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We developed a numerical model of thermal convection of highly viscous incompressible fluids, aiming at reproducing plate tectonics in the framework of mantle convection. A two-dimensional basally-heated convection is considered under the Boussinesq approximation in a half of cylindrical annulus whose inner and outer radii are close to those of the Earth’s mantle. The viscosity is assumed to nonlinearly depend on “degree of damage” as well as temperature and pressure. The heart of the present rheology model lies in the hysteresis between the “intact” and “damaged” branches at low and high stress, respectively. The hysteresis induces the dependence on stress-history in viscosity for a particular range of applied stress, which enables us to distinguish the stiff plate interiors and weak plate boundaries. In a series of calculations by systematically varying the temperature-dependence in viscosity, we obtained a regime of convection where the nature of highly viscous cold fluid is quite similar to that of the Earth’s plates at an intermediate temperature-dependence; the layer of cold viscous fluid is divided into several pieces of rigid plates each of which horizontally moves, and the surface heat flow decreases with the distance from the divergent margin (ridge) in accordance with the half-space cooling. A careful analysis on the mechanical states in the cold thermal boundary layer (cTBL) showed that the occurrence of the “plate-like” (PL) convection is closely related to the hysteresis in viscosity; the PL convection takes place only when the stress level σ cTBL in cTBL, estimated from the ridge-push force, can induce the stress-history dependence in viscosity. By comparing the convecting flow structures in our experiments with the earlier ones Using 2-D Cartesian geometry, we also found that σ cTBL is almost unchanged for both cases, which results in the occurrence of the PL mode under very similar conditions regardless of the model geometries. Our findings not only highlight the ultimate importance of stress-history-dependent rheology in the self-consistent reproduction of tectonics plates, but also offer hints for future attempts toward integrated models of mantle convection and plate tectonics in three-dimensional spherical geometry. Graphical Abstract

Solar chimneys may induce natural ventilation through solar radiation. However, sufficient theoretical studies are needed as a basis to fully exploit passive design in practical green building design. In this work, we investigate the heat transfer properties of turbulent natural convective flows in a combined solar chimney with a thermal flux at the absorption wall by means of theoretical analysis and numerical simulations. Two different flow patterns have been found, one with a clear thermal boundary layer flow pattern and the other without, based on high Rayleigh numbers. For flow development in these two flow regimes, the transient scaling analysis is performed separately and the control mechanism for each phase is presented. Some new scale relationships are established to characterize the ventilation performance of solar chimneys, including thermal boundary layer thickness δT, velocity vT, mass flow m, and so on. For the distinct thermal boundary layers, δT,s ~ HΓ2/5/Bo1/5κ2/5, vT,s ~ Bo2/5κ4/5Γ1/5/H, m ~ ρBo1/5κ2/5Γ3/5. For nonobvious thermal boundary layers, vT,f ~ Bo1/3κ/H2/3W1/3, m ~ ρBo1/3κ/A2/3. The important scale relationships are validated using corresponding numerical simulation data, such as the mass flow rate scale M ~ (Γ/κ)3/5Bo1/5 in the distinct thermal boundary layer flow state, and so on. The air changes per hour and heat exchange efficiencies are calculated for a solar chimney with a fixed height‐to‐width ratio to provide a basis for the design of a solar chimney. Theoretical analysis and numerical study of natural convection inside combined solar chimney.

During summer daytime, the surface PM 2.5 concentration tends to rise briefly in the west coast of Bohai Sea, which might be related to the thermal internal boundary layer (TIBL) formed by the land-sea thermal interaction. In this study, we investigated the relationship between land-sea air temperature and pollutant concentration in summer over a coastal region of northern China using an unmanned aerial vehicle (UAV)-measurement platform to obtain vertical meteorological data and pollutant concentration. In midday, when only considered onshore winds, PM 2.5 concentration was significantly higher than that in not considered onshore winds, meanwhile the high positive correlation between land-sea temperature difference and particle concentration was identified. It can be seen from the UAV observed profiles that the TIBLs were formed at the bottom of the atmospheric layer in the daytime with height values in the range of 44–97 m, resulting from the impact of onshore winds caused by land-sea thermal difference. This land-sea thermal difference influences the atmospheric boundary layer (ABL) and TIBL structures, also the PM 2.5 concentration diffusion. We found that larger land-sea temperature difference could induce lower coastal ABL height and larger potential temperature vertical gradients below TIBL, even delaying the stable layer establishment. When TIBL and ABL heights increased, as a result, the height of the maximum PM 2.5 concentration also increased. In addition, TIBL could lead to an increase in surface PM 2.5 concentration lasting for 2 hours during the daytime. Our results establish the relationship between land-sea temperature difference and particle diffusion, and have an important role in coastal air quality forecast.

Using GRIMM-1107 aerosol sampler, GOES-9 DCD satellite images, HYSPLIT model of backward trajectory and 3D-meteorological WRF-3.6 model, high particulate matter concentrations were investigated at Gangneung city in the Korean east coast which consists of Mt. Taeglyung in its west and the East Sea in its east on 00:00LST March 26~00:00 LST 4 April 2004. During a Yellow Dust period, the maximum PM10 (PM2.5 and PM1) concentration at the city was about 3.3 (1.1 and 1.01) times higher than one in the non-dust period. After the transported dust from the Gobi Desert and Nei-Mongo by strong northwesterly wind passed over Mt. Taegulyang and moved down toward the city. Then the dust was trapped inside a calm cavity generated by the confront of internal gravity waves (IGW) over the city and the eastward movement of the trapped dust is prohibited by the easterly onshore wind from the East Sea, and the trapped dust further combined with particulate and gaseous emitted from the road vehicles and heating boilers of the city at 09:00LST, March 30 (beginning time of office hours), causing high PM concentrations. On mid-day, as the combined dust due to daytime sufficient thermal convection rises up to the top of the thermal internal boundary layer (TIBL) of a 300 m depth from the coast to the top of the mountain, the ground-based PM concentrations in the city are much lower at 15:00LST due to the higher thickness of the TIBL than at 09:00LST. At night, particulates emitted from many road vehicles after the end of office hours and residential heating boilers could combine with both dust transported from the Nei-Mongo and falling dust uplifted from the ground surface of the city during the day, and they were trapped inside a calm cavity by the IGV under much shallower stable nocturnal surface inversion layer than the TIBL, causing more dust to be accumulated near the surface and showing the maximum PM concentrations at 20:00 LST.

Sonic nozzles are widely used as flow measurement and transfer standard. The thermal effect of sonic nozzle is significant at low Reynolds number. It includes two correction factors, CT for the thermal boundary layer and Ca for constrained thermal deformation of throat area. Firstly, using the similarity solution, the formula for correction factor CT over wall temperature range from 0.8T0 to 1.2T0 was obtained. For g = 1.33, CT = 1 - 3.800Re-1/2DT/T0; for g = 1.4, CT = 1 - 3.845Re-1/2DT/T0; for g = 1.67, CT = 1 - 4.010Re-1/2DT/T0. Secondly, thermal and stress models for partially constrained expansion were built. Unlike the free expansion, truth slopes of Ca for three nozzles are +1.74×10-6, -2.75×10-5 and -3.61×10-5, respectively. Lastly, the experimental data of copper nozzle was used to validate present results. It revealed that modified experimental values are in good agreement with the present result.

Using super-large-scale particle image velocimetry (SLPIV), we investigate the spatial structure of the near-wall region in the fully rough atmospheric surface layer with Reynolds number $Re_{\\unicode[STIX]{x1D70F}}\\sim O(10^{6})$ . The field site consists of relatively flat, snow-covered farmland, allowing for the development of a fully rough turbulent boundary layer under near-neutral thermal stability conditions. The imaging field of view extends from 3 m to 19 m above the ground and captures the top of the roughness sublayer and the bottom of an extensive logarithmic region. The SLPIV technique uses natural snowfall as seeding particles for the flow imaging. We demonstrate that SLPIV provides reliable measurements of first- and second-order velocity statistics in the streamwise and wall-normal directions. Our results in the logarithmic region show that the structural features identified in laboratory studies are similarly present in the atmosphere. Using instantaneous vector fields and two-point correlation analysis, we identify vortex structures sharing the signature of hairpin vortex packets. We also evaluate the zonal structure of the boundary layer by tracking uniform momentum zones (UMZs) and the shear interfaces between UMZs in space and time. Statistics of the UMZs and shear interfaces reveal the role of the zonal structure in determining the mean and variance profiles. The velocity difference across the shear interfaces scales with the friction velocity, in agreement with previous studies, and the size of the UMZs scales with wall-normal distance, in agreement with the attached eddy framework.

The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

We perform direct numerical simulations of wall sheared Rayleigh–Bénard convection for Rayleigh numbers up to $Ra=10^{8}$, Prandtl number unity and wall shear Reynolds numbers up to $Re_{w}=10\\,000$. Using the Monin–Obukhov length $L_{MO}$ we observe the presence of three different flow states, a buoyancy dominated regime ($L_{MO}\\lesssim \\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$; with $\\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$ the thermal boundary layer thickness), a transitional regime ($0.5H\\gtrsim L_{MO}\\gtrsim \\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$; with $H$ the height of the domain) and a shear dominated regime ($L_{MO}\\gtrsim 0.5H$). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed $Ra$ and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number $Nu$ effectively scales as $Nu\\sim Ra^{\\unicode[STIX]{x1D6FC}}$ with $\\unicode[STIX]{x1D6FC}\\ll 1/3$, while we find $\\unicode[STIX]{x1D6FC}\\simeq 0.30$ in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is $\\unicode[STIX]{x1D6FC}>1/3$, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.

We investigate the interplay between large-scale patterns, so-called superstructures, in the fluctuation fields of temperature$\\unicode[STIX]{x1D703}$and vertical velocity$w$in turbulent Rayleigh–Bénard convection at large aspect ratios. Earlier studies suggested that velocity superstructures were smaller than their thermal counterparts in the centre of the domain. However, a scale-by-scale analysis of the correlation between the two fields employing the linear coherence spectrum reveals that superstructures of the same size exist in both fields, which are almost perfectly correlated. The issue is further clarified by the observation that, in contrast to the temperature, and unlike assumed previously, superstructures in the vertical-velocity field do not result in a peak in the power spectrum of$w$. The origin of this difference is traced back to the production terms of the$\\unicode[STIX]{x1D703}$and$w$variance. These results are confirmed for a range of Rayleigh numbers$Ra=10^{5}{-}10^{9}$; the superstructure size is seen to increase monotonically with$Ra$. Furthermore, the scale distribution of the temperature fluctuations in particular is pronouncedly bimodal. In addition to the large-scale peak caused by the superstructures, there exists a strong small-scale peak. This ‘inner peak’ is most intense at a distance of$\\unicode[STIX]{x1D6FF}_{\\unicode[STIX]{x1D703}}$from the wall and is associated with structures of size${\\approx}10\\unicode[STIX]{x1D6FF}_{\\unicode[STIX]{x1D703}}$, where$\\unicode[STIX]{x1D6FF}_{\\unicode[STIX]{x1D703}}$is the thermal boundary layer thickness. Finally, based on the vertical coherence relative to a reference height of$\\unicode[STIX]{x1D6FF}_{\\unicode[STIX]{x1D703}}$, a self-similar structure is identified in the velocity field (vertical and horizontal components) but not in the temperature.