Research article

A two- to three-dimensional wake transition mechanism induced by the angle of attack of a NACA0012 airfoil

  • A high-order spectral element method was used to perform three-dimensional direct numerical simulations of the flow past a NACA0012 airfoil. We considered a Reynolds number Re=1000 and two different angles of attack, α=11 and α=16, to study the two- to three-dimensional wake transition. A boundary layer separation was observed for both angles of attack with the separation point closer to the leading edge for α=16. The downstream of the airfoil exhibited streamwise vortical structures formed in the braid regions connecting the primary vortices for α=16, while only shed vortices were observed for α=11. The formation of these streamwise structures were explained by the presence of a reverse flow from the lower surface for α=16, enhancing shearing effects. The early-stage development of the three-dimensional wake, in the case of α=16, was characterized by the formation of a spanwise sinusoidal velocity whose amplitude increased exponentially over time. The flow on the upper surface experienced a higher strain field which pulled up small disturbances from the airfoil surface and formed regions of concentrated vortical structures. These structures were subjected to stretching under the strain field and later advected downstream of the airfoil.

    Citation: Hussein Kokash, G. Gilou Agbaglah. A two- to three-dimensional wake transition mechanism induced by the angle of attack of a NACA0012 airfoil[J]. Metascience in Aerospace, 2024, 1(3): 329-345. doi: 10.3934/mina.2024015

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  • A high-order spectral element method was used to perform three-dimensional direct numerical simulations of the flow past a NACA0012 airfoil. We considered a Reynolds number Re=1000 and two different angles of attack, α=11 and α=16, to study the two- to three-dimensional wake transition. A boundary layer separation was observed for both angles of attack with the separation point closer to the leading edge for α=16. The downstream of the airfoil exhibited streamwise vortical structures formed in the braid regions connecting the primary vortices for α=16, while only shed vortices were observed for α=11. The formation of these streamwise structures were explained by the presence of a reverse flow from the lower surface for α=16, enhancing shearing effects. The early-stage development of the three-dimensional wake, in the case of α=16, was characterized by the formation of a spanwise sinusoidal velocity whose amplitude increased exponentially over time. The flow on the upper surface experienced a higher strain field which pulled up small disturbances from the airfoil surface and formed regions of concentrated vortical structures. These structures were subjected to stretching under the strain field and later advected downstream of the airfoil.



    Abbreviations: OC: Ovarian cancer; ncRNA: Non-coding RNA; lncRNAs: Long non-coding RNAs; GC: Gastric cancer; GO: Gene ontology; KEGG: Kyoto Encyclopedia of Genes and Genomes

    Ovarian cancer (OC) is one of the most common gynecological malignant tumors and has been one of the leading causes of cancer-related death in western countries [1,2,3,4,5]. Of note, the incidence of OC is also increasing in China. Despite surgery and chemotherapy have been widely used in the treatment of OC, the prognosis of OC remained to be unsatisfied. Therefore, further understanding of the molecular mechanisms involved in the development of OC is still an urgent need for the diagnosis and treatment of this disease.

    Non-coding RNA (ncRNA) is a class of RNA modules which have no protein-coding function. Recently, ncRNAs had been revealed to play a crucial role in human diseases. Emerging evidence has shown that long non-coding RNAs (lncRNAs) played important roles in both physiological and pathological processes of cancers [6,7,8]. LncRNA could affect a variety of biological processes, such as autophagy, proliferation, apoptosis, differentiation, and cell cycle, in cells. For example, lncRNA Fendrr played an important role in the development of heart and body wall in the mouse, and the lack of Fendrr lead to abnormal mouse embryonic development [9]. Thomas et al. found hundreds of TNFα-induced inflammation-related lncRNAs in mice, in which Lethe was involved in the negative feedback of inflammatory signals [10]. H19 is overexpressed in gastric cancer (GC) tissues and promotes GC proliferation, migration, invasion, and metastasis [11]. Recent studies also demonstrated that lncRNA HOST2 [12], LSINCT5 [13], HOTAIR [14], NEAT1 [15] were dysregulated in OC and associated with the occurrence and progression of OC.

    LncRNA XIST is the first lncRNA reported to be involved in the regulation of X chromosome inactivation. Recent studies have shown that XIST is dysregulated in multiple cancer types, including gastric, liver, nasopharyngeal carcinoma, cervical, non-small cell lung, glioma, pancreatic, osteosarcoma, colorectal, and breast cancer. In cervical cancer, XIST competitively binds to miR-200a to promote tumor progression [16]. In non-small cell lung cancer, XIST inhibits tumor cell proliferation and EMT progression by modulating miR-137 to regulateNotch-1 signaling pathway [17]. However, the functional roles and expression pattern of XIST in OC remain unclear. The present study aimed to explore whether XIST could serve as a new diagnostic target in OC.

    The present study used TCGA (The cancer genome atlas) to analysis the XIST expression levels. The TCGA database, including a total of 305 OC samples (23 Stage Ⅱ OC samples, 244 Stage Ⅲ OC samples, and 38 Stage Ⅳ OC samples). The Kaplan-Meier plotter database was used to analyze the correlation between XIST and survival time in patients.

    The TCGA database was used to analyze XIST co-expressed genes. Gene Ontology (GO) analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) Pathway analysis were performed on the top 1000 co-expressed genes by using the DAVID database [18,19] (https://David.ncifcrf.gov/). The interaction network between proteins was performed using the STRING (https://string-db.org/) database. The Starbase database was used to predict the regulatory cascade of XIST-miRNAs. Pearson’s correlation coefficient ≥ 0.4 is selected as a candidate, and the network was presented by Cytoscape.

    The statistical analysis was performed using SPSS version 17.0 software. T-test and Mann-Whitney U-test statistics were used to perform the statistical significance of differences between two groups; One-way ANOVA was used to perform the statistical significance of differences between multiple groups. The survival curve was performed by the Kaplan-Meier method. P < 0.05 was selected as significant.

    To explore the expression levels of XIST in OC, we first used the GTEx database to determine the expression of XIST in multiple human tissues, including ovary, cervix, uterus, testes, brains, and kidney. The results showed that the expression level of XIST in the human ovary, cervix, uterus was significantly higher than that in other tissues (Figure 1A).

    Figure 1.  LncRNA XIST was highly expressed in ovarian tissues. (A) GTEx database analysis showed that XIST expression levels in ovary, cervix, and uterus were significantly higher than other tissues of humans. (B) The GEPIA database analysis showed that the expression level of XIST in ovarian cancer was significantly lower than that in normal tissues. (C) TCGA data showed that the expression level of lncRNA XIST was significantly higher in Stage Ⅲ and Stage Ⅳ ovarian cancer than in Stage Ⅱ. (D) The TCGA database analysis showed that the overall survival time of patients with a high expression level of XIST was significantly longer than that of patients with the low expression level of XIST. P < 0.05 was statistically significant.

    Next, we analyzed the expression of XIST in OC tissues and normal ovarian tissues by using the GEPIA database, which contained RNA sequencing data of 88 normal ovarian tissues and 426 OC samples by integrating TCGA and GTEx databases. As shown in Figure 1B, our results showed that the XIST was significantly downregulated in OC compared to normal tissues (Figure 1B, p < 0.05).

    Furthermore, we analyze the correlation between its expression and stage. Totally, there are 305 OC samples that were with well-defined pathological stages in the TCGA dataset was used to conduct the analysis. The results showed that XIST was significantly downregulated in Stage Ⅲ OC compared that in Stage Ⅱ OC (Figure 1C, p < 0.05) and significantly downregulated in Stage Ⅳ OC compared that in Stage Ⅱ OC (Figure 1C, p < 0.05). However, no significant difference of XIST levels was observed between Stage Ⅲ OC and Stage Ⅳ OC samples.

    To further explore the role of XIST in OC, the present study first analyzed the relationship between XIST and survival time in OC by using the TCGA database. The results showed that higher XIST expression levels were associated with longer overall survival time (Figure 1D, p < 0.05).

    The present study also used the Kaplan-Meier plotter datasets to further explore the relationship between XIST and survival time in different types of OC. The present study found that upregulated XIST was positively correlated with longer survival time in OC (Figure 2A, p < 0.001), Serous OC (Figure 2C, p < 0.001), Grade 1 + 2 OC (Figure 2D, p < 0.01), Grade 3 OC (Figure 2E, p < 0.001), Stage Ⅲ + Ⅳ OC (Figure 2G, p < 0.001). However, the present study did not find the correlation between XIST and survival time in endometrial OC (Figure 2B) and Stage Ⅰ + Ⅱ OC (Figure 2F).

    Figure 2.  High expression of XIST was positively correlated with the long survival time of patients with ovarian cancer. Kaplan-Meier plotter data results displayed positive relationship between high XIST expression and long survival time of patients with ovarian cancer (A, p < 0.001), serous ovarian cancer (C, p < 0.001), Grade 1 + 2 ovarian cancer (D, p < 0.01), Grade 3 ovarian cancer (E, p < 0.001), Stage Ⅲ + Ⅳ ovarian cancer (G, p < 0.001). However, no significant difference of XIST levels was observed between Stage Ⅲ OC and Stage Ⅳ OC samples (F). P < 0.05 was statistically significant.

    The present study first analyzed the co-expressed gene of XIST by using TCGA database, and the most significant 1000 co-expressed genes were selected. Gene Ontology analysis (GO analysis) was further used to predict the potential roles of XIST in OC. The results revealed that XIST is involved in a series of biological processes including transcription, protein phosphorylation, transport, protein ubiquitination, DNA repair, ciliary morphogenesis, RNA splicing, cilia assembly, mRNA processing, and cell cycle regulation (Figure 3A). Molecular Function analysis showed that XIST could participate in many functions, including DNA binding, ATP binding, nucleic acid binding, poly (A) RNA binding, transcription factor activity, RNA binding, protein serine/threonine kinase activity, nucleoside Acid binding, protein kinase activity (Figure 3B). KEGG analysis showed that XIST affected many signaling pathways, including taste, mRNA monitoring, Fanconi anemia, small cell lung cancer, ECM-receptor interaction, NF-κB, protein digestion and absorption, transcriptional dysregulation in cancer, lysine degradation, amebic disease (Figure 3C).

    Figure 3.  Bioinformatics analysis revealed the function and role of lncRNA XIST in ovarian cancer. Biological process analysis of XIST (A), molecular function (Molecular Function) analysis (B), KEGG signaling pathway analysis (C). P < 0.05 was statistically significant.

    The present study constructed XIST‑mediated PPI networks by using the top 1000 co-expressing genes of XIST via the STRING database. The results identified three core networks. Among them, Module 1 included 12 core proteins (P2RY4, DRD2, TAS2R4, TAS2R5, TAS2R10, AS2R3, NPBWR2, GRM6, TAS2R39, OXER1, GABBR1, TAS2R50, Figure 4A), Module 2 included 11 core proteins (KBTBD10, KLHL3, HERC2, WSB1, ASB14, FBXL8, ANAPC4, ASB16, RLIM, ASB6, HERC1, Figure 4B) and Module 3 included 9 core proteins (CCDC41, CEP152, CEP164, FBF1, OFD1, CEP290, AHI1) TTBK2, AKAP9, Figure 4C).

    Figure 4.  Protein-protein interaction network mediated by XIST. (A) Hub PPI network 1 of XIST co-expressing genes. Blue nodes represent XIST co-expressing genes. This network included 12 core proteins (P2RY4, DRD2, TAS2R4, TAS2R5, TAS2R10, AS2R3, NPBWR2, GRM6, TAS2R39, OXER1, GABBR1, TAS2R50). (B) Hub PPI network 2 of XIST co-expressing genes. Blue nodes represent XIST co-expressing genes. This network included 11 core proteins (KBTBD10, KLHL3, HERC2, WSB1, ASB14, FBXL8, ANAPC4, ASB16, RLIM, ASB6, HERC1). (C) Hub PPI network 3 of XIST co-expressing genes. Blue nodes represent XIST co-expressing genes. This network included 9 core proteins (CCDC41, CEP152, CEP164, FBF1, OFD1, CEP290, AHI1 TTBK2, and AKAP9). P < 0.05 was statistically significant.

    Recent studies have found that XIST could participate in the regulation of tumor progression as a natural miRNA sponge. However, the mechanisms of XIST in OC remained unclear. Therefore, the present study systematically and comprehensively constructed an XIST-mediated endogenous competitive RNA interaction network. This study predicted the XIST-miRNAs regulatory cascade by using the Starbase database and then used the same method to predict the XIST-miRNAs-mRNAs regulatory cascade. Only XIST-mRNAs with positive correlation expression were selected for the construction of ceRNAs networks based on co-expression analysis results.

    The network included 202 miRNAs and 462 mRNAs as shown in Figure 5. Ten of these miRNAs were identified as the core regulator of the network, including hsa-miR-590-3p, hsa-miR-340-5p, hsa-miR-181b-5p, hsa-miR-424-5p, hsa-miR-15b-5p, hsa-miR-495-3p, hsa-miR-15a-5p, hsa-miR-181a-5p, hsa-miR-181d-5p, hsa-miR-30c-5p, hsa-miR-497-5p, hsa-miR-16- 5p, hsa-miR-30e-5p, hsa-miR-181c-5p, involved in the regulation of up to 100 different mRNAs. The present study also found that DDX3X, CHD9, POU2F1, YOD1, MAT2A, BRWD1, INO80D, GPCPD1, and MDM4 were regulated by more than 100 different miRNAs, suggesting that they acted as key XIST regulatory genes.

    Figure 5.  ceRNA network mediated by XIST. Red nodes represent the XIST. Blue nodes represent the predictive miRNAs of XIST. Green nodes represent the predictive mRNAs of XIST. P < 0.05 was statistically significant.

    Emerging studies demonstrated lncRNAs play important roles in regulating cell proliferation, apoptosis, and differentiation. For example, lncRNA loc285194 played as a tumor suppressor function by competitively binding to miR-211 in colorectal cancer [20]. UCA1 is overexpressed in liver cancer and sponged miR-216b to inhibit tumor growth [21]. MALAT1 could cause microvascular dysfunction in diabetic patients [22]. Exploring the roles of lncRNAs in human diseases could provide novel biomarkers for prognosis and treatment.

    OC is one of the most common gynecological malignant tumors. Previous studies had reported that lncRNA played an important role in the development and progression of OC. A series of lncRNAs are abnormally expressed in OC, such as GAS5 [23], TP73-AS1 [24], CCAT1, and MALAT1 [25]. LncRNA could regulate a series of OC related biological processes such as proliferation, cycle, and apoptosis. For instance, Lnc-OC1 promotes proliferation and migration of OC cells by competitively binding to miR-34a and miR-34c [26]. LncRNA CTD-2020K17.1 has been reported as an oncogene to promote OC metastasis, invasion, and proliferation [27]. However, it should be noted that the functions of most lncRNAs in OC are still unclear. Several previous studies indicated XIST might be associated with the development of OC. However, there is still a lack of systematic analysis to support XIST as a target for clinical diagnosis in OC. Then in the silico analysis based on multiple platforms in this study showed that the expression level of XIST was significantly increased in normal ovary, uterus, and cervix tissues, while the expression level was significantly decreased in OC tissues.

    Further analysis showed that XIST expression levels in advanced-grade OC were significantly lower than in low-grade OC. Moreover, the overexpression of XIST was positively correlated with the longer survival time of patients with OC, Serous OC, Grade 1 + 2 OC, Grade 3 OC, and Stage Ⅲ + Ⅳ OC. These analyses showed that XIST could serve as a potential diagnostic marker for OC.

    Emerging studies have shown that in addition to routine functional assays in vitro and in vivo, the widespread use of bioinformatics tools such as protein-protein interaction networks and endogenous competitive RNA networks plays an important role in uncovering the underlying pathogenesis of the human disease. To explore the potential functions and mechanisms of XIST in OC, the present study first performed co-expression analysis and bioinformatic analysis and identified three core interaction networks included 12 core proteins, 11 core proteins, and 9 core proteins respectively. The results revealed that XIST was involved in the biological processes of transcription, protein phosphorylation, transport, protein ubiquitination, DNA repair, ciliary morphogenesis, RNA splicing, DNA binding, ATP binding. KEGG signaling pathway analysis showed that XIST affected many signaling pathways, including taste, mRNA monitoring, Fanconi anemia, small cell lung cancer, ECM-receptor interaction, NF-κB, protein digestion and absorption, transcriptional dysregulation in cancer, lysine degradation, and amebic disease.

    Previous studies show XIST plays an important regulatory role in the development of multiple tumors, including gastric cancer, hepatocellular carcinoma, and breast cancer. XIST, as one of the longest lncRNAs in mammals, previous reports have shown that XIST plays a wide range of endogenous competitive RNA in cells, affecting multiple miRNA activity included miR-137, miR-200c, miR-155, miR-320 and miR-34a [28,29,30]. For example, XIST can inhibit the proliferation and metastasis of breast cancer cells by affecting the miR-155/CDX1 cascade control axis. The present study first systematically constructed OC-specific XIST-mediated endogenous competitive RNA network. Several studies in OC also demonstrated that XIST had a regulatory role in cancer progression. However, these reports are often contradictory. For example, Zuo et al. found XIST promoted malignant behavior of epithelial OC, while Wang et al. demonstrated that XIST has anticancer effects on epithelial OC cells through inverse downregulation of hsa-miR-214-3p. Of note, with the development of bioinformatics analysis, emerging studies revealed that bioinformatics analysis could provide more clues to understand the potential roles of genes in human diseases. The network included 202 miRNAs and 462 mRNAs, of which 10 miRNAs were identified as the core regulatory factors of this network, including hsa-miR-590-3p, hsa-miR-340-5p, hsa-miR-181b-5p, which regulated more than 100 different mRNAs in the network. These miRNAs played an important regulatory role in OC. For example, miR-590-3p could promote the proliferation and metastasis of OC by regulating FOXA2. miR-424 could inhibit the metastasis, invasion, and epithelial-mesenchymal transition of OC.

    In this study, there also exist some limitations. Firstly, the expression levels of XIST in OC and normal tissues should be detected to validate the bioinformatics analysis in future study. Secondly, the specific functions of XIST had not been further excavated in this study. Further experimental validation would be required for future verification.

    In summary, the present study showed lncRNA XIST was significantly down-regulated in OC and was associated with the development of OC. Overexpression of XIST was significantly associated with longer survival time in patients with OC. Also, our analysis also showed that lncRNA XIST was closely related to biological processes such as transcription, protein phosphorylation, transport, protein ubiquitination, and DNA repair, which provided a theoretical basis for the diagnosis and treatment of OC.

    All authors declare no conflicts of interest in this paper



    [1] Romeo G, Frulla G, Cestino E, et al. (2004) HELIPLAT: Design, aerodynamic, structural analysis of long-endurance solar-powered stratospheric platform. J Aircraft 41: 1505–1520. https://doi.org/10.2514/1.2723 doi: 10.2514/1.2723
    [2] Hassanalian M, Abdelkefi A (2017) Classifications, applications, and design challenges of drones: A review. Prog Aerosp Sci 91: 99–131.https://doi.org/10.1016/j.paerosci.2017.04.003 doi: 10.1016/j.paerosci.2017.04.003
    [3] Carmichael BH (1981) Low-Reynolds number airfoil survey. 165803, NASA.
    [4] Lin YF, Lam K, Zou L, et al. (2013) Numerical study of flows past airfoils with wavy surfaces. J Fluid Struct 36: 136–148. https://doi.org/10.1016/j.jfluidstructs.2012.09.008 doi: 10.1016/j.jfluidstructs.2012.09.008
    [5] Zhang W, Cheng W, Gao W, et al. (2015) Geometrical effects on the airfoil flow separation and transition. Comput Fluids 116: 60–73. https://doi.org/10.1016/j.compfluid.2015.04.014 doi: 10.1016/j.compfluid.2015.04.014
    [6] Karasu I, Genç MS, Açikel HH (2013) Numerical study on low Reynolds number flows over an Aerofoil. J Appl Mech Eng 2: 1000131.
    [7] Amiralaei MR, Alighanbari H, Hashemi SM (2010) An investigation into the effects of unsteady parameters on the aerodynamics of a low Reynolds number pitching airfoil. J Fluids Struct 26: 979–993. https://doi.org/10.1016/j.jfluidstructs.2010.06.004 doi: 10.1016/j.jfluidstructs.2010.06.004
    [8] Mueller TJ (1999) Aerodynamic Measurements at Low Reynolds Numbers for Fixed Wing Micro-Air Vehicles, in: RTO AVT/VKI Special Course on Development and Operation of UAVs for Military and Civil Applications, Hessert Center for Aerospace Research, University of Notre Dame, VKI, Belgium, 13–17.
    [9] Munday PM, Taira K, Suwa T, et al. (2015) Nonlinear Lift on a Triangular Airfoil in Low-Reynolds-Number Compressible Flow. J Aircraft 52: 924–931. https://doi.org/10.2514/1.C032983 doi: 10.2514/1.C032983
    [10] Kurtulus DF (2016) On the wake pattern of symmetric airfoils for different incidence angles at Re = 1000. Int J Micro Air Veh 8: 109–139. https://doi.org/10.1177/1756829316653700 doi: 10.1177/1756829316653700
    [11] Rossi E, Colagrossi A, Oger G, et al. (2018) Multiple bifurcations of the flow over stalled airfoils when changing the Reynolds number. J Fluid Mech 846: 356–391. https://doi.org/10.1017/jfm.2018.189 doi: 10.1017/jfm.2018.189
    [12] Genç MS, Karasu İ, Açıkel HH (2012) An experimental study on aerodynamics of NACA2415 aerofoil at low Re numbers. Exp Therm Fluid Sci 39: 252–264. https://doi.org/10.1016/j.expthermflusci.2012.01.029 doi: 10.1016/j.expthermflusci.2012.01.029
    [13] Ducoin A, Loiseau JC, Robinet JC (2016) Numerical investigation of the interaction between laminar to turbulent transition and the wake of an airfoil. Eur J Mech B-Fluid 57: 231–248. https://doi.org/10.1016/j.euromechflu.2016.01.005 doi: 10.1016/j.euromechflu.2016.01.005
    [14] Shelton A, Abras J, Hathaway B, et al. (2005) An investigation of the numerical prediction of static and dynamic stall. in: Proceedings of the 61st American Helicopter Society Annual Forum, 61: 1826.
    [15] Genç MS (2010) Numerical Simulation of Flow over a Thin Aerofoil at a High Reynolds Number Using a Transition Model. P I Mech Eng C-J Mec 224: 2155–2164. https://doi.org/10.1243/09544062JMES2121 doi: 10.1243/09544062JMES2121
    [16] Hain R, Kähler C J, Radespiel R (2019) Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils. J Fluid Mech 630: 129–153. https://doi.org/10.1017/S0022112009006661 doi: 10.1017/S0022112009006661
    [17] Jones LE, Sandberg RD, Sandham ND (2008) Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J Fluid Mech 602: 175–207. https://doi.org/10.1017/S0022112008000864 doi: 10.1017/S0022112008000864
    [18] Zhou Y, Alam MM, Yang HX, et al. (2011) Fluid forces on a very low Reynolds number airfoil and their prediction. Int J Numer Method H 32: 329–339. https://doi.org/10.1016/j.ijheatfluidflow.2010.07.008 doi: 10.1016/j.ijheatfluidflow.2010.07.008
    [19] Wang S, Zhou Y, Alam MM, et al. (2014) Turbulent intensity and Reynolds number effects on an airfoil at low Reynolds numbers. Phys Fluids 26: 115107. https://doi.org/10.1063/1.4901969 doi: 10.1063/1.4901969
    [20] Hoarau Y, Braza M, Ventikos Y, et al. (2003) Organized modes and the three-dimensional transition to turbulence in the incompressible flow around a NACA0012 wing. J Fluid Mech 496: 63–72. https://doi.org/10.1017/S0022112003006530 doi: 10.1017/S0022112003006530
    [21] Huang RF, Wu JY, Jeng JH, et al. (2001) Surface flow and vortex shedding of an impulsively started wing. J Fluid Mech 441: 265–292. https://doi.org/10.1017/S002211200100489X doi: 10.1017/S002211200100489X
    [22] Lissaman PBS (1983) Low-Reynolds-Number Airfoils. Annu Rev Fluid Mech 15: 223–239.
    [23] Klose BF, Spedding GR, Jacobs GB (2021) Direct numerical simulation of cambered airfoil aerodynamics at Re = 20,000. arXiv. https://doi.org/10.48550/arXiv.2108.04910
    [24] Williamson CHK (1988) The existence of two stages in the transition to three‐dimensionality of a cylinder wake. Phys Fluids 31: 3165–3168.
    [25] Williamson CHK (1996) Vortex dynamics in the cylinder wake. Ann Rev Fluid Mech 28: 477–539.
    [26] Barkley D, Henderson RD (1996) Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J Fluid Mech 322: 215–241. https://doi.org/10.1017/S0022112096002777 doi: 10.1017/S0022112096002777
    [27] Robichaux J, Balachandar S, Vanka SP (1999) Three-dimensional Floquet instability of the wake of square cylinder. Phys Fluids 11: 560–578. https://doi.org/10.1063/1.869930 doi: 10.1063/1.869930
    [28] Saha AK, Biswas G, Muralidhar K (2003) Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Int J Heat Fluid Flow 24: 54–66. https://doi.org/10.1016/S0142-727X(02)00208-4 doi: 10.1016/S0142-727X(02)00208-4
    [29] Luo SC, Tong XH, Khoo BC (2007) Transition phenomena in the wake of a square cylinder. J Fluids Struct 23: 227–248. https://doi.org/10.1016/j.jfluidstructs.2006.08.012 doi: 10.1016/j.jfluidstructs.2006.08.012
    [30] Luo SC, Chew YT, Ng YT (2003) Characteristics of square cylinder wake transition flows. Phys Fluids 15: 2549–2559. https://doi.org/10.1063/1.1596413 doi: 10.1063/1.1596413
    [31] Barkley D, Tuckerman LS, Golubitsky M (2000) Bifurcation theory for three-dimensional flow in the wake of a circular cylinder Phys Rev E 61: 5247–5252. https://doi.org/10.1103/PhysRevE.61.5247 doi: 10.1103/PhysRevE.61.5247
    [32] Blackburn HM, Lopez JM (2003) On three-dimensional quasiperiodic Floquet instabilities of two-dimensional bluff body wakes. Phys Fluids 15: L57–L60. https://doi.org/10.1063/1.1591771 doi: 10.1063/1.1591771
    [33] Meneghini JR, Carmo BS, Tsiloufas SP, et al. (2011) Wake instability issues: From circular cylinders to stalled airfoils. J Fluids Struct 27: 694–701. https://doi.org/10.1016/j.jfluidstructs.2011.03.018 doi: 10.1016/j.jfluidstructs.2011.03.018
    [34] Deng J, Sun L, Shao X (2017) Floquet stability analysis in the wake of a NACA0015 airfoil at post-stall angles of attack. Phys Fluids 29: 094104. https://doi.org/10.1063/1.5003578 doi: 10.1063/1.5003578
    [35] He W, Gioria RS, Pérez JM, et al. (2017) Linear instability of low Reynolds number massively separated flow around three NACA airfoils. J Fluid Mech 811: 701–741. https://doi.org/10.1017/jfm.2016.778 doi: 10.1017/jfm.2016.778
    [36] Gupta S, Zhao J, Sharma A, et al. (2023) Two- and three-dimensional wake transitions of a NACA0012 airfoil. J Fluid Mech 954: A26. https://doi.org/10.1017/jfm.2022.958 doi: 10.1017/jfm.2022.958
    [37] Kouser T, Xiong Y, Yang D, et al. (2021) Direct numerical simulations on the three-dimensional wake transition of flows over NACA0012 airfoil at Re = 1000. Int J Micro Air Veh 13: 1–15. https://doi.org/10.1177/17568293211055656 doi: 10.1177/17568293211055656
    [38] Xia T, Dong H, Yang L, et al. (2021) Investigation on flow structure and aerodynamic characteristics over an airfoil at low Reynolds number–A review. AIP Adv 11: 050701. https://doi.org/10.1063/5.0044717 doi: 10.1063/5.0044717
    [39] Patera AT (1984) A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J Comput Phys 54: 468–488.
    [40] Fischer P, Kruse J, Mullen J, et al. Nek5000: Open source spectral element CFD solver. Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL, Available from: https://nek5000.mcs.anl.gov/index.php/MainPage2.
    [41] Deville MO, Fischer PF, Mund EH (2002) High-Order Methods for Incompressible Fluid Flow, Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press.
    [42] Cummings RM, Morton SA, Mason WH (2015) Applied Computational Aerodynamics, Cambridge Aerospace Series, Cambridge University Press.
    [43] Hoarau Y, Braza M, Ventikos Y, et al. (2006) First stages of the transition to turbulence and control in the incompressible detached flow around a NACA0012 wing. Int J Heat Fluid Fl 27: 878–886. https://doi.org/10.1016/j.ijheatfluidflow.2006.03.026 doi: 10.1016/j.ijheatfluidflow.2006.03.026
    [44] Uranga A, Persson PO, Drela M, et al. (2011) Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a discontinuous galerkin method. Int J Numer Meth Eng 87: 232–261. https://doi.org/10.1002/nme.3036 doi: 10.1002/nme.3036
    [45] Khalid MSU, Akhtar I (2012) Characteristics of Flow Past a Symmetric Airfoil at Low Reynolds Number: A Nonlinear Perspective. ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 167–175. https://doi.org/10.1115/IMECE2012-87389
    [46] Hongquan Z(1998) Centrifugal instability and the rib vortices in the cylinder wake. Acta Mech Sinica 14: 104–112. https://doi.org/10.1007/BF02487745 doi: 10.1007/BF02487745
    [47] Agbaglah G, Mavriplis C (2017) Computational analysis of physical mechanisms at the onset of three-dimensionality in the wake of a square cylinder. J Fluid Mech 833: 631–647. https://doi.org/10.1017/jfm.2017.713 doi: 10.1017/jfm.2017.713
    [48] Agbaglah G, Mavriplis C (2019) Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics. J Fluid Mech 870: 419–432. https://doi.org/10.1017/jfm.2019.265 doi: 10.1017/jfm.2019.265
    [49] Kokash H, Agbaglah GG (2022) On the origin of mode B instability of the wake of a square cylinder. Phys Fluids 34: 074116. https://doi.org/10.1063/5.0101403 doi: 10.1063/5.0101403
    [50] Kouser T, Xiong Y, Yang D, et al. (2022) Numerical study on drag reduction and wake modification for the flows over a hydrofoil in presence of surface heterogeneity. Adv Mech Eng 14: 1–14. https://doi.org/10.1177/168781402210753 doi: 10.1177/168781402210753
    [51] Lasheras JC, Choi H (1988) Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J Fluid Mech 189: 53–86. https://doi.org/10.1017/S0022112088000916 doi: 10.1017/S0022112088000916
    [52] Pierrehumbert RT, Widnall SE (1982) The two- and three-dimensional instabilities of a spatially periodic shear layer. J Fluid Mech 114: 59–59. https://doi.org/10.1017/S0022112082000044 doi: 10.1017/S0022112082000044
    [53] Tseng CC, Hu HA (2015) Flow dynamics of a pitching foil by eulerian and lagrangian viewpoints. AIAA J 54: 2. https://doi.org/10.2514/1.J053619 doi: 10.2514/1.J053619
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