Mean Temperature Gradient Research Articles

Statistics of incremental averages of passive scalar fluctuations

Whereas statistical moments of differences of turbulent quantities measured over a given separation (viz., structure functions) have been extensively studied, statistics of incremental sums (or equivalently averages, e.g., Σθ≡[θ(x+r)+θ(x)]/2) of the same quantities have only been the subject of recent research. The present work investigates incremental averages of a turbulent passive scalar (temperature), measured in nearly homogeneous, and isotropic (passive and active), grid-generated turbulence, for turbulent Reynolds numbers in the range 94≤Rλ(≡urmsλ/ν)≤582. The scalar field is generated by the action of the turbulent velocity field against an imposed mean temperature gradient. Following the approach of Mouri and Hori [Phys. Fluids 22, 115110 (2010)] for the velocity field, we examine statistics of incremental averages of the passive scalar field as a function of separation (viz., incremental average structure functions) for different Reynolds numbers, comparing them with both the results of Mouri and Hori, as well as the corresponding incremental average structure functions for the velocity field for the flows studied herein. While the statistics of Σθ are primarily large-scale quantities, and would therefore be expected to be flow dependent, they exhibit certain similarities to the statistics of incremental averages of velocity (Σuα), measured both in the flow under consideration as well as the different classes of flows studied by Mouri and Hori. Finally, we derive a scale-dependent evolution equation for the incremental average of the scalar field fluctuations, Σθ. We discuss its relationship to Yaglom's four-thirds law for differences in passive scalar fluctuations and compare the results with the experimental data.

Reexamining the Gradient and Countergradient Representation of the Local and Nonlocal Heat Fluxes in the Convective Boundary Layer

Abstract Turbulent mixing in the daytime convective boundary layer (CBL) is carried out by organized nonlocal updrafts and smaller local eddies. In the upper mixed layer of the CBL, heat fluxes associated with nonlocal updrafts are directed up the local potential temperature gradient. To reproduce such countergradient behavior in parameterizations, a class of planetary boundary layer schemes adopts a countergradient correction term in addition to the classic downgradient eddy-diffusion term. Such schemes are popular because of their simple formulation and effective performance. This study reexamines those schemes to investigate the physical representations of the gradient and countergradient (GCG) terms, and to rebut the often-implied association of the GCG terms with heat fluxes due to local and nonlocal (LNL) eddies. To do so, large-eddy simulations (LESs) of six idealized CBL cases are performed. The GCG fluxes are computed a priori with horizontally averaged LES data, while the LNL fluxes are diagnosed through conditional sampling and Fourier decomposition of the LES flow field. It is found that in the upper mixed layer, the gradient term predicts downward fluxes in the presence of positive mean potential temperature gradient but is compensated by the upward countergradient correction flux, which is larger than the total heat flux. However, neither downward local fluxes nor larger-than-total nonlocal fluxes are diagnosed from LES. The difference reflects reduced turbulence efficiency for GCG fluxes and, in terms of physics, conceptual deficiencies in the GCG representation of CBL heat fluxes.

Direct numerical simulation of turbulent flow and heat transfer in a spatially developing turbulent boundary layer laden with particles

Direct numerical simulations of particle-laden flows in a spatially developing turbulent thermal boundary layer over an isothermally heated wall have been performed with realistic fully developed turbulent inflow boundary conditions. To the authors’ best knowledge, this is the first time the effects of inertial solid particles on turbulent flow and heat transfer in a flat-plate turbulent boundary layer have been investigated, using a two-way coupled Eulerian–Lagrangian method. Results indicate that the presence of particles increases the mean streamwise velocity and temperature gradients of the fluid in the near-wall region. As a result, the skin-friction drag and heat transfer are significantly enhanced in the particle-laden flows with respect to the single-phase flow. The near-wall sweep and ejection motions are suppressed by the particles and hence the Reynolds shear stress and wall-normal turbulent heat flux are attenuated, which leads to reductions in the production of the turbulent kinetic energy and temperature fluctuations. In addition, the coherence and spacing of the near-wall velocity and temperature streaky structures are distinctly increased, while the turbulent vortical structures appear to be disorganized under the effect of the particles. Moreover, the intensity of the streamwise vortices decreases monotonically with increasing particle inertia.

Exploitation of differential temperature-sensitivities of crops for improved resilience of tropical smallholder cropping systems to climate change: A case study with temperature responses of tomato and chilli

Increasing air temperatures due to long-term global climate change are predicted to exert substantial negative impacts on a majority of agricultural crops in the tropics, where most smallholder farms have a mixture of crops. Modification of the composition of cropping systems by incorporating crop species with greater growth and yield performance at higher temperatures is an important adaptation option. Accordingly, the principal objective of the present work was to demonstrate the feasibility of utilizing the differential temperature sensitivities of tropical crops to increase resilience of smallholder farming systems in the tropics to climate change, taking tomato and chilli in a case study. Tomato (cv. Thilina) and chilli (cv. MI-Green) crops were grown with adequate water, nutrients and recommended crop protection in a multi-locational field experiment traversing an altitudinal gradient (15–1200 m), which represented a gradient in seasonal mean temperature (Ta) ranging from 18.7 to 30 °C, over four consecutive seasons (Dec. 2012–Oct. 2014) in the humid- and sub-humid zones of Sri Lanka. Temperature response functions were estimated by linear regression of growth and yield parameters against Ta. Across the tested range of Ta, fruit yield of tomato showed a significant negative linear trend with increasing Ta (@ 2.83 Mg ha−1 °C−1) while the pod yield of chilli showed a significant positive linear trend (@ 0.51 Mg ha−1 °C−1). While the total biomass accumulation followed the same trend as fruit/pod yield, the harvest index of both crops showed significant negative trends, thus indicating the sensitivity of reproductive processes to increasing temperature. In tomato, fruit yield was significantly positively correlated to individual fruit weight, which decreased significantly with increasing temperature. In contrast, in chilli, pod yield was significantly positively correlated to number of pods per plant, which increased significantly with increasing temperature. These findings demonstrate the possibility of increasing the resilience of annual cropping systems in the tropical zone to future climate change by modifying their species composition via replacement of crops that are sensitive to higher temperatures (e.g. tomato) with those that are tolerant (e.g. chilli). The corresponding response functions to seasonal temperature extremes showed that biomass production, its partitioning to yield and yield of both crops were more sensitive to increases in seasonal mean daytime maximum temperature than to increases in night-time minimum temperature. However, yield responses to the diurnal temperature difference showed that differential sensitivity of the two crops to night-time minimum temperatures also played a significant role in determining their yield responses. These findings are useful in designing future cropping systems with greater resilience to climate change.

Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate epsilon , the length scale of energy-containing eddies mathcal {L}, a turbulence anisotropy parameter varGamma , the Richardson number Ri, and the normalized rate of destruction of temperature variance eta _theta equiv epsilon _theta /epsilon . Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin–Obukhov similarity theory, where z is the height above the Earth’s surface, and L is the Obukhov length corresponding to {Ri,eta _theta }. Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale sim 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.

On the Reduced North Atlantic Storminess during the Last Glacial Period: The Role of Topography in Shaping Synoptic Eddies

AbstractThe North Atlantic storminess of Last Glacial Maximum (LGM) fully coupled climate simulations is generally less intense than that of their preindustrial (PI) counterparts, despite having stronger baroclinicity. An explanation for this counterintuitive result is presented by comparing two simulations of the IPSL full climate model forced by Paleoclimate Modelling Intercomparison Project Phase 3 (PMIP3) LGM and PI conditions. Two additional numerical experiments using a simplified dry general circulation model forced by idealized topography and a relaxation in temperature provide guidance for the dynamical interpretation. The forced experiment with idealized Rockies and an idealized Laurentide Ice Sheet has a less intense North Atlantic storm-track activity than the forced experiment with idealized Rockies only, despite similar baroclinicity. Both the climate and idealized runs satisfy or support the following statements. The reduced storm-track intensity can be explained by a reduced baroclinic conversion, which itself comes from a loss in eddy efficiency to tap the available potential energy as shown by energetic budgets. The eddy heat fluxes are northeastward oriented in the western Atlantic in LGM and are less well aligned with the mean temperature gradient than in PI. The southern slope of the Laurentide Ice Sheet topography forces the eddy geopotential isolines to be zonally oriented at low levels in its proximity. This distorts the tubes of constant eddy geopotential in such a way that they tilt northwestward with height during baroclinic growth in LGM while they are more optimally westward tilted in PI.

The effect of an axial mean temperature gradient on communication between one-dimensional acoustic and entropy waves

This work performs a theoretical and numerical analysis of the communication between one-dimensional acoustic and entropy waves in a duct with a mean temperature gradient. Such a situation is highly relevant to combustor flows where the mean temperature drops axially due to heat losses. A duct containing a compact heating element followed by an axial temperature gradient and choked end is considered. The proposed jump conditions linking acoustic and entropy waves on either side of the flame show that the generated entropy wave is generally proportional to the mean temperature ratio across the flame and the ratio [Formula: see text], where [Formula: see text] is the flame transfer function. It is inversely proportional to the Mach number immediately downstream of the flame M2. The acoustic and entropy fields in the region of axial mean temperature gradient are calculated using four approaches: (1) using the full three linearised Euler equations as the reference; (2) using two linearised Euler equations in which the acoustic and entropy waves are assumed independent (thus allowing the extent of communication between the acoustic and entropy wave to be evaluated); (3) using a Helmholtz solver which neglects mean flow effects and (4) using a recently developed analytical solution. It is found that the communication between the acoustic and entropy waves is small at low Mach numbers; it rises with increasing Mach number and cannot be neglected when the mean Mach number downstream of the heating element exceeds 0.1. Predictions from the analytical method generally match those from the full three linearised Euler equations, and the Helmholtz solver accurately determines the acoustic field when [Formula: see text].

Was That Assumption Necessary? Reconsidering Boundary Conditions for Analytical Solutions to Estimate Streambed Fluxes

AbstractTwo common refrains about using the one‐dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency‐domain solutions to estimate thermal diffusivity and 1‐D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.

Infrared thermography as a noninvasive method to assess scrotal insulation on sperm production in beef bulls

This study evaluated the thermoregulation and spermatogenic changes by scrotal temperature gradient using infrared thermography in testicular compromised bulls. Bulls were insulated (n=6) for 72hr and control animals (n=3) remained without insulation during all the experimental period. Seminal evaluation was performed prior, at insult removal and once per week for 13 consecutive weeks. Mean temperature gradient in insulated animals was lower at the time of insulation removal compared to the week prior and after the insult (p<.05). Two weeks after insult, sperm motility was lower in insulated compared to control animals (p<.01) and spermatozoa total defects were higher in insulated compared to control animals (p<.05). Two and seven weeks after insult, the major defects were higher in insulated compared to control animals (p<.05). Scrotal temperature gradient showed a positive correlation with sperm mass motion (p<.01) and a negative correlation with ocular globe temperature (p<.01) in insulated animals. The infrared thermography can be used to evaluate ocular globe temperature in bulls; however, it is only effective to detect changes in scrotal temperature gradient at the insult removal.

A new device for vein localization and effect of application of disinfectant spray on its efficiency

Abstract A functional device was developed to immediately show the localization of veins by detecting a temperature increase on the skin directly above them. Our new idea, compared to other developments, is the comparison of temperatures between a small, ideally punctiform, skin area, and a larger circularly surrounding area. This is realized by two infrared temperature sensors, one with a small field of view, and the other one with a larger field of view. The position of the vein is indicated by two laser modules, which beams cross in one spot, when the device is held in a defined distance to the skin. If the device is held over a vein, the laser spot lightens up. The device was tested in ten study participants. Cooling of the skin by disinfectant spray prior to the measurements increases the temperature gradient and thereby improves the efficiency of the device. Temperature profiles of four skin areas of each study participant were measured before and one minute after application of disinfectant spray. After application of disinfectant spray, a temperature difference of more than 0.3 K between a measuring point above a vein and points 15 mm next to this could be found in 36 out of 40 measurements (90%), compared to 26 out of 40 (65%) before disinfection. The mean temperature gradient could be increased from 0.476 K to 1.03 K (p &lt; 0.001).

Mechanisms underlying recent decadal changes in subpolar North Atlantic Ocean heat content

AbstractThe subpolar North Atlantic (SPNA) is subject to strong decadal variability, with implications for surface climate and its predictability. In 2004–2005, SPNA decadal upper ocean and sea‐surface temperature trends reversed from warming during 1994–2004 to cooling over 2005–2015. This recent decadal trend reversal in SPNA ocean heat content (OHC) is studied using a physically consistent, observationally constrained global ocean state estimate covering 1992–2015. The estimate's physical consistency facilitates quantitative causal attribution of ocean variations. Closed heat budget diagnostics reveal that the SPNA OHC trend reversal is the result of heat advection by midlatitude ocean circulation. Kinematic decompositions reveal that changes in the deep and intermediate vertical overturning circulation cannot account for the trend reversal, but rather ocean heat transports by horizontal gyre circulations render the primary contributions. The shift in horizontal gyre advection reflects anomalous circulation acting on the mean temperature gradients. Maximum covariance analysis (MCA) reveals strong covariation between the anomalous horizontal gyre circulation and variations in the local wind stress curl, suggestive of a Sverdrup response. Results have implications for decadal predictability.

Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores

We study rapidly-rotating Boussinesq convection driven by internal heating in a full sphere. We use a numerical model based on the quasi-geostrophic approximation for the velocity field, whereas the temperature field is three-dimensional. This approximation allows us to perform simulations for Ekman numbers down to 1e-8, Prandtl numbers relevant for liquid metals (~0.1) and Reynolds numbers up to 3e4. Persistent zonal flows composed of multiple jets form as a result of the mixing of potential vorticity. For the largest Rayleigh numbers computed, the zonal velocity is larger than the convective velocity despite the presence of boundary friction. The convective structures and the zonal jets widen when the thermal forcing increases. Prograde and retrograde zonal jets are dynamically different: in the prograde jets (which correspond to weak potential vorticity gradients) the convection transports heat efficiently and the mean temperature tends to be homogenised; by contrast, in the cores of the retrograde jets (which correspond to steep gradients of potential vorticity) the dynamics is dominated by the propagation of Rossby waves, resulting in the formation of steep mean temperature gradients and the dominance of conduction in the heat transfer process. Consequently, in quasi-geostrophic systems, the width of the retrograde zonal jets controls the efficiency of the heat transfer.

Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.

The one-dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow

This paper presents an analytical solution for the one-dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow. A wave equation for the pressure perturbation is derived which relies on very few assumptions. An analytical solution for this is derived using an adapted WKB approximation. The solution is a superposition of waves travelling in either direction and thus provides physical insight. It is also very easy to calculate. The proposed solution is applied to ducts with a mean temperature profile which varies axially with (i) a linear and (ii) a partial sine wave profile: predictions are compared to those obtained by numerically solving the linearised Euler equations (LEEs). The analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate-to-high subsonic Mach numbers. It always performs well when the frequency exceeds a certain value; when the mean temperature profile is linear, it also performs well to very low frequencies. This increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner, axially segmenting the temperature profile into regions that can be approximated as linear. The acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied: |k0|>|α|, where k0 is the local wave number when there is no mean flow and α is the normalised mean density gradient. The proposed solution is extensively compared to previous analytical solutions, and is found to be more accurate and reliable, especially at higher Mach numbers. The entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the LEEs. It is found to remain very small across all operating conditions, such that both the entropy wave and its impact on the acoustic field can be neglected.

Entropy Generation Analysis and Performance Evaluation of Turbulent Forced Convective Heat Transfer to Nanofluids

The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS) model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases of effective properties. The uniform heat flux is enforced at the tube wall. To confirm the validity of the numerical approach, the results have been compared with empirical correlations and analytical formula. The self-similarity profiles of local entropy generation are also studied, in which the peak values of entropy generation by direct dissipation, turbulent dissipation, mean temperature gradients and fluctuating temperature gradients for different Reynolds number as well as different particle concentration are observed. In addition, the effects of Reynolds number, volume fraction of nanoparticles and heat flux on total entropy generation and Bejan number are discussed. In the results, the intersection points of total entropy generation for water and four nanofluids are observed, when the entropy generation decrease before the intersection and increase after the intersection as the particle concentration increases. Finally, by definition of Ep, which combines the first law and second law of thermodynamics and attributed to evaluate the real performance of heat transfer processes, the optimal Reynolds number Reop corresponding to the best performance and the advisable Reynolds number Read providing the appropriate Reynolds number range for nanofluids in convective heat transfer can be determined.

Influence of texture on thermal transport in streamwise-aligned superhydrophobic turbulent channels

A series of Direct Numerical Simulations (DNS) is performed for a systematic study of thermal transport in a periodic turbulent channel bounded by superhydrophobic surface (SHS) walls at a friction Reynolds number of Reτ=180. The SHS examined here is comprised of interspersed ridges and cavities aligned along the mean streamwise flow direction. The SHS is modelled as a planar surface consisting of spanwise-alternating regions of free-shear and no-slip boundary conditions. Water is considered as the bulk fluid where the SHS surface is assumed to be in a Cassie-Baxter state with non-wetting cavities containing air. The ridges are maintained at a constant temperature while heat transfer through the air/water interface supported by the ridges is assumed negligible and is modelled as adiabatic. Phase averaged statistics were obtained for a range of relative periodicity widths. Reorganisation of secondary flow structures owing to an increase in SHS feature width and its effect on thermal transport are analyzed with a particular focus on phase-averaged statistics. The relative feature width or periodicity length is found to influence strongly on thermal performance, or the average Nusselt number. A reduction in the turbulent Prandtl number is observed in the buffer region due to an increase in thermal eddy diffusivity relative to the momentum eddy diffusivity. The amount of heat transfer and mixing depend upon the periodicity length, and there is a reduction in the heat transfer along with the drag-reduction. A substantial decrease in the temperature fluctuations is observed in the vicinity of the wall as the production of temperature variance is diminished with an increase in the periodicity length, primarily due to a reduction in the mean temperature gradient in the wall-normal direction.

Validation of buoyancy driven spectral tensor model using HATS data

We present a homogeneous spectral tensor model for wind velocity and temperature fluctuations, driven by mean vertical shear and mean temperature gradient. Results from the model, including one-dimensional velocity and temperature spectra and the associated co-spectra, are shown in this paper. The model also reproduces two-point statistics, such as coherence and phases, via cross-spectra between two points separated in space. Model results are compared with observations from the Horizontal Array Turbulence Study (HATS) field program (Horst et al. 2004). The spectral velocity tensor in the model is described via five parameters: the dissipation rate (ϵ), length scale of energy-containing eddies (L), a turbulence anisotropy parameter (Γ), gradient Richardson number (Ri) representing the atmospheric stability and the rate of destruction of temperature variance (ηθ).

Simultaneous kHz-rate temperature and velocity field measurements in the flow emanating from angled and trenched film cooling holes

To design more efficient film cooling geometries for gas turbines, non-intrusive measurements of the flow temperature, velocity and derived quantities like the turbulent heat flux are needed in well-defined, generic flow configurations. With this aim we have applied thermographic particle image velocimetry (thermographic PIV) to investigate the flow emanating from angled and trenched cooling holes in a closed-loop optically-accessible wind tunnel facility. BAM:Eu2+ thermographic phosphor particles were seeded into the flow as a tracer. A pulsed high-speed UV laser was used to excite the particles and the luminescence was detected using two high-speed cameras to determine the temperature field by a two-colour ratiometric approach. The velocity field was measured using ordinary high-speed PIV. The simultaneously measured fields were sampled at a rate of 6kHz in a vertical plane through the centreline of the symmetrical single-row cooling holes. The flowrate and temperature of the cooling air and heated main flow were chosen to achieve density and momentum flux ratios of 1.6 and 8 respectively. For these conditions the average and RMS temperature fields show that for ordinary angled holes the jet is detached from the surface. In contrast, the trenched geometry leads to a cooling film attached to the surface. However, time-resolved image sequences show instances where hot air breaks through the cooling film and almost reaches the surface. Similar image sequences for the angled holes show that the detached coolant jet becomes unstable downstream and pockets of cold air are ejected into the main flow. This intermittency may in part explain the observation that the measured turbulent heat flux is oriented towards the cold core, but deviates from the direction of the mean temperature gradient, thereby contradicting the simple gradient diffusion hypothesis commonly used in RANS simulations.

Transition to geostrophic convection: the role of the boundary conditions

Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotating while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier–Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\times 10^{10}$, at constant Prandtl number $Pr=1$, and vary the Ekman number in the range $Ek=1.3\times 10^{-7}$ to $Ek=2\times 10^{-6}$, which satisfies both requirements of supercriticality and strong rotation. We focus on the differences between the application of no-slip versus stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at $Ek\approx 9\times 10^{-7}$ for $Ra=1\times 10^{10}$ and at $Ek\approx 3\times 10^{-7}$ for $Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in $Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat-transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions, the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

Influence of Canopy Seasonal Changes on Turbulence Parameterization within the Roughness Sublayer over an Orchard Canopy

Abstract In this observational study, the role of tree phenology on the atmospheric turbulence parameterization over 10-m-tall and relatively sparse deciduous vegetation is quantified. Observations from the Canopy Horizontal Array Turbulence Study (CHATS) field experiment are analyzed to establish the dependence of the turbulent exchange of momentum, heat, and moisture, as well as kinetic energy on canopy phenological evolution through widely used parameterization models based on 1) dimensionless gradients or 2) turbulent kinetic energy (TKE) in the roughness sublayer. Observed vertical turbulent fluxes and gradients of mean wind, temperature, and humidity, as well as velocity variances, are used in combination with empirical dimensionless functions to calculate the turbulent exchange coefficient. The analysis shows that changes in canopy phenology influence the turbulent exchange of all quantities analyzed in this study. The turbulent exchange coefficients of those quantities are twice as large near the canopy top for a leafless canopy than for a full-leaf canopy under unstable and near-neutral conditions. This turbulent exchange coefficient difference is related to the differing penetration depths of the turbulent eddies organized at the canopy top, which increase for a canopy without leaves. The TKE and dissipation analysis under near-neutral atmospheric conditions additionally shows that TKE exchange increases for a leafless canopy because of reduced TKE dissipation efficiency relative to that when the canopy is in full-leaf stage. The study closes with discussion surrounding the implications of these findings for parameterizations used in large-scale models.