scholarly journals South Adriatic Recipes: Estimating the Vertical Mixing in the Deep Pit

2020 ◽  
Vol 7 ◽  
Author(s):  
Vanessa Cardin ◽  
Achim Wirth ◽  
Maziar Khosravi ◽  
Miroslav Gačić
Keyword(s):  
Time Series ◽  
Heat Equation ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Temperature Structure ◽  
Temperature Profiles ◽  
Eof Analysis ◽  
Vertical Temperature ◽  
Current Events ◽  
Sill Depth

The available historical oxygen data show that the deepest part of the South Adriatic Pit remains well-ventilated despite the winter convection reaching only the upper 700 m depth. Here, we show that the evolution of the vertical temperature structure in the deep South Adriatic Pit (dSAP) below the Otranto Strait sill depth (780 m) is described well by continuous diffusion, a continuous forcing by heat fluxes at the upper boundary (Otranto Strait sill depth) and an intermittent forcing by rare (several per decade) deep convective and gravity-current events. The analysis is based on two types of data: (i) 13-year observational data time series (2006–2019) at 750, 900, 1,000, and 1,200 m depths of the temperature from the E2M3A Observatory and (ii) 55 vertical profiles (1985–2019) in the dSAP. The analytical solution of the gravest mode of the heat equation compares well to the temperature profiles, and the numerical integration of the resulting forced heat equation compares favorably to the temporal evolution of the time-series data. The vertical mixing coefficient is obtained with three independent methods. The first is based on a best fit of the long-term evolution by the numerical diffusion-injection model to the 13-year temperature time series in the dSAP. The second is obtained by short-time (daily) turbulent fluctuations and a Prandtl mixing length approximation. The third is based on the zero and first modes of an Empirical Orthogonal Function (EOF) analysis of the time series between 2014 and 2019. All three methods are compared, and a diffusivity of approximately κ = 5 · 10−4m2s−1 is obtained. The eigenmodes of the homogeneous heat equation subject to the present boundary conditions are sine functions. It is shown that the gravest mode typically explains 99.5% of the vertical temperature variability (the first three modes typically explain 99.85%) of the vertical temperature profiles at 1 m resolution. The longest time scale of the dissipative dynamics in the dSAP, associated with the gravest mode, is found to be approximately 5 years. The first mode of the EOF analysis (85%) represents constant heating over the entire depth, and the zero mode is close to the parabolic profile predicted by the heat equation for such forcing. It is shown that the temperature structure is governed by continuous warming at the sill depth and deep convection and gravity current events play less important roles. The simple model presented here allows evaluation of the response of the temperature in the dSAP to different forcings derived from climate change scenarios, as well as feedback on the dynamics in the Adriatic and the Mediterranean Sea.

scholarly journals South Adriatic Recipes: Estimating the Vertical Mixing in the Deep Pit

2021 ◽  
Author(s):  
Achim Wirth ◽  
Vanessa Cardin ◽  
Maziar Khosravi ◽  
Miroslav Gačić
Keyword(s):  
Time Series ◽  
Heat Equation ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Temperature Structure ◽  
Temperature Profiles ◽  
Eof Analysis ◽  
Vertical Temperature ◽  
Current Events ◽  
Sill Depth

<p>The available historical oxygen data show that the deepest part of the South Adriatic Pit remains well-ventilated despite the winter convection reaching only the upper 700 m depth. Here, we show that the evolution of the vertical temperature structure in the deep South Adriatic Pit (dSAP) below the Otranto Strait sill depth (780 m) is described well by continuous diffusion, a continuous forcing by heat fluxes at the upper boundary (Otranto Strait sill depth) and an intermittent forcing by rare (several per decade) deep convective and gravity-current events. The analysis is based on two types of data: (i) 13-year observational data time series (2006–2019) at 750, 900, 1,000, and 1,200 m depths of the temperature from the E2M3A Observatory and (ii) 55 vertical profiles (1985–2019) in the dSAP. The analytical solution of the gravest mode of the heat equation compares well to the temperature profiles, and the numerical integration of the resulting forced heat equation compares favorably to the temporal evolution of the time-series data. The vertical mixing coefficient is obtained with three independent methods. The first is based on a best fit of the long-term evolution by the numerical diffusion-injection model to the 13-year temperature time series in the dSAP. The second is obtained by short-time (daily) turbulent fluctuations and a Prandtl mixing length approximation. The third is based on the zero and first modes of an Empirical Orthogonal Function (EOF) analysis of the time series between 2014 and 2019. All three methods are compared, and a diffusivity of approximately κ = 5 · 10<sup>−4</sup>m<sup>2</sup>s<sup>−1</sup> is obtained. The eigenmodes of the homogeneous heat equation subject to the present boundary conditions are sine functions. It is shown that the gravest mode typically explains 99.5% of the vertical temperature variability (the first three modes typically explain 99.85%) of the vertical temperature profiles at 1 m resolution. The longest time scale of the dissipative dynamics in the dSAP, associated with the gravest mode, is found to be approximately 5 years. The first mode of the EOF analysis (85%) represents constant heating over the entire depth, and the zero mode is close to the parabolic profile predicted by the heat equation for such forcing. It is shown that the temperature structure is governed by continuous warming at the sill depth and deep convection and gravity current events play less important roles. The simple model presented here allows evaluation of the response of the temperature in the dSAP to different forcings derived from climate change scenarios, as well as feedback on the dynamics in the Adriatic and the Mediterranean Sea.</p>

Circulation and Temperature Structure in Large Marine Enclosures

1977 ◽  
Vol 34 (8) ◽  
pp. 1095-1104 ◽  
Author(s):  
J. H. Steele ◽  
D. M. Farmer ◽  
E. W. Henderson
Keyword(s):  
Vertical Mixing ◽  
Temperature Structure ◽  
Temperature Profiles ◽  
Turbulent Diffusivity ◽  
Mixing Energy ◽  
Physical Measurements ◽  
Average Coefficient ◽  
Different Depths ◽  
External Fluctuations ◽  
Shed Light

Certain physical measurements intended to shed light on the circulation in large plastic enclosures (60–2000 m3) induced by the changing environment in which they are moored are described. Layers of dye were generally seen to diffuse vertically although some important advection effects were also observed. Estimates of an average coefficient of turbulent diffusivity yielded values in the range.05–.26 cm2∙s−1.Measurements taken with recording thermistor chains both inside and outside the enclosures show strong damping of external fluctuations with periods significantly less than 1 day. Various possible sources of mixing energy are considered and it is concluded that thermal forcing through the wall may be significant and could account for the observed range of coefficients.The significance of the observed mixing and circulation to the ecology of the enclosures is discussed. Of particular importance is the vertical mixing of nutrients that influences phytoplankton sinking rates and thus plays a crucial role in determining variations in algal concentration at different depths. Key words: mixing, enclosures, controlled ecosystem pollution experiment, circulation, temperature profiles

scholarly journals Global data set of long-term summertime vertical temperature profiles in 153 lakes

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Rachel M. Pilla ◽  
Elizabeth M. Mette ◽  
Craig E. Williamson ◽  
Boris V. Adamovich ◽  
Rita Adrian ◽  
...  
Keyword(s):  
Time Series ◽  
Thermal Structure ◽  
Ecological Change ◽  
Thermal Gradients ◽  
Temperature Profiles ◽  
Vertical Temperature ◽  
Data Set ◽  
Long Term Trends

AbstractClimate change and other anthropogenic stressors have led to long-term changes in the thermal structure, including surface temperatures, deepwater temperatures, and vertical thermal gradients, in many lakes around the world. Though many studies highlight warming of surface water temperatures in lakes worldwide, less is known about long-term trends in full vertical thermal structure and deepwater temperatures, which have been changing less consistently in both direction and magnitude. Here, we present a globally-expansive data set of summertime in-situ vertical temperature profiles from 153 lakes, with one time series beginning as early as 1894. We also compiled lake geographic, morphometric, and water quality variables that can influence vertical thermal structure through a variety of potential mechanisms in these lakes. These long-term time series of vertical temperature profiles and corresponding lake characteristics serve as valuable data to help understand changes and drivers of lake thermal structure in a time of rapid global and ecological change.

Prediction of Temperature Profiles in Fluid Bed Boilers

1978 ◽  
Vol 100 (3) ◽  
pp. 508-513 ◽  
Author(s):  
J. L. Hodges ◽  
R. C. Hoke ◽  
R. Bertrand
Keyword(s):  
Large Scale ◽  
Solid Material ◽  
Temperature Gradients ◽  
Temperature Profiles ◽  
Mixing Height ◽  
Vertical Temperature ◽  
Bed Temperature ◽  
Fluid Bed ◽  
Solids Mixing ◽  
Vertical Tubes

Data acquired in the Exxon Research and Engineering Company’s fluid bed boiler program indicate that the arrangement and orientation of internal boiler tubes has a strong effect on the measured bed temperature profile. Horizontally oriented tubes yield much steeper temperature gradients than do vertical tubes. Excessive vertical temperature gradients in coal fired fluid bed boilers can either limit coal feed rates or result in the formation of agglomerates of solid material which are destructive of bed internals. This study represents an attempt to understand the influence of orientation on vertical temperature profiles in fluid bed boilers. A back-mixing model for solids recirculation was developed and applied to the prediction of bed temperatures. Bubbling bed theory is not suitable for estimating solids circulation rates in pressurized beds of large particles with immersed tubes. However, by introducing the concept of a solids mixing height it was possible to estimate solid movement. The solids mixing height and vertical boiler tube dimensions were correlated in a manner which resulted in good agreement between theoretical and experimental bed temperature profiles. It is felt that this simple model may prove quite useful in the design of large scale commercial fluid bed boilers.

Eigenvalue Expansion Approach to Study Bio-Heat Equation

2016 ◽  
Vol 07 (02) ◽  
pp. 1650002
Author(s):  
M. A. Khanday ◽  
Khalid Nazir
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Metabolic Pathways ◽  
Biological Tissues ◽  
Temperature Profiles ◽  
Order Partial Differential Equation ◽  
Eigenvalue Method ◽  
Thermal Disturbance ◽  
Heat Processes ◽  
Eigenvalue Expansion

A mathematical model based on Pennes bio-heat equation was formulated to estimate temperature profiles at peripheral regions of human body. The heat processes due to diffusion, perfusion and metabolic pathways were considered to establish the second-order partial differential equation together with initial and boundary conditions. The model was solved using eigenvalue method and the numerical values of the physiological parameters were used to understand the thermal disturbance on the biological tissues. The results were illustrated at atmospheric temperatures [Formula: see text]C and [Formula: see text]C.

Wireless probes for measuring vertical temperature profiles in borehole heat exchangers (BHEs)

2021 ◽  
Author(s):  
Simon Schüppler ◽  
Roman Zorn ◽  
Hagen Steger ◽  
Philipp Blum
Keyword(s):  
Measurement Uncertainty ◽  
Fiber Optics ◽  
Heat Exchangers ◽  
Measurement Errors ◽  
High Reliability ◽  
Temperature Profiles ◽  
Measured Temperature ◽  
Distributed Temperature Sensing ◽  
Vertical Temperature ◽  
Borehole Heat Exchangers

<p>The measurement of the undisturbed ground temperature (UGT) serves to design low-temperature geothermal systems, in particular borehole heat exchangers (BHEs), and to monitor shallow aquifers. Wireless and miniaturized probes such as the Geosniff (GS) measurement sphere, which are characterized by an autarkic energy supply and equipped with pressure and temperature sensors, are increasingly being used for the measurement of highly resolved vertical temperature profiles. The measurement probe sinks along the course of the BHE with a selectable measurement frequency to the bottom of the BHE and is useable for initial measurements as well as long term groundwater monitoring. To ensure quality assurance and further improvement of this emerging technology, the analysis of measurement errors and uncertainties of wireless temperature measurements (WTMs) is indispensable. Thus, we provide an empirical laboratory analysis of random, systematic, and dynamic measurement errors, which lead to the measurement uncertainty of WTMs using the GS as a representative device. We subsequently transfer the analysed uncertainty to measured vertical temperature profiles of the undisturbed ground at a BHE site in Karlsruhe, Germany. The precision and accuracy of 0.011 K and -0.11 K, respectively, ensure a high reliability of the GS measurements. The largest measurement uncertainty is obtained within the first five meters of descent resulting from the thermal time constant τ of 4 s. The measured temperature profiles are qualitatively compared with common Distributed Temperature Sensing (DTS) using fiber optic cables and punctual Pt-100 sensors. Wireless probes are also suitable to correct temperature profiles recorded with fiber optics with systematic errors of up to -0.93 K. Various boundary conditions such as the inclination of the BHE pipes or changes of the viscosity and density of the BHE fluid effect the descent rate of the GS of up to 40 %. We additionally provide recommendations for technical implementations of future measurement probes and contribute to an improved understanding and further development of WTMs.</p>

Entrainment and Transport in Idealized Three-Dimensional Gravity Current Simulation

2006 ◽  
Vol 23 (9) ◽  
pp. 1249-1269 ◽  
Author(s):  
Yu-Heng Tseng ◽  
David E. Dietrich
Keyword(s):  
Gravity Current ◽  
Vertical Mixing ◽  
Three Dimensional ◽  
Ocean Model ◽  
Numerical Dissipation ◽  
Good Convergence ◽  
Low Viscosity ◽  
Denmark Strait ◽  
Dimensional Gravity ◽  
Fine Resolution

Abstract A purely z-coordinate Dietrich/Center for Air Sea Technology (DieCAST) ocean model is applied to the Dynamics of Overflow Mixing and Entrainment (DOME) idealized bottom density current problem that is patterned after the Denmark Strait. The numerical results show that the background viscosity plays a more important role than the chosen coordinate system in the entrainment and mixing if the background viscosity is not small enough. Both higher horizontal viscosity and coarser resolution leads to slower along-slope propagation. Reducing vertical mixing parameterization also leads to slower along-slope propagation with thicker plume size vertically. The simulation gives consistent results for the moderate- and fine-resolution runs. At a very coarse grid the dense water descends more slowly and is mainly dominated by diffusion. Time-averaged downstream transport and entrainment are not very sensitive to viscosity after the flow reaches its quasi-steady status. However, more realistic eddies and flow structures are found in low-viscosity runs. The results show good convergence of the resolved flow as expected and clarify the effects of numerical dissipation/mixing on overflow modeling. Larger numerical dissipation is not required nor recommended in z-coordinate models.

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