we characterize the statistical properties of the mixing. We also study the entrainment of the ambient fluid by the flow. An accurate parametrization of the mixing and entrainment can be a valuable input for ocean circulation models.

scholarly journals Diagnosing diapycnal mixing from passive tracers

2020 ◽  
Author(s):  
XIAOZHOU RUAN ◽  
RAFFAELE FERRARI
Keyword(s):  
Turbulent Flows ◽  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Small Scale ◽  
Mixing Rates ◽  
High Bias ◽  
Passive Tracers ◽  
Microstructure Measurements

AbstractTurbulent mixing across density surfaces transforms abyssal ocean waters into lighter waters and is vital to close the deepest branches of the global overturning circulation. Over the last twenty years, mixing rates inferred from in-situ microstructure profilers and tracer release experiments (TREs) have provided valuable insights in the connection between small-scale mixing and large-scale ocean circulation. Problematically, estimates based on TREs consistently exceed those from collocated in-situ microstructure measurements. These differences have been attributed to a low bias in the microstructure estimates which can miss strong, but rare, mixing events. Here we demonstrate that TRE estimates can suffer from a high bias, because of the approximations generally made to interpret the data. We first derive formulas to estimate mixing from the temporal growth of the second moment of a tracer patch by extending Taylor’s celebrated formula to account for both density stratification and variations in mixing rates. The formulas are validated with tracers released in numerical simulations of turbulent flows and then used to discuss biases in the interpretation of TREs based estimates and how to possibly overcome them.

Integrated Design and Multi-Objective Optimization of a Single Stage Heat-Pump Turbocompressor

2013 ◽  
Author(s):  
J. Schiffmann
Keyword(s):  
Design Optimization ◽  
High Efficiency ◽  
Integrated Design ◽  
Heat Pumps ◽  
Small Scale ◽  
Multi Objective Optimization ◽  
Design Constraints ◽  
Multi Objective ◽  
Wide Range ◽  
Standard Design

Small scale turbomachines in domestic heat pumps reach high efficiency and provide oil-free solutions which improve heat-exchanger performance and offer major advantages in the design of advanced thermodynamic cycles. An appropriate turbocompressor for domestic air based heat pumps requires the ability to operate on a wide range of inlet pressure, pressure ratios and mass flows, confronting the designer with the necessity to compromise between range and efficiency. Further the design of small-scale direct driven turbomachines is a complex and interdisciplinary task. Textbook design procedures propose to split such systems into subcomponents and to design and optimize each element individually. This common procedure, however, tends to neglect the interactions between the different components leading to suboptimal solutions. The authors propose an approach based on the integrated philosophy for designing and optimizing gas bearing supported, direct driven turbocompressors for applications with challenging requirements with regards to operation range and efficiency. Using previously validated reduced order models for the different components an integrated model of the compressor is implemented and the optimum system found via multi-objective optimization. It is shown that compared to standard design procedure the integrated approach yields an increase of the seasonal compressor efficiency of more than 12 points. Further a design optimization based sensitivity analysis allows to investigate the influence of design constraints determined prior to optimization such as impeller surface roughness, rotor material and impeller force. A relaxation of these constrains yields additional room for improvement. Reduced impeller force improves efficiency due to a smaller thrust bearing mainly, whereas a lighter rotor material improves rotordynamic performance. A hydraulically smoother impeller surface improves the overall efficiency considerably by reducing aerodynamic losses. A combination of the relaxation of the 3 design constraints yields an additional improvement of 6 points compared to the original optimization process. The integrated design and optimization procedure implemented in the case of a complex design problem thus clearly shows its advantages compared to traditional design methods by allowing a truly exhaustive search for optimum solutions throughout the complete design space. It can be used for both design optimization and for design analysis.

scholarly journals A broadbanded pressure differential wave energy converter based on dielectric elastomer generators

2021 ◽  
Author(s):  
Michele Righi ◽  
Giacomo Moretti ◽  
David Forehand ◽  
Lorenzo Agostini ◽  
Rocco Vertechy ◽  
...  
Keyword(s):  
Wave Energy ◽  
Large Deformations ◽  
Dielectric Elastomer ◽  
Wave Energy Converter ◽  
Pressure Differential ◽  
Design Stage ◽  
Small Scale ◽  
Energy Converter ◽  
Wide Range ◽  
The Waves

AbstractDielectric elastomer generators (DEGs) are a promising option for the implementation of affordable and reliable sea wave energy converters (WECs), as they show considerable promise in replacing expensive and inefficient power take-off systems with cheap direct-drive generators. This paper introduces a concept of a pressure differential wave energy converter, equipped with a DEG power take-off operating in direct contact with sea water. The device consists of a closed submerged air chamber, with a fluid-directing duct and a deformable DEG power take-off mounted on its top surface. The DEG is cyclically deformed by wave-induced pressure, thus acting both as the power take-off and as a deformable interface with the waves. This layout allows the partial balancing of the stiffness due to the DEG’s elasticity with the negative hydrostatic stiffness contribution associated with the displacement of the water column on top of the DEG. This feature makes it possible to design devices in which the DEG exhibits large deformations over a wide range of excitation frequencies, potentially achieving large power capture in a wide range of sea states. We propose a modelling approach for the system that relies on potential-flow theory and electroelasticity theory. This model makes it possible to predict the system dynamic response in different operational conditions and it is computationally efficient to perform iterative and repeated simulations, which are required at the design stage of a new WEC. We performed tests on a small-scale prototype in a wave tank with the aim of investigating the fluid–structure interaction between the DEG membrane and the waves in dynamical conditions and validating the numerical model. The experimental results proved that the device exhibits large deformations of the DEG power take-off over a broad range of monochromatic and panchromatic sea states. The proposed model demonstrates good agreement with the experimental data, hence proving its suitability and effectiveness as a design and prediction tool.

scholarly journals A Threat of Farmers’ Suicide and the Opportunity in Organic Farming for Sustainable Agricultural Development in India

2019 ◽  
Vol 11 (8) ◽  
pp. 2400 ◽  
Author(s):  
Karthikeyan Mariappan ◽  
Deyi Zhou
Keyword(s):  
Organic Farming ◽  
Tamil Nadu ◽  
Agricultural Development ◽  
Small Scale ◽  
Conventional Farming ◽  
Wide Range ◽  
Significant Difference ◽  
Small Scale Farmers ◽  
The Cost ◽  
Input Cost

Agriculture is the main sources of income for humans. Likewise, agriculture is the backbone of the Indian economy. In India, Tamil Nadu regional state has a wide range of possibilities to produce all varieties of organic products due to its diverse agro-climatic condition. This research aimed to identify the economics and efficiency of organic farming, and the possibilities to reduce farmers’ suicides in the Tamil Nadu region through the organic agriculture concept. The emphasis was on farmers, producers, researchers, and marketers entering the sustainable economy through organic farming by reducing input cost and high profit in cultivation. A survey was conducted to gather data. One way analysis of variance (ANOVA) has been used to test the hypothesis regards the cost and profit of rice production. The results showed that there was a significant difference in profitability between organic and conventional farming methods. It is very transparent that organic farming is the leading concept of sustainable agricultural development with better organic manures that can improve soil fertility, better yield, less input cost and better return than conventional farming. The study suggests that by reducing the cost of cultivation and get a marginal return through organic farming method to poor and small scale farmers will reduce socio-economic problems such as farmers’ suicides in the future of Indian agriculture.

scholarly journals A multi-site, year-round turbulence microstructure atlas for the deep perialpine Lake Garda

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Sebastiano Piccolroaz ◽  
Bieito Fernández-Castro ◽  
Marco Toffolon ◽  
Henk A. Dijkstra
Keyword(s):  
Turbulent Mixing ◽  
Meteorological Data ◽  
Time Of Day ◽  
Monthly Basis ◽  
Lake Garda ◽  
Standardized Protocol ◽  
Wide Range ◽  
Buoyancy Driven Convection ◽  
Monitoring Activity ◽  
Additional Monitoring

AbstractA multi-site, year-round dataset comprising a total of 606 high-resolution turbulence microstructure profiles of shear and temperature gradient in the upper 100 m depth is made available for Lake Garda (Italy). Concurrent meteorological data were measured from the fieldwork boat at the location of the turbulence measurements. During the fieldwork campaign (March 2017-June 2018), four different sites were sampled on a monthly basis, following a standardized protocol in terms of time-of-day and locations of the measurements. Additional monitoring activity included a 24-h campaign and sampling at other sites. Turbulence quantities were estimated, quality-checked, and merged with water quality and meteorological data to produce a unique turbulence atlas for a lake. The dataset is open to a wide range of possible applications, including research on the variability of turbulent mixing across seasons and sites (demersal vs pelagic zones) and driven by different factors (lake-valley breezes vs buoyancy-driven convection), validation of hydrodynamic lake models, as well as technical studies on the use of shear and temperature microstructure sensors.

scholarly journals Modelling the atmosphere of lava planet K2-141b: implications for low- and high-resolution spectroscopy

2020 ◽  
Vol 499 (4) ◽  
pp. 4605-4612
Author(s):  
T Giang Nguyen ◽  
Nicolas B Cowan ◽  
Agnibha Banerjee ◽  
John E Moores
Keyword(s):  
Steady State ◽  
Ocean Circulation ◽  
Scale Height ◽  
High Resolution Spectroscopy ◽  
Return Flow ◽  
High Dispersion ◽  
Magma Ocean ◽  
Steady State Flow ◽  
Wide Range ◽  
Very High

ABSTRACT Transit searches have uncovered Earth-size planets orbiting so close to their host star that their surface should be molten, so-called lava planets. We present idealized simulations of the atmosphere of lava planet K2-141b and calculate the return flow of material via circulation in the magma ocean. We then compare how pure Na, SiO, or SiO2 atmospheres would impact future observations. The more volatile Na atmosphere is thickest followed by SiO and SiO2, as expected. Despite its low vapour pressure, we find that a SiO2 atmosphere is easier to observe via transit spectroscopy due to its greater scale height near the day–night terminator and the planetary radial velocity and acceleration are very high, facilitating high dispersion spectroscopy. The special geometry that arises from very small orbits allows for a wide range of limb observations for K2-141b. After determining the magma ocean depth, we infer that the ocean circulation required for SiO steady-state flow is only 10−4 m s−1, while the equivalent return flow for Na is several orders of magnitude greater. This suggests that a steady-state Na atmosphere cannot be sustained and that the surface will evolve over time.

Electromechanical fields in a hollow piezoelectric cylinder under non-uniform load: flexoelectric effect

2021 ◽  
pp. 108128652110207
Author(s):  
Olha Hrytsyna
Keyword(s):  
Analytical Solutions ◽  
Point Group ◽  
The Body ◽  
Small Scale ◽  
Gradient Theory ◽  
Local Mass ◽  
Wide Range ◽  
Mass Displacement ◽  
Local Mass Displacement ◽  
Local Gradient

The relations of a local gradient non-ferromagnetic electroelastic continuum are used to solve the problem of an axisymmetrical loaded hollow cylinder. Analytical solutions are obtained for tetragonal piezoelectric materials of point group 4 mm for two cases of external loads applied to the body surfaces. Namely, the hollow pressurized cylinder and a cylinder subjected to an electrical voltage V across its thickness are considered. The derived solutions demonstrate that the non-uniform electric load causes a mechanical deformation of piezoelectric body, and vice versa, the inhomogeneous radial pressure of the cylinder induces its polarization. Such a result is obtained due to coupling between the electromechanical fields and a local mass displacement being considered. In the local gradient theory, the local mass displacement is associated with the changes to a material’s microstructure. The classical theory does not consider the effect of material microstructure on the behavior of solid bodies and is incapable of explaining the mentioned phenomena. It is also shown that the local gradient theory describes the size-dependent properties of piezoelectric nanocylinders. Analytical solutions to the formulated boundary-value problems can be used in conjunction with experimental data to estimate some higher-order material constants of the local gradient piezoelectricity. The obtained results may be useful for a wide range of appliances that utilize small-scale piezoelectric elements as constituting blocks.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

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