Thermal Energy Dissipation Rates Research Articles

Statistics of kinetic and thermal energy dissipation rates in vibrational turbulent Rayleigh–Bénard convection with rough surface

In this paper, the statistical properties of the kinetic εu and thermal εθ dissipation rates in two-dimensional (2D) turbulent Rayleigh–Bénard convection (RBC) are studied by using the thermal lattice Boltzmann method (LBM). A series of direct numerical simulations (DNS) are implemented in a square cell with the unit aspect ratio for the Rayleigh number Ra = 108 and Prandtl number Pr = 4.38. The roughness height h* and vary the vibration frequency ω* from 0 to 1000 are fixed in the vibrational RBC with rough plates to explore their effect on the kinetic and thermal dissipation rates. The global features indicate that the εu and εθ are more intense in the regions with high gradients of velocity and temperature, which is in good agreement with the previous work. The scalings of Nu∼ω *0.55±0.1 and Re∼0.59±0.2 are proposed between the ensemble averaged Nusselt number Nu and Reynolds number Re. The probability density functions (PDFs) of both logarithmic kinetic dissipation rate lg εu and thermal dissipation rate lg εθ are not conformed to the log-normal distributions. Through the analysis of the time-averaged εu and εθ vertical profiles, it is further demonstrated that the local dissipation rates from the boundary layer region are still the major contribution in the vibrational RBC with rough plates.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional thermal vibrational convection

We investigate the statistical properties of kinetic ϵu and thermal ϵθ energy dissipation rates in two-dimensional (2D) thermal vibrational convection (TVC). Direct numerical simulations were conducted in a unit aspect ratio box across a dimensionless angular frequency range of 103≤ω≤107 for amplitudes 0.001≤a≤0.1, with a fixed Prandtl number of 4.38. Our findings indicate ϵu is primarily associated with the characteristics of the vibration force, while ϵθ is more related to the large-scale columnar structures. Both energy dissipation rates exhibit a power-law relationship with the oscillational Reynolds number Reos. ϵu exhibits a scaling relation as ⟨ϵu⟩V,t∼a−1Reos0.93±0.01, while ϵθ exhibits two distinct scaling behaviors, i.e., ⟨ϵθ⟩V,t∼a−1Reos1.97±0.04 for Reos<Reos,cr and ⟨ϵθ⟩V,t∼a−1Reos1.31±0.02 for Reos>Reos,cr, where the fitted critical oscillational Reynolds number is approximately Reos,cr≈80. The different scaling of ⟨ϵθ⟩V,t is determined by the competition between the thermal boundary layer and the oscillating boundary layer. Moreover, the probability density functions (PDFs) of both dissipation rates deviate significantly from the lognormal distribution and exhibit a bimodal shape. By partitioning the contributions from the boundary layer and bulk regions, it is shown that the bulk contributes to the small and moderate dissipation rates, whereas the high dissipation rates are predominantly contributed by the boundary layer. As Reos increases, the heavy tail of the PDFs becomes more pronounced, revealing an enhanced level of small-scale intermittency. This small-scale intermittency is mainly caused by the influence of BL due to vibration. Our study provides insight into the small-scale characteristics of 2D TVC, highlighting the non-trivial scaling laws and intermittent behavior of energy dissipation rates with respect to vibration intensity.

Low-Prandtl-number effects on global and local statistics in two-dimensional Rayleigh–Bénard convection

We present global and local statistical properties of turbulent Rayleigh–Bénard (RB) convection at low Prandtl numbers in this work. A series of high resolution two-dimensional (2D) direct numerical simulations are carried out in a square box for the Prandtl number ranges 0.005≤Pr≤0.07 and 0.01≤Pr≤0.15 at Rayleigh numbers Ra=107 and Ra=108, respectively. The global heat and momentum transport expressed as Nusselt number Nu and Reynolds number Re are found to scale as Nu∼Pr0.14 and Re∼Pr−0.82 for Ra=107, and Nu∼Pr0.11Re∼Pr−0.93 for Ra=108. The local velocity fluctuation at the cell center shows larger amplitudes at lowered Pr, indicating a stronger turbulence in the bulk. The magnitudes of kinetic and thermal energy dissipation rates in the bulk also increase with the decreasing of Pr, due to the intensified velocity gradient and larger thermal diffusivity, respectively. In the cell central region, probability density functions (PDFs) of velocity show a bimodal distribution, and it approaches the Gaussian distribution at higher Pr, while the PDFs of temperature display a stretched exponential shape with intermittent behavior. The kinetic energy spectra further reveal that the velocity cascade follows the Bolgiano–Obukhov scaling in the bulk of the convective flow.

The effect of tilt on turbulent thermal convection for a heated soap bubble

We use direct numerical simulation (DNS) to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator. In the DNS, the bubble is tilted by an angle δ∈[0°,90°], the Rayleigh number is varied between Ra∈[3×106,3×109], and the Prandlt number is fixed at Pr = 7. The DNS reveals two qualitatively different flow regimes: the dynamic plume regime (DPR) and the stable plume regime (SPR). In the DPR, small dynamic plumes constantly emerge from random locations on the equator and dissipate on the bubble. In the SPR, the flow is dominated by a single large and stable plume rising from the lower edge of the bubble. The scaling behavior of the Nusselt number Nu and Reynolds number Re is different in these two regimes, with Nu∝Ra0.3 for the DPR and Nu∝Ra0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re∝Ra0.48 and Re∝Ra0.53 depending on Ra and δ, while in the SPR, the scaling lies between Re∝Ra0.44 and Re∝Ra0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (εT′ and εu′, respectively) are also very different in the DPR and SPR. The probability density functions (PDF) of the normalized log εT′ and log εu′ are close to a Gaussian PDF for small fluctuations but deviate considerably from a Gaussian at large fluctuations in the DPR. In the SPR, the PDFs of normalized log εT′ and log εu′ deviate considerably from a Gaussian PDF even for small values. The globally averaged thermal energy dissipation rate due to the mean temperature field was shown to exhibit the scaling ⟨ε⟨T⟩⟩B∝Ra−0.23 in the DPR and ⟨ε⟨T⟩⟩B∝Ra−0.28 in the SPR. The globally averaged kinetic energy dissipation rate due to the mean velocity field is shown to exhibit the scaling ⟨ε⟨u⟩⟩B∝Ra−0.47 in the DPR (the exponent reduces from 0.47 to 0.43 as δ is increased up to 30°). In the SPR, the behavior changes considerably to ⟨ε⟨u⟩⟩B∝Ra−0.27. For the turbulent dissipation rates, the results indicate the scaling ⟨εT′⟩B∝Ra−0.18 and ⟨εu′⟩B∝Ra−0.29 in the DPR. However, the dependencies of ⟨εT′⟩B and ⟨εu′⟩B on Ra cannot be described by power-laws in the SPR.

Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We study the connection between extreme events of thermal and kinetic energy dissipation rates in the bulk of three-dimensional Rayleigh-Bénard convection and the wall shear stress patterns at the top and the bottom plates that enclose the layer. Zero points of this two-dimensional vector field stand for detachments of strong thermal plumes. If their position at the opposite plates and a given time is close then they can be considered as precursors for high-amplitude bulk dissipation events triggered by plume collisions or close passings. This scenario requires a breaking of the synchronicity of the boundary layer dynamics at both plates which is found to be in line with a transition of the bulk derivative statistics from Gaussian to intermittent. Our studies are based on three-dimensional high-resolution direct numerical simulations for moderate Rayleigh numbers between and .

Modular, Flexible, Low-Cost Microstructure Measurements: The Epsilometer

AbstractThe Epsilometer (“epsi”) is a small (7 cm diameter × 30 cm long), low-power (0.15 W), and extremely modular microstructure package measuring thermal and kinetic energy dissipation rates, χ and ε. Both the shear probes and FP07 temperature sensors are fabricated in house following techniques developed by Michael Gregg at the Applied Physics Laboratory/University of Washington (APL/UW). Sampling eight channels (two shear, two temperature, three-axis accelerometer, and a spare for future sensors) at 24 bit precision and 325 Hz, the system can be deployed in standalone mode (battery power and recording to microSD cards) for deployment on autonomous vehicles, wave powered profilers, or it can be used with dropping body termed the “epsi-fish” for profiling from boats, autonomous surface craft or ships with electric fishing reels or other simple winches. The epsi-fish can also be used in real-time mode with the Scripps “fast CTD” winch for fully streaming, altimeter-equipped, line-powered, rapid-repeating, near-bottom shipboard profiles to 2200 m. Because this winch has a 25 ft (~7.6 m) boom deployable outboard from the ship, contamination by ship wake is reduced one to two orders of magnitude in the upper 10–15 m. The noise floor of ε profiles from the epsi-fish is ~10−10 W kg−1. This paper describes the fabrication, electronics, and characteristics of the system, and documents its performance compared to its predecessor, the APL/UW Modular Microstructure Profiler (MMP).

Variance of Bottom Water Temperature at the Continental Margin of the Northern South China Sea

AbstractHigh‐resolution temperature variation was examined about 40 days near the ocean bottom at 20 sites within an area of 110 × 120 km2 close to the continental margin of the northern South China Sea (depth ≈ 4,000 m). The monitoring depth (0.5 m above the bottom) was presumably within the lower part of the bottom mixed layer, compared to its median thickness of 63 m. At all sites, the bottom water had temperature variance less than 0.01°C, and it alternatively varied in the near‐quiescent and internal wave states with time interval of diurnal period or even longer. Spectra of temperature variation showed that diurnal frequency dominated over the internal wave band. At different sites, the transition between internal wave band of scaling −2 and the inertial subrange turbulence of scaling −5/3 cannot easily be discriminated, attributed to the different intermittent presences of internal waves (tides). However, the resolved viscous‐convective and viscous‐diffusive subranges in the temperature spectrum provide the opportunity to evaluate the thermal (χ) and kinetic energy (ɛ) dissipation rates near the ocean bottom at each site. Close to a seamount, χ and ɛ were inferred to be about 1.2 × 10−12 °C2s−1 and 7.2 × 10−10 m2s−3, respectively, and they were strongly modulated by the diurnal internal tides. In the flat abyssal plain, χ and ɛ were much weaker, about at 3.2 × 10−14 °C2s−1 and 1.7 × 10−11 m2s−3, respectively. The spatial distribution of the nominal thermal χ, kinetic energy ɛ and the turbulent diffusivity Kρ indicated that they varied in the ranges [3.9 × 10−15 1.9 × 10−12] °C2s−1, [2.0 × 10−12 1.1 × 10−9] m2s−3, and [8.3 × 10−6 5.2 × 10−3] m2s−1, respectively, representing the different influences of internal waves and local topography.

Temporal-Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh-Taylor Mixing Zone.

In this work, the temporal–spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh–Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal–spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal–spatial dissipation-rate characteristic in the 3D turbulent Rayleigh–Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 106 ≤ Ra ≤ 107 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra0.25 and Re = 6.11Ra0.50, respectively, indicating that scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relatively lower Ra, while they approach the Gaussian profile at relatively higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re.

Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number

We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Bénard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-Bénard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106,3×106, and 107, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.

Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection

We investigate the statistical properties of the kinetic$\unicode[STIX]{x1D700}_{u}$and thermal$\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}$energy dissipation rates in two-dimensional (2-D) turbulent Rayleigh–Bénard (RB) convection. Direct numerical simulations were carried out in a box with unit aspect ratio in the Rayleigh number range$10^{6}\leqslant Ra\leqslant 10^{10}$for Prandtl numbers$Pr=0.7$and 5.3. The probability density functions (PDFs) of both dissipation rates are found to deviate significantly from a log-normal distribution. The PDF tails can be well described by a stretched exponential function, and become broader for higher Rayleigh number and lower Prandtl number, indicating an increasing degree of small-scale intermittency with increasing Reynolds number. Our results show that the ensemble averages$\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$and$\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$scale as$Ra^{-0.18\sim -0.20}$, which is in excellent agreement with the scaling estimated from the two global exact relations for the dissipation rates. By separating the bulk and boundary-layer contributions to the total dissipations, our results further reveal that$\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$and$\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$are both dominated by the boundary layers, corresponding to regimes$I_{l}$and$I_{u}$in the Grossmann–Lohse (GL) theory (J. Fluid Mech., vol. 407, 2000, pp. 27–56). To include the effects of thermal plumes, the plume–background partition is also considered and$\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$is found to be plume dominated. Moreover, the boundary-layer/plume contributions scale as those predicted by the GL theory, while the deviations from the GL predictions are observed for the bulk/background contributions. The possible reasons for the deviations are discussed.

Predictive Modeling of a Paradigm Mechanical Cooling Tower: I. Adjoint Sensitivity Model

Cooling towers discharge waste heat from an industrial process into the atmosphere, and are essential for the functioning of large energy-producing plants, including nuclear reactors. Using a numerical simulation model of the cooling tower together with measurements of outlet air relative humidity, outlet air and water temperatures enables the quantification of the rate of thermal energy dissipation removed from the respective process. The computed quantities depend on many model parameters including correlations, boundary conditions, material properties, etc. Changes in these model parameters will induce changes in the computed quantities of interest (called “model responses”). These changes are quantified by the functional derivatives (called “sensitivities”) of the model responses with respect to the model parameters. These sensitivities are computed in this work by applying the general Adjoint Sensitivity Analysis Methodology (ASAM) for nonlinear systems. These sensitivities are needed for: (i) ranking the parameters in their importance to contributing to response uncertainties; (ii) propagating the uncertainties (covariances) in these model parameters to quantify the uncertainties (covariances) in the model responses; (iii) performing predictive modeling, including assimilation of experimental measurements and calibration of model parameters to produce optimal predicted quantities (both model parameters and responses) with reduced predicted uncertainties.

Global and local statistics in turbulent convection at low Prandtl numbers

Statistical properties of turbulent Rayleigh–Bénard convection at low Prandtl numbers $Pr$, which are typical for liquid metals such as mercury or gallium ($Pr\simeq 0.021$) or liquid sodium ($Pr\simeq 0.005$), are investigated in high-resolution three-dimensional spectral element simulations in a closed cylindrical cell with an aspect ratio of one and are compared to previous turbulent convection simulations in air for $Pr=0.7$. We compare the scaling of global momentum and heat transfer. The scaling exponent $\unicode[STIX]{x1D6FD}$ of the power law $Nu=\unicode[STIX]{x1D6FC}Ra^{\unicode[STIX]{x1D6FD}}$ is $\unicode[STIX]{x1D6FD}=0.265\pm 0.01$ for $Pr=0.005$ and $\unicode[STIX]{x1D6FD}=0.26\pm 0.01$ for $Pr=0.021$, which are smaller than that for convection in air ($Pr=0.7$, $\unicode[STIX]{x1D6FD}=0.29\pm 0.01$). These exponents are in agreement with experiments. Mean profiles of the root-mean-square velocity as well as the thermal and kinetic energy dissipation rates have growing amplitudes with decreasing Prandtl number, which underlies a more vigorous bulk turbulence in the low-$Pr$ regime. The skin-friction coefficient displays a Reynolds number dependence that is close to that of an isothermal, intermittently turbulent velocity boundary layer. The thermal boundary layer thicknesses are larger as $Pr$ decreases and conversely the velocity boundary layer thicknesses become smaller. We investigate the scaling exponents and find a slight decrease in exponent magnitude for the thermal boundary layer thickness as $Pr$ decreases, but find the opposite case for the velocity boundary layer thickness scaling. A growing area fraction of turbulent patches close to the heating and cooling plates can be detected by exceeding a locally defined shear Reynolds number threshold. This area fraction is larger for lower $Pr$ at the same $Ra$, but the scaling exponent of its growth with Rayleigh number is reduced. Our analysis of the kurtosis of the locally defined shear Reynolds number demonstrates that the intermittency in the boundary layer is significantly increased for the lower Prandtl number and for sufficiently high Rayleigh number compared to convection in air. This complements our previous findings of enhanced bulk intermittency in low-Prandtl-number convection.

Kinetic and thermal energy dissipation rates in two-dimensional Rayleigh-Taylor turbulence

The statistical properties of the kinetic εu and thermal εθ energy dissipation rates in two-dimensional Rayleigh-Taylor (RT) turbulence are studied by means of direct numerical simulations at small Atwood number and unit Prandtl number. Although εθ is important but εu can be neglected in the energy transport processes, the probability density functions of εu and εθ both show self-similarity properties during the RT evolution. The distributions are well fitted by a stretched exponential function and found to depart distinctly from the log-normal distribution for small amplitudes. Within the turbulent range, the intense dissipation events occur near the interfaces of hot and cold fluids, leading to a strong positive correlation between εu and εθ. Our results further reveal that although there is no constant fractal dimension for the fluid interfaces within the inertial range, the local fractal dimensions obtained at different times share similar scale-dependence.

Photothermal microscopy: imaging of energy dissipation from photosynthetic complexes.

An idea of a photothermal imaging microscopy (PTIM) is proposed, along with its realization based on a dependence of fluorescence anisotropy of dye molecules on heat emission in their nearest vicinity. Erythrosine B was selected as a fluorophore convenient to report thermal deactivation of the excited pigment-protein complex isolated from the photosynthetic apparatus of plants (LHCII), owing to the relatively large spectral gap between the fluorescence emission bands of chlorophyll a and a probe. Comparison of the simultaneously recorded images based on fluorescence lifetime of LHCII and fluorescence anisotropy of erythrosine shows a high rate of thermal energy dissipation from the aggregated forms of the complex and, possibly, thermal energy transmission along the protein supramolecular structures. Relatively high resolution of this novel microscopic technique, comparable to the fluorescence lifetime microscopy, enables its application in a nanoscale imaging and in nanothermography.

Gravity Wave–Fine Structure Interactions. Part II: Energy Dissipation Evolutions, Statistics, and Implications

Abstract Part I of this paper employs four direct numerical simulations (DNSs) to examine the dynamics and energetics of idealized gravity wave–fine structure (GW–FS) interactions. That study and this companion paper were motivated by the ubiquity of multiscale GW–FS superpositions throughout the atmosphere. These DNSs exhibit combinations of wave–wave interactions and local instabilities that depart significantly from those accompanying idealized GWs or mean flows alone, surprising dependence of the flow evolution on the details of the FS, and an interesting additional pathway to instability and turbulence due to GW–FS superpositions. This paper examines the mechanical and thermal energy dissipation rates occurring in two of these DNSs. Findings include 1) dissipation that tends to be much more localized and variable than that due to GW instability in the absence of FS, 2) dissipation statistics indicative of multiple turbulence sources, 3) strong influences of FS shears on instability occurrence and turbulence intensities and statistics, and 4) significant differences between mechanical and thermal dissipation rate fields having potentially important implications for measurements of these flows.

Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh-Bénard convection

Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.

Effect of Particle Size and Relative Density on Powdery Fe3O4 Microwave Heating

In recent years, microwave energy is expected to be a heat source of high temperature process aiming for CO2 reduction and energy conservation owing to the possibility of volumetric heating. In order to examine the applicability of microwave heating to ironmaking, it is important to investigate the microwave heating of raw materials of ironmaking such as Fe3O4. In this study, the effect of particle size and relative density on microwave absorptivity of powdery Fe3O4 was elucidated by the heating curves. Powdery Fe3O4 samples having different particle sizes and relative densities and bulk Fe3O4 samples were heated at the positions of the H (magnetic) and E (electric) field maxima in a 2.45 GHz single-mode microwave cavity. Sample temperatures abruptly increase and become constant after a while. At a constant temperature, the energy balance is attained, i.e., the rate of microwave energy absorption is equal to the rate of thermal energy dissipation. Assuming that the thermal energy dissipation rate due to convection and radiation heat fluxes is only a function of the sample temperature, the microwave absorptivity could be evaluated by the temperature at the steady state. It has been found that the microwave absorptivity of Fe3O4 powder decreases with an increase in relative density. On the other hand, the microwave absorptivity hardly depends on the particle size, which may be due to its quite a large penetration depth of Fe3O4 compared to metal.

Photoprotection processes under water stress and recovery in Mediterranean plants with different growth forms and leaf habits

The response of photoprotection mechanisms to a short‐term water stress period followed by rewatering, to simulate common episodic water stress periods occurring in Mediterranean areas, was studied in 10 potted plants representative of different growth forms and leaf habits. During water stress and recovery, relative water content, stomatal conductance, leaf pigment composition, electron transport rates, maximum quantum efficiency of PSII photochemistry (Fv/Fm), thermal energy dissipation and photorespiration rates (Pr) were determined. All the species analyzed proved to be strongly resistant to photoinactivation of PSII under the imposed water stress conditions. The responses of the analyzed parameters did not differ largely among species, suggesting that Mediterranean plants have similar needs and capacity for photoprotection under episodic water stress periods regardless of their growth form and leaf habit. A general pattern of photoprotection emerged, consisting in maintenance or increase of Pr at mild stress and the increase of the thermal energy dissipation at more severe stress. Adjustments in pigment pool sizes were not an important short‐term response to water stress. The increase of thermal energy dissipation because of water stress depended mostly on the de‐epoxidation state of xanthophylls, although the slope and kinetics of such relationship strongly differed among species, suggesting species‐dependent additional roles of de‐epoxidated xanthophylls. Also, small decreases in Fv/Fm at predawn during water stress were strongly correlated with maintained de‐epoxidation of the xanthophylls cycle, suggesting that a form of xanthophyll‐dependent sustained photoprotection was developed during short‐term water stress not only in evergreen but also in semideciduous and annual species.

Antioxidants and xanthophyll cycle-dependent energy dissipation in Cucurbita pepo L. and Vinca major L. acclimated to four growth PPFDs in the field

The acclimation of photochemistry, xanthophyll cycledependent energy dissipation, and antioxidants was characterized in leaves of Cucurbita pepo L. and Vinca major L. that developed under photosynthetic photon flux densities (PPFDs) ranging from deep shade to full sunlight in the field. The predominant acclimatory response of leaf pigment composition was an increase in the xanthophyll cycle pool size with increasing growth PPFD. In both species, the estimated rate of thermal energy dissipation at midday increased with increasing PPFD and midday levels of zeaxanthin and antheraxanthin per chlorophyll were closely correlated with the levels of non-photochemical fluorescence quenching under all growth PPFD regimes. However, at full sunlight there appeared to be considerably higher levels of xanthophyll cycle-dependent energy dissipation in V. major compared with pumpkin while estimated rates of photochemistry exhibited the reverse trend. Leaf activities of the antioxidant enzymes ascorbate peroxidase and superoxide dismutase, as well as ascorbate content, increased with increasing growth PPFD in both plant species. Activities/contents were higher under 100% full sunlight and increased more strongly from intermediate growth PPFDs to 100% full sunlight in V. major than in C. pepo. These patterns of acclimation are similar to those exhibited by xanthophyll cycle-dependent energy dissipation. The patterns of acclimation of glutathione reductase are discussed in the context of the multiple roles for reduced glutathione. Catalase acclimated in a manner consistent with its role in scavenging H2O2 generated via photo respiration and/or mitochondrial respiration. Leaf α-tocopherol did not exhibit growth PPFD-dependent trends.