Thin Boundary Layer Model Research Articles

Thermal structure regulates the dynamics of carbon dioxide flux in alpine saline lake on the Qinghai-Tibet Plateau, China

Thermal stratification and mixing play important roles in the physicochemical composition of lakes and affect the geochemical cycle. However, the regulation of lake carbon exchange at the water-air interface by seasonal thermal structures remains unclear, especially for alpine saline lake on the Qinghai-Tibet Plateau (QTP). Based on continuous field sampling, carbon dioxide flux (FCO2) at the water-air interface in Qinghai Lake during the ice-free period was quantitatively analyzed by thin boundary layer model, as well as the driving factors of the change in FCO2 at the water-air interface. The findings revealed that the FCO2 was −22.16 ± 11.73 mmol m−2d−1 during the stratification period, and − 45.32 ± 29.67 mmol m−2d−1 during the mixing period. We found that thermal stratification limits the matter-energy exchange between the upper and bottom water columns, and carbonate precipitation results in a higher FCO2 than during mixing stage. However, the mixing process reduces the limiting effect of thermal stratification. During the carbonate process, water with higher salinity and pH at the bottom of the water column enters the upper part of the water column, reducing the partial pressure of carbon dioxide (pCO2) in the water column and causing the absorption of CO2 by the lake. Thermal stratification affects the vertical material-energy exchange and atmospheric CO2 uptake of lake. The present study further explains the possible underlying regulation of CO2 uptake in saline lake on the QTP involving the varied thermal structure.

Urbanization and weather dynamics co-dominated the spatial-temporal variation in pCO2 and CO2 fluxes in small montanic rivers draining diverse landscapes

Rivers have been widely reported as important CO2 emitters to the atmosphere. Rapid urbanization has a profound impact on the carbon biogeochemical cycle of rivers, leading to enhanced riverine CO2 evasions. However, it is still unclear whether the spatial–temporal patterns of CO2 emissions in the rivers draining diverse landscapes dominated by urbanization were stable, especially in mountainous areas. This study carried out a two-year investigation of water environmental hydrochemistry in three small mountainous rivers draining urban, suburban and rural landscapes in southwestern China, and CO2 partial pressure (pCO2) and fluxes (fCO2) in surface water were measured using headspace equilibrium method and classical thin boundary layer model. The average pCO2 and fCO2 in the highly urbanized river were of 4783.6 μatm and 700.0 mmol m−2 d−1, conspicuously higher than those in the rural river (1525.9 μatm and 123.2 mmol m−2 d−1), and the suburban river presented a moderate level (3114.2 μatm and 261.2 mmol m−2 d−1). It provided even clearer evidence that watershed urbanization could remarkably enhance riverine CO2 emissions. More importantly, the three rivers presented different longitudinal variations in pCO2, implying diversified spatial patterns of riverine CO2 emissions as a result of urbanization. The urban land can explain 49.6–69.1% of the total spatial variation in pCO2 at the reach scale, indicating that urban land distribution indirectly dominated the longitudinal pattern of riverine pCO2 and fCO2. pCO2 and fCO2 in the three rivers showed similar temporal variability with higher warm-rainy seasons and lower dry seasons, which are significantly controlled by weather dynamics, including monthly temperature and precipitation, but seem to be impervious to watershed urbanization. High temperature-stimulated microorganisms metabolism and riched-CO2 runoff input lead much higher pCO2 in warm-rainy seasons. However, it showed more sensitivity of pCO2 to monthly weather dynamics in urbanized rivers than that in rural rivers, and warm-rainy seasons showed hot moments of CO2 evasion for urban rivers. TOC, DOC, TN, pH and DO were the main controls on pCO2 in the urban and suburban rivers, while only pH and DO were connected with pCO2 in the rural rivers. This indicated differential controls and regulatory processes of pCO2 in the rivers draining diverse landscapes. Furthermore, it suggested that pCO2 calculated by the pH-total alkalinity method would obviously overestimate pCO2 in urban polluted rivers due to the inevitable influence of non-carbonate alkalinity, and thus, a relatively conservative headspace method should be recommended. We highlighted that urbanization and weather dynamics co-dominated the multiformity and uncertainty in spatial–temporal patterns of riverine CO2 evasions, which should be considered when modeling CO2 dynamics in urbanized rivers.

Thin boundary layer model underestimates greenhouse gas diffusion from inland waterways

Inland waters are significant sources of atmospheric greenhouse gas (GHG) emissions. The thin boundary layer (TBL) model is often employed as a means of estimating GHG diffusion in inland waters based on gas transfer velocity (k) at the air-water interface, with k being subject to regulation by near-surface turbulence that is primarily driven by wind speed in many cases. This wind speed-based estimation of k (wind-k), however, can introduce substantial uncertainty for turbulent waterways where wind speed does not accurately represent overall turbulence. In this study, GHG diffusion in the Beijing-Hangzhou Grand Canal (China), the first and longest man-made canal in the world, was estimated using the TBL model, revealing that this model substantially underestimated GHG diffusion when relying on wind-k. Strikingly, the carbon dioxide, methane, and nitrous oxide diffusions were respectively underestimated by 159%, 162%, and 124% when using this model. These findings are significant for developing more reliable approaches to evaluate GHG emissions from inland waterways.

Patterns and drivers of CH4 concentration and diffusive flux from a temperate river–reservoir system in North China

Freshwater reservoirs are regarded as an important anthropogenic source of methane (CH4) emissions. The temporal and spatial variability of CH4 emissions from different reservoirs results in uncertainty in the estimation of the global CH4 budget. In this study, surface water CH4 concentrations were measured and diffusive CH4 fluxes were estimated via a thin boundary layer model in a temperate river–reservoir system in North China, using spatial (33 sites) and temporal (four seasons) monitoring; the system has experienced intensive aquaculture disturbance. Our results indicated that the dissolved CH4 concentration in the reservoir ranged from 0.07 to 0.58 µmol/L, with an annual average of 0.13 ± 0.10 µmol/L, and the diffusive CH4 flux across the water–air interface ranged from 0.66 to 3.61 μmol/(m2•hr), with an annual average of 1.67 ± 0.75 μmol/(m2•hr). During the study period, the dissolved CH4 concentration was supersaturated and was a net source of atmospheric CH4. Notably, CH4 concentration and diffusive flux portrayed large temporal and spatial heterogeneity. The river inflow zone was determined to be a hotspot for CH4 emissions, and its flux was significantly higher than that of the tributary and main basin; the CH4 flux in autumn was greater than that in other seasons. We also deduced that the CH4 concentration/diffusive flux was co-regulated mainly by water temperature, water depth, and water productivity (Chla, trophic status). Our results highlight the importance of considering the spatiotemporal variability of diffusive CH4 flux from temperate reservoirs to estimate the CH4 budget at regional and global scales.

Characteristics of carbon source greenhouse gas flux in the water–air formation in the middle and upper reaches of the Three Gorges Reservoir

Abstract This study selected five points in the middle and upper mainstream of the Three Gorges Reservoir area. Starting from May 2016, the greenhouse gases CO2 and CH4 from the water–air formation at the sampling points have been monitored month by month for 10 months. Using the headspace balance method and the thin boundary layer model estimation method, we obtained the CO2 and CH4 partial pressure ranges and the water–air formation diffusion flux at the mainstream point. It is found that the CH4 partial pressure of water body is significantly positively correlated with water temperature, and significantly negatively correlated with DO; the CH2 partial pressure of water body is positively correlated with water temperature, but negatively correlated with conductivity, DO, pH and wind speed. The diffusion fluxes of CH4 and CO2 at the water–air formation are positively correlated with CH4 partial pressure and water temperature, and negatively correlated with ph, DO and conductivity. It is also found that the reservoir has a certain mitigation effect on the release of CO2 from the river water body, and the CH4 diffusion flux at the water–air formation is roughly equivalent.

Estimation of CO2 emission in reservoir coupling floating chamber and thin boundary layer methods

With the growing development of hydropower projects all over the world, the excessive greenhouse gas (GHG) emissions from increasing reservoirs have drawn public concern. While precise evaluations of GHG emissions are urgently needed, the widely applied methods including floating chamber (FC) method and thin boundary layer (TBL) method are unsatisfactory. In this paper, a new methodology of estimating CO2 emission coupling FC and TBL methods was proposed. Three efforts were achieved stepwise:1) the CO2 transfer coefficient was determined combining the measurements of FC method and TBL model; 2) a semi-empirical model connecting gas-water transfer coefficient and near-surface water turbulence in reservoir was proposed; 3) finally, since surface turbulence in the reservoir could be describe in detail by numerical simulation, integration thousands of discrete cells of local fluxes could be applied to estimate the total CO2 emission with an improved precision. Nine locations in Xiangjiaba Reservoir were selected as a demo study for applying the method, the CO2 emission in the whole reservoir was about 1.37 kg/s. With a deeper insight into the law of gas transfer and an elaborate consideration of the whole reservoir, this study is expected to provide a new approach and technical support to estimate the CO2 emissions accurately in reservoirs.

Diffusive CH4 fluxes from aquaculture ponds using floating chambers and thin boundary layer equations

Static floating chambers (FCs) are the conventional method to measure CH4 fluxes across the water-air interface in ponds, while thin boundary layer (TBL) modelling is increasingly used to estimate CH4 fluxes. In this study, both FCs measurements and TBL models of gas transfer velocity were used to determine CH4 evasion from aquaculture ponds in southeastern China. The surface water CH4 concentrations ranged from 0.4 to 9.1 μmol L-1 with an average of 4.8 ± 0.8 μmol L-1. CH4 flux was always positive, indicating the ponds as a persistent CH4 source to air. Mean CH4 flux based on different TBL models showed large variations, ranging between 19 and 316 μmol m−2 h−1. Compared against the direct measurement FCs, three TBL models developed for the open sea, flowing estuarine system and lentic ecosystem (TBLW92a, TBLRC01, and TBLCL98, respectively) overestimated CH4 emission by 40–200%, while the wind tunnel-based TBL model (TBLLM86) underestimated CH4 emission. Two TBL models developed for lakes (TBLW92b and TBLCW03) gave estimates similar to FCs.

On extension of near-wall domain decomposition to turbulent compressible flows

For modeling turbulent flow, the near-wall domain decomposition (NDD) approach initially proposed by the second author and recently developed in a number of papers proved to be very efficient. It leads to a non-overlapping domain decomposition with a Robin-to-Dirichlet map between an inner (near-wall) and outer regions. The regions are linked with each other via interface boundary conditions of Robin type which equivalently replace both the boundary conditions at the wall and simplified governing equations in the inner region. As has been shown, this approach can reduce the computational time by one order of magnitude while retaining sufficiently high accuracy. In the current paper, for the first time the technique is extended to compressible gas flows. In addition, it is modified to include an exact domain decomposition applied to the original Reynolds-averaged Navier-Stokes equations (RANS) without any simplifications near the wall. The efficiency and accuracy of the algorithm are demonstrated on a number of test cases with the use of the Spalart-Allmaras turbulence model for compressible flows implemented in the in-house code “FlowModellium”. Apart from the approximate NDD (ANDD) based on the thin boundary layer model, for the first time an exact NDD (ENDD) is implemented. The interface boundary conditions in both ANDD and ENDD approaches are consistent. Thereby, the ENDD can effectively complete the ANDD approach when it is needed.

Nitrous oxide emissions from cascade hydropower reservoirs in the upper Mekong River

Nitrous oxide is a powerful greenhouse gas, and its emissions from single reservoirs have been extensively studied; however, it still remains unclear about nitrous oxide emission patterns in cascade reservoirs. In this study, nitrous oxide emissions from cascade hydropower reservoirs were investigated using the thin boundary layer model in the heavily dammed upper Mekong River. Meanwhile, sediment denitrification for nitrous oxide production was analysed using the stable isotope method and the quantitative polymerase chain reaction method. Our results demonstrated that nitrous oxide emissions (0.47–1.08 μg m−2h−1) in the upper Mekong River were much lower than the global mean level (19.60 μg m−2h−1), but were increased by dam constructions; nitrous oxide emissions exhibited an increase trend along the flow direction in the cascade reservoirs. Sediment accumulation by dams supplied sufficient nitrogen substrates and organic carbon, creating hotspots of denitrification at the transition zone in reservoirs. As the elevation decreased, the increase in temperature enhanced microbial denitrification at the active zone, and thereby increased nitrous oxide production with the prolonged residence time. This study advanced our knowledge on nitrous oxide emissions from cascade hydropower systems.

Water-Air Interface CO2 Exchange Flux of Typical Lakes in a Mountainous Area of the Western Chongqing and Their Influencing Factors

To examine the mountainous lake CO2 evasion in Southwest China, partial pressures of carbon dioxide[p(CO2)] and the CO2 exchange flux[F(CO2)] via the water-air interface of nine mountainous lakes in Chongqing, China, have been studied in summer using the thin boundary layer model (TBL) and floating chambers. Key water quality parameters were concomitantly measured. The results indicate that the pCO2 in the mountainous lakes in western Chongqing ranges from 2.1 to 45.0 Pa, with a mean value of (18.1±12.1) Pa. The mean CO2 fluxes calculated by the TBL model and chamber method are (-8.0±2.9), (-3.4±3.6), and (-7.1±22.3) mmol·(m2·d)-1, respectively. The p(CO2) and F(CO2) have positive correlations with the wind speed and ORP but negative correlations with the pH. Our study indicates that mountainous lakes are atmospheric sinks of CO2 and the TBL model should be cautiously adopted.

Daily Variation of CO2 Flux at Water-Air Interface and Analysis of Its Affecting Factors in a Typical River of the Three Gorges Reservoir

Diurnal and seasonal characterization of CO2 partial pressure p(CO2) and CO2 areal flux F(CO2) at the water-air interface in an anthropogenic river in the Three Gorges Reservoir area was studied. A tributary of the Jialing River in Chongqing Municipality was chosen, and daily and seasonal samples were taken in summer and autumn, focusing on riverine p(CO2), F(CO2), and their associated controls. Henry's law combined with the thin boundary layer model was adopted to estimate the CO2 flux via the water-air interface. The results indicated that F(CO2) was not high on average, namely (87.8±27.5) mmol·(m2·d)-1 and (139.2±34.0) mmol·(m2·d)-1 in summer and autumn, respectively. The water-air interface F(CO2) showed significant hourly, daily, and seasonal variations. CO2 release peaked around 09:00 and then slightly decreased. We also found that pH, alkalinity, water, and temperature were significantly related to p(CO2) and F(CO2), whereas pH and alkalinity were the best predictors of F(CO2). This study aids understanding of the impacts of urbanization on CO2 emissions in the rivers and helps to re-evaluate local riverine CO2 budgets.

Carbon release from boreal peatland open water pools: Implication for the contemporary C exchange

AbstractWhile peatland ecosystems overall are long‐term net carbon (C) sinks, the open water pools that are characteristic of boreal peatlands have been found to be C sources to the atmosphere. However, the contribution of these pools to the ecosystem level C budget is often ignored even if they cover a significant area of the peatland surface. Here we examine the annual CO2 and CH4 ecosystem‐atmosphere exchange, including the release following ice melt, from pools in a boreal maritime peatland, in order to estimate the annual loss of C from these water bodies. Over a 16 month period, dissolved CO2 and CH4 were measured periodically in five pools while continuous measurements of CO2 were made in one pool using a nondispersive infrared (NDIR) sensor. Fluxes were calculated using the thin boundary layer model and the eddy covariance technique (spring release only). We calculated an annual C release from pools of 103.3 g C m−2 yr−1 of which 15% was released during the spring ice melt. This release is the same order of magnitude, but with the opposite sign, as the average net ecosystem carbon balance for pool‐free northern peatlands (−22 to −70 g C m−2 yr−1). We discuss the origin of the released C, as the magnitude of the release could have a significant impact on the contemporary C exchange of boreal peatlands.

Annual follow-up of gross diffusive carbon dioxide and methane emissions from a boreal reservoir and two nearby lakes in Québec, Canada

Abstract. Surface water pCO2 and pCH4 measurements were taken in the boreal zone of Québec, Canada, from summer 2006 to summer 2008 in Eastmain 1 reservoir and two nearby lakes. The goal of this follow-up was to evaluate annual greenhouse gas (GHG) emissions, including spring emissions (N.B. gross emissions for reservoir), through flux calculations using the thin boundary layer model. Our measurements underscored the winter CO2 accumulation due to ice cover and the importance of a reliable estimate of spring diffusive emissions as the ice breaks up. We clearly demonstrated that in our systems, diffusive CH4 flux (in terms of CO2 equivalent) were of minor importance in the GHG emissions (without CH4 accumulation under ice), with diffusive CO2 flux generally accounting for more than 95% of the annual diffusive flux. We also noted the extent of spring diffusive CO2 emissions (23% to 52%) in the annual carbon budget.

Release of CO2 and CH4 from small wetland lakes in western Siberia

CO2 and CH4 fluxes were measured from three small wetland lakes located in the middle taiga and forest tundra zones onWest Siberian Lowlands (WSL), the world’s largest wetland area. Fluxes were measured during summer 2005 using floating chambers and were validated against the thin boundary layer model based on the relationship between gas exchange and wind speed. All studied lakes were supersaturated with CO2 and CH4, and acted on a seasonal basis as sources of these greenhouse gases to the atmosphere. Daily mean CO2 fluxes measured with chambers ranged from near the zero to 3.1 g CO2 m-2 d-1 and corresponding CH4 fluxes from 1.1 to 120 mg CH4 m-2 d-1. CH4 ebullition (0.65–11 mg CH4 m-2 d-1) was detected in two of the lakes. Total carbon evasion from the studied lakes during the active season was 23–66 g C m-2, of which more than 90% was released as CO2-C. The carbon loss per unit area from the studied lakes was of similar magnitude as previously reported values of net carbon uptake of Siberian peatlands. This emphasizes the importance of small water-bodies in the carbon balance of West Siberian landscape.

Acoustic Scattering by a Fluid-Encapsulating Spherical Viscoelastic Membrane Including Thermoviscous Effects

AbstractThis study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a fluid-filled viscoelastic spherical membrane immersed in an unbounded viscous heat-conducting compressible fluid. The thermoviscous effects in the fluid are incorporated by application of a thin boundary layer model. The dynamic viscoelastic properties of the spherical membrane are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak-Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the basic acoustic quantities, such as the scattered far-field pressure directivity pattern, and the scattering cross section are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid thermoviscosity-related mechanisms, dynamic viscoelastic properties of the obstacle can be of significance in sound scattering. The presented analysis is of practical interest in development of contrast agents for echocardiographic research with potential clinical applications.

A practical surface panel method to predict velocity distribution around a three-dimensional hydrofoil including boundary layer effects

A practical, low order and potential-based surface panel method is presented to predict the flow around a three-dimensional rectangular foil section including the effect of boundary layer. The method is based on a boundary-integral formulation, known as the “Morino formulation” and the boundary layer effect is taken into account through a complementary thin boundary layer model. The numerical approach used in the method presents a strongly convergent solution based on the iterative wake roll-up and contraction model including the boundary layer effect. The method is applied to a three-dimensional foil section for which the velocity distribution around the foil was measured using a 2D Laser Doppler Velocimetry system in a large cavitation tunnel. Comparison of the predicted velocity distributions both inside and outside of the boundary layer of the foil as well as the boundary layer shapes obtained from the numerical model show fairly good correlation with the measurements, indicating the robustness and practical worthiness of the proposed method.

Model analysis of boundary residual stress and its effect on toughness in thin boundary layered yttria-stabilized tetragonal zirconia polycrystalline ceramics

The average thermal residual stress in a continuous boundary phase in polycrystalline ceramic composites was calculated with a simple thin boundary layer model, and a criterion for the self-cracking of the boundary phase was derived under a certain assumption. From the proposed model, the toughness of the materials can be increased by both tensile and compressive stress at boundaries when the crack propagates transgranularly. The toughness will be increased when the stress at boundary is compressive for intergranular fracture mode. The maximum increase is predicted to be achieved at boundary phase contents below 33%. The experimental results for yttria-stabilized tetragonal zirconia polycrystalline ceramics doped with different kinds of grain-boundary phase is in a qualitative agreement with the prediction by the model, but the toughness increase is largely dependent on the distribution feature of glass phases.

Boundary stress and its effect on toughness in thin boundary layered and particulate composites: model analysis and experimental test on Y-TZP-based ceramic composites

The average thermal residual stress in continuous boundary phase of polycrystalline ceramic composites was calculated with a simple thin boundary layer model and a criterion for the self-cracking of the boundary phase was derived under a certain assumption. From the proposed model, the toughness of the materials can be increased by both tensile and compressive stress at boundaries when the crack propagates transgranularly; and will be increased when the stress at boundary is compressive for intergranular fracture mode. The maximum increase is predicted to be achieved at the boundary phase content not higher than 33%. The experimental results with Y-TZP doped with different kinds of grain boundary phase show a qualitative agreement with the prediction by the model but the toughness increase is largely dependent on the distribution feature of glass phases. From the ideal particle-in-infinite matrix model, the average stress in matrix and in particle for possible practical system was estimated and compared with the thin boundary layer model. The criterion for the self-cracking in matrix and in particle or at the particle–matrix interface was derived with stress intensity factor approach. From the existing periodic stress field model for particulate composite, the toughness increase is found not to increase monotonously with the content of second phase. Alternatively a maximum toughness increase is found, which is predicted to be achieved at the particulate phase content of 14·3 vol%. The experimental results on Y-TZP/Al 2O 3 composites were compared with the prediction of the model.

Thickness Dependence of Effective Composition for Amorphous TbFe Films

An attempt is made to explain the deviation to the Fe-rich side of the ``effective'' composition of RF sputtered, amorphous TbFe films. The results indicate that the effective composition apparently varies as a function of film thickness, and this cannot be explained using the present model. A thin boundary-layer model is proposed which assumes: 1) these layers are formed at both the film-substrate and film-air boundaries; 2) this layer thickness is independent of the total film thickness; and 3) there are exchange couplings between the boundary layer and the middle layer.