The K-type and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 adjacent to an isothermally heated vertical surface are investigated by means of three-dimensional direct numerical simulation (DNS). These two types of transitions refer to different flow features at the transitional stage from laminar to turbulence caused by two different types of perturbations. To excite the K-type transition, superimposed Tollmien–Schlichting (TS) and oblique waves of the same frequency are introduced into the boundary layer. It is found that a three-layer longitudinal vortex structure is present in the boundary layer undergoing the K-type transition. The typical aligned $\wedge$-shaped vortices characterizing the K-type transition are observed for the first time in pure natural convection boundary layers. For exciting the H-type transition, superimposed TS and oblique waves of different frequencies, with the frequency of the oblique waves being half of the frequency of the TS waves, are introduced into the boundary layer. Unlike the three-layer longitudinal vortex structure observed in the K-type transition, a double-layer longitudinal vortex structure is observed in the boundary layer undergoing the H-type transition. The successively staggered $\wedge$-shaped vortices characterizing the H-type transition are also observed in the downstream boundary layer. The staggered pattern of $\wedge$-shaped vortices is considered to be caused by temporal modulation of the TS and oblique waves. Interestingly the flow structures of both the K-type and H-type transitions observed in the natural convection boundary layer are qualitatively similar to those observed in Blasius boundary layers. However, an analysis of turbulence energy production suggests that the turbulence energy production by buoyancy rather than Reynolds stresses dominates the K-type and H-type transitions. In contrast, the turbulence energy production by Reynolds stresses is the only factor contributing to the transition in Blasius boundary layers.

The instability characteristics and resonance of a natural convection boundary layer adjacent to an isothermally heated vertical surface are investigated using direct stability analyses. The detailed streamwise evolution of the boundary-layer frequencies is visualized via the power spectra of the temperature time series in the thermal boundary layer. It is found that the entire thermal boundary layer may be divided into three distinct regions according to the frequency profile, which include an upstream low-frequency region, a transitional region (with both low- and high-frequency bands) and a downstream high-frequency region. The high-frequency band in the downstream region determines the resonance characteristics of the thermal boundary layer, which can be triggered by a single-mode perturbation at frequencies within the high-frequency band. The single-mode perturbation experiments further reveal that the maximum resonance of the thermal boundary layer is triggered by a perturbation at the characteristic frequency of the boundary layer. For the boundary-layer flow at $\mathit{Ra}= 3. 6\times 1{0}^{10} $ and $\mathit{Pr}= 7$, a net heat transfer enhancement of up to 44 % is achieved by triggering resonance of the boundary layer. This significant enhancement of heat transfer is due to the resonance-induced advancement of the laminar–turbulent transition, which is found to be dependent on the perturbation frequency and amplitude. Evidence from different perspectives revealing the same position of the transition are provided and discussed. The outcomes of this investigation demonstrate the prospect of a resonance-based approach for enhancing heat transfer.

With rapid urbanization, population growth and anthropogenic activities, an increasing number of major cities across the globe are facing severe urban heat islands (UHI). UHI can cause complex impacts on the urban environment and human health, and it may bring more severe effects under heatwave (HW) conditions. In this paper, a holistic review is conducted to articulate the findings of the synergies between UHI and HW and corresponding mitigation measures proposed by the research community. It is worth pointing out that most studies show that urban areas are more vulnerable than rural areas during HWs, but the opposite is also observed in some studies. Changes in urban energy budget and major drivers are discussed and compared to explain such discrepancies. Recent studies also indicate that increasing albedo, vegetation fraction and irrigation can lower the urban temperature during HWs. Research gaps in this topic necessitate more studies concerning vulnerable cities in developing countries. Moreover, multidisciplinary studies considering factors such as UHI, HW, human comfort, pollution dispersion and the efficacy of mitigation measures should be conducted to provide more accurate and explicit guidance to urban planners and policymakers.

The present study aimed to investigate whether 17β-estradiol (E2) exerts protective effects on bone deterioration induced by ovariectomy (OVX) through the ephA2/ephrinA2 signaling pathway in rats. Female rats were subjected to OVX, sham surgeryor OVX+E2 treatment. Levels of biomarkers were measured in serum and urine. Hematoxylin and eosin staining was performed on paraffin-embedded bone sections. Expression of genes and proteins was analyzed by reverse transcription-quantitative polymerase chain reaction and western blotting, respectively. Bone mineral density (BMD) was analyzed by dual-energy X-ray absorptiometry. Trabecular bone microarchitecture was also evaluated. Osteoclastogenesis was induced by in vitro culturing with mouse receptor activator of nuclear factor κB ligand (RANKL) and macrophage colony-stimulating factor 1. small interfering RNA was designed to knockdown ehpA2 receptor and its ligand ephrinA2. Results of the present study demonstrated that E2 had suppressive effects on OVX-induced body weight gain and bone turnover factors in serum and urine. E2 inhibited the bone resorption function of osteoclasts by inhibiting the production of tartrate-resistant acid phosphatase-5b and RANKL, and induced bone formation function of osteoblasts by prompting runt-related transcription factor 2, Sp7 transcription factor and collagen alpha-1(I) chain expression in bone marrow cells. E2 treatment significantly increased the tibia BMD and prevented the deterioration of trabecular microarchitecture compared with the OVX group. Moreover, E2 significantly decreased the OVX-stimulated expression of ephA2 and ephrinA2. EphA2 or ephrin A2 knockdown significantly suppressed osteoclastogenesis in vitro. In conclusion, E2 can attenuate OVX-induced bone deterioration partially through the suppression of the ephA2/ephrinA2 signaling pathway. Therefore EphA2/ephrinA2 signaling pathway may be a potential target for osteoporosis treatment.

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