3.1 An overview of collected data
Two different data sources (Scopus and WOS) have been used for getting the data for this study. Biblioshiny and Microsoft Excel software have been used for creating various plots, bar charts and tables shown in this paper. The dataset contains a total of 603 publications of various types as shown in Table 1. Data sets from Scopus (www.scopus.com) and WOS (www.webofscience.com) were merged and then data cleaning was done to remove duplicate and irrelevant entries. There are a total of 179 sources of publications contributing to this dataset. The data contains different types of publications including articles (N = 492) accounting for 81.59% of the total data, while the conference papers/proceedings (N = 94) account for 15.59% of the total publications, and the remaining data includes: number of book chapters = 4 (0.66%) and number of review papers = 13 (2.16%). The first research paper (as per the dataset) involving active drag reduction using computational/numerical methods for turbulent channel/pipe flows was published in the year 1984. Figure 2 shows the yearly production of papers from the year 1984 till the date of collection of this data. The figure shows three different regions in the use of computational fluid dynamics (CFD) techniques for research in the field of drag reduction in pipe or channel flows involving active flow control techniques. In the early days of using CFD from 1984 to 200148–51 as shown in Fig. 3, we can see very few publications (N = 26) which can be attributed to the limited computational resources availability in terms of both hardware and software. The second phase from 2002 to 201652–54 as shown in Fig. 4 saw an increase in publications (n = 215) due to an increase in computational resources both in terms of hardware as well as software which resulted in better researcher interest in this domain of research. The third phase (2017-present, Fig. 5) shows a clear upward trend55–57, with far more publications (N = 362) than the previous two phases. This suggests that drag reduction using active flow control techniques remains an active area of research and that more researchers are contributing to the field with the availability of better hardware and software computational resources and with the use of artificial intelligence, machine learning58 and deep learning techniques59 in fluid mechanics-related research.
The total publications (Fig. 2) got into double figures for the first time in the year 2002. This can be attributed to the advancement of technology in terms of far more computationally powerful computers, availability of more accurate and faster commercial and open source software and universities coming up with their in-house codes which can give results in less time using the available resources. Maximum total publications to date have been in the year 2022 (74 publications). A total of 1347 authors are involved in these publications with a total of 24 authors publishing a total of 27 single-authored documents. Total citations received were 11257 till the date of compiling the data for this paper (average citation per document being 18.67). Out of a total of 603 documents, 80 (13.27%) are without any citations. Figure 6 shows the number and percentage of citations for different kinds of documents and it can be seen that the articles have the maximum number of citations (N = 9340, 83.00%).
Table 1 Overview of collected data from the year 1984 to 1st October 2023
Total Documents | 603 |
Articles | 492 (81.59%) |
Books | 0 (0.00%) |
book chapters | 4 (0.66%) |
Conference/proceeding papers | 94 (15.59%) |
review papers | 13 (2.16%) |
Sources (Journals, Books etc.) | 179 |
Period | 1984:2023 |
Average citations per document | 18.67 |
Authors | 1347 |
Authors of single-authored documents | 24 |
Single-authored documents | 27 |
Co-Authors per document | 3.34 |
Annual Growth Rate % | 9.38% |
International co-authorships % | 21.39% |
3.2 Top ten researchers and Co-Author collaboration network
The top ten authors (based on total number of publications) are shown in Table 2. The affiliation information including the country of these authors is obtained from their most recent publications in the data collected. All top 10 authors have actively published papers in this research domain in the last 3 years as seen from the last column in the table which shows the latest year of publication of the authors, which shows that it is an active research domain. Three authors in this list are from Japan (Fukagata K, Hasegawa Y and Kasagi N with 18, 10 and 10 publications respectively), and three are from China (Xu C, Yu B and Huang W with 12, 11 and 9 publications respectively), one is from Italy (Quadrio M with 19 publications), one is from the UK (Leschziner M with 13 publications), one is from Germany (Gatti D with 10 publications) and one is from Sweden (Schlatter P with 10 publications) and within this list of top ten most productive authors, Quadrio M from Italy has a maximum number of citations (N = 661) followed by Fukagata K from Japan (N = 589) with Quadrio M having h-index of 10 and Fukagata K having an h-index of 11 respectively.
Table 2 Top 10 researchers (Based on the number of publications)
S. No | Name of Author | Full Name, Affiliation/Country | Number of Publications | Number of Citations | h-index | Year of 1st Publication | Year of last Publication |
1 | Quadrio M | Maurizio Quadrio, Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy | 19 | 661 | 10 | 2003 | 2023 |
2 | Fukagata K | Koji Fukagata, Department of Mechanical Engineering, Keio University, Yokohama, 223–8522, Japan | 18 | 589 | 11 | 2005 | 2022 |
3 | Leschziner M | Michael A. Leschziner, Department of Mechanical Engineering, University of Sheffield, United Kingdom | 13 | 466 | 11 | 2005 | 2021 |
4 | Xu C | Chun-Xiao Xu, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China | 12 | 262 | 9 | 2002 | 2019 |
5 | Yu B | Bo Yu, School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing, 102617, China | 11 | 243 | 6 | 2003 | 2020 |
6 | Gatti D | Davide Gatti, Institute for Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstr. 10, 76131 Karlsruhe, Germany | 10 | 135 | 6 | 2013 | 2022 |
7 | Hasegawa Y | Yosuke Hasegawa, Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Tokyo 153–8505, Japan | 10 | 123 | 5 | 2010 | 2023 |
8 | Kasagi N | Yosuke Hasegawa, The University of Tokyo, Japan | 10 | 361 | 8 | 1996 | 2020 |
9 | Schlatter P | Philipp Schlatter, KTH Royal institute of Technology, 100 44, Stockholm, Sweden | 10 | 146 | 5 | 2015 | 2023 |
10 | Huang W | Wei-Xi Huang, AML, Department of Engineering Mechanics, Tsinghua University , Beijing 100084, China | 9 | 118 | 6 | 2013 | 2020 |
Figure 7 shows a collaboration network of authors who have collaborated for at least four publications. The size of each node is an indicator of the number of publications of the researcher, with larger nodes indicating more publications. The thickness of the lines connecting the nodes represents the strength of the collaboration between two researchers, with thicker lines indicating more collaborative publications. Figure 7 shows eleven distinct clusters in different colours. Authors who have collaborated are placed in the same cluster, but some authors have also collaborated with a few authors outside their cluster. All authors from the top ten scholars shown in Table 2 are present in different clusters, clearly indicating that the top authors with the highest number of publications have strong collaboration networks.
The largest cluster (Pink) has 13 authors having affiliation with the following countries: Germany (Gatti D and Frohnapfel B), Italy (Quadrio M, Cimarelli A), Sweden (Schlatter P, Vinuesa R, and Orlu R), and Japan (Fukagata K, Kametani Y, Mamori H, Kasagi N, and Hasegawa Y) and Austria (Atzori M). The second-largest cluster (brown) has 7 scholars affiliated with the following countries: the USA (Hussain F and Yao J), China (Chen X, Cheng X, Zhou Y, and Wong C), and Germany (Schroder W). The third cluster (Orange) has 6 scholars including 4 from China (Yu B, Wei J, Pang M, and Li F) and 2 from Japan (Kawaguchi Y, and Tsukahara T). The fourth cluster has 5 scholars all from the UK (Leschziner M, Ricco P, Touber E, Skote M, and Agostini L). The next big cluster has 4 authors all from China (Xu C, Huang W, Deng B, and Cui G). The 3-node clusters include authors from China (Chen W, Gao D, and Huang Y), and the USA (Karniadakis G, Maxey M, and Xu J). The 2-node clusters include researchers from India (Baig M and Fuaad P), the USA (Jovanovic M and Moarref R), and China (Fang J and Lu L). All of the 10 top most productive authors (see Table 2) can be seen in Fig. 7 highlighting the fact that these authors have strong collaboration networks.
3.3 Bibliometric Coupling of Sources: A Measure of Research Collaboration and Impact
Figure 8 shows clusters of publication sources. Bibliometric coupling based on sources (journals) is a way to see the similarity between journals (sources) by counting the number of same articles they cite. Two sources having a significant number of the same publications in their citations can show that they are very likely to be similar in type of publications (i.e. in terms of topics covered). Editors of the publishing houses usually choose articles relevant to the scope and aim of their journals and which are widely acceptable to the journal’s audience. Figure 8 shows two clusters: the bigger one (red) consists of 18 sources focussing on research related to active flow control in turbulent channel flows primarily making use of the direct numerical simulation (DNS) technique, while the 2nd cluster consists of 7 sources focussed on research topics involving drag reduction especially in boundary layer region making use of numerical simulations.
3.4 Collaboration networks for Countries and Institutes and leading countries in research publications
3.4.1 Leading Countries in Research Publications
Table 3 displays the top 10 countries that have the highest number of publications, along with their total citations. The top 3 countries in this domain of research are China (142), USA (111) and Japan (57). The remaining top contributing countries are shown in Table 3. Similarly for citations top 3 nations are USA (3648), Japan (1291) and UK (1215) with other top cited countries shown in Table 3. The top contributing countries include 8 developed nations while only 2 developing nations (India and Iran) are on this list. It clearly shows most of the work in this research domain has been carried out in developed nations. Out of the total 603 publications only 47 that is 7.80% publications are from developing nations, while the remaining 92.20% are from developed nations. It clearly shows that there is a long way to go for the developing nations as far as research in the domain of using CFD for studying drag reduction in turbulent channel or pipe flows using active flow control techniques is concerned.
Table 3 Leading countries based on the number of publications
S. No | Country | Number of Publications | % of total publications | No of Citations | % of total citations |
1 | CHINA | 142 | 23.55 | 1204 | 10.70 |
2 | USA | 111 | 18.41 | 3648 | 32.41 |
3 | JAPAN | 57 | 9.12 | 1291 | 10.79 |
4 | UK | 55 | 9.45 | 1215 | 11.47 |
5 | GERMANY | 34 | 5.64 | 515 | 4.57 |
6 | FRANCE | 30 | 4.98 | 368 | 3.27 |
7 | ITALY | 24 | 3.98 | 378 | 3.36 |
8 | SOUTH KOREA | 18 | 2.99 | 367 | 3.26 |
9 | INDIA | 17 | 2.82 | 113 | 1.00 |
10 | IRAN | 11 | 1.82 | 81 | 0.72 |
3.4.2 Country Collaboration Network
Country collaboration networks are representative of research links between various countries and these maps can tell us whether there exists a strong research collaboration in the given domain between various countries. The dots (nodes) represent nations, and the lines joining these nodes represent relationships between countries. A node’s significance in a network can be measured in terms of its betweenness and closeness centrality values. Betweenness centrality measures the frequency of a given country (represented as a node) becoming a bridge for some other countries (nodes), and closeness centrality is an indication that the given country is much closer to other countries (nodes). Both these factors can be useful in studying and analysing the country's collaboration networks to understand how various countries are collaborating in a given area of research and which countries are doing the most significant amount of work in the domain. From Fig. 9 and Table 4, we can see that the USA has the highest betweenness value followed by the UK, Germany and, China while the UK has the highest closeness centrality value followed by the USA, China and Germany. It clearly shows that these four countries are the most significant as far as country collaboration is concerned.
Figure 9 shows 8 different clusters with the largest cluster consisting of 9 nations: China, Germany, Netherlands, France, Italy, Sweden, Canada, Austria, and Russia. Another large cluster has 7 countries: USA, Japan, Spain, Korea, Brazil, Israel, and Egypt. The third largest cluster consists of 4 countries (UK, Ireland, Australia, and Norway) while the remaining clusters are relatively smaller consisting of either 1 or 2 countries as shown. Strong collaboration networks between various top 10 countries shown in Table 3 are visible here.
Table 4 Top 10 collaborative nations based on Betweenness and Closeness values
S. No | Node | Betweenness | Closeness |
1 | USA | 221.6085425 | 0.018518519 |
2 | United Kingdom | 195.4582313 | 0.018867925 |
3 | Germany | 78.49913132 | 0.016666667 |
4 | China | 58.0895428 | 0.016949153 |
5 | Netherlands | 39.13987947 | 0.015873016 |
6 | France | 38.88533888 | 0.014925373 |
7 | Switzerland | 35 | 0.012048193 |
8 | India | 33.70329172 | 0.014285714 |
9 | Japan | 24.73669224 | 0.015151515 |
10 | Italy | 18.74112031 | 0.014705882 |
3.4.3 Institute Collaboration Network
Figure 10 shows the collaboration network between various institutions (to which different authors are affiliated). These collaboration networks are significant since they provide detailed information regarding the evolution of institute-level collaborations with the passage of time and these also give significant information about the frequency of collaboration among various institutes shown in clusters and how research-related knowledge is shared among various institutes which eventually can improve significantly the overall research credentials of those institutions and these network plots can also provide information about which institutes are most prominently sharing information. Figure 9 shows 8 different clusters with thickness of the lines connecting the nodes indicating the strength of collaboration that can be in terms of frequency of publications between the two institutes with thicker lines representing stronger collaboration. The biggest cluster (brown) has 14 nodes (institutes) with strong collaboration between contributors like ‘Centre national de la recherche scientifique (CNRS)’, ‘Udice-french research universities’, and ‘Université Paris-Saclay’. Other major contributors in this cluster include ‘Imperial College London ’, ‘National Office for Aerospace Studies and Research (ONERA)’, ‘CNRS Institute for Engineering and Systems Sciences (INSIS)’ etc. The second big cluster (purple) has 7 nodes with strong collaboration between ‘Helmholtz Association’ and ‘Royal Institute of Technology’ in this cluster. The third big cluster (blue) has 7 institutes including Harbin Institute of Technology, Beihang University etc. The fourth cluster (Red) has 6 institutes including the University of Minnesota system, Florida State University etc. The other four clusters include 2 members each.
3.5 Leading Journals and Publications: Submissions and Citations
The most productive sources (Journals) in the field of using CFD and active drag reduction techniques in turbulent channel/pipe flows are listed in Table 5. The data for this analysis was collected from 179 different sources, and the top 10 most productive journals shown in Table 5 contribute greater than 50% of the total publications (N = 603) and citations (N = 11257) in this domain. The highest-ranked journal is ‘Journal of Fluid Mechanics’, contributing 83 publications to the dataset, the second biggest contributor is ‘Physics of Fluids’, with 66 publications, and the third largest contributor is ‘AIAA Journal’, with 39 publications. The top 10 journals have a total of 309 publications, which account for 51.24% of the total published work, and a total of 7940 citations, which account for 70.53% of the total citation which clearly shows that these sources (Journals) are the most preferred ones for authors working in this field and these are the most relevant journals for this kind of research work. Out of the top 10 journals, nine are Scopus quartile 1 (Q1) and one is quartile 2 (Q2) journal. All the top 10 journals are SCIE indexed, as shown in Table 5.
Table 5 Top 10 journals having the highest number of publications
Rank | Journal Name | Affiliation | Publications | Citations | Scopus Quartile | WOS |
1 | Journal of Fluid Mechanics | Cambridge Univ Press, UK | 83 | 3356 | Q1 | SCIE |
2 | Physics of Fluids | American Institute Of Physics, USA | 66 | 1913 | Q1 | SCIE |
3 | AIAA Journal | American Institute of Aeronautics, USA | 39 | 665 | Q1 | SCIE |
4 | International Journal of Heat And Fluid Flow | Elsevier Science Inc., USA | 32 | 868 | Q1 | SCIE |
5 | Flow Turbulence And Combustion | Springer, Netherlands | 21 | 204 | Q2 | SCIE |
6 | Physical Review Fluids | Amer Physical Soc, USA | 17 | 132 | Q1 | SCIE |
7 | Ocean Engineering | Pergamon-Elsevier Science Ltd, England | 16 | 177 | Q1 | SCIE |
8 | Journal of Turbulence | Taylor & Francis Ltd, England | 13 | 214 | Q1 | SCIE |
9 | Experiments in Fluids | Springer, USA | 12 | 339 | Q1 | SCIE |
10 | Aerospace Science And Technology | Elsevier France-Editions, France | 10 | 72 | Q1 | SCIE |
Table 6 shows the top 10 most cited published works along with other information such as their first author, year of publication, digital object identifier (DOI), total citations, average citations per year and normalized total citations. These publications are from year 1994 to 2007. Normalized total citation is an indicator of the impact of the citations for a research paper in comparison to other published works in the same area of research and it is preferable to use normalized citation count rather than total citations. It can be taken as the ratio of citations of a research paper and the average number of citations obtained by published works in the same area of research within the same year in which the paper was published. Five papers in Table 6 are from the source titled ‘Journal of Fluid Mechanics’, while two are from ‘Physics of Fluids’ journal, and one each from: ‘International Journal for Numerical Methods in Fluids’, ‘Progress in Aerospace Sciences’ and, ‘International Journal for Numerical Methods in Engineering’ journals. It clearly shows that authors are publishing their works in the top journals in this domain.
The titles of the top 10 cited papers are not mentioned in the tabular form but are given here in the text. The 1st paper in Table 6 titled ‘Active turbulence control for drag reduction in wall-bounded flows’ is a study which presents a technique for achieving drag reduction by modifying the boundary layer using direct numerical simulation method60. The 2nd paper in this table titled ‘DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms’ discusses obtaining drag reduction in turbulent channel flows by using the suction/blowing technique and the authors used direct numerical simulations for studying the same61. The 3rd paper titled ‘A reduced-order approach for optimal control of fluids using proper orthogonal decomposition’ discusses drag reduction for backwards-facing step geometry using the proper orthogonal decomposition (POD) technique. This technique is active drag control and can be used for turbulent flows62. The 4th article titled ‘Critical assessment of turbulent drag reduction through spanwise wall oscillations’ discusses drag reduction by making use of spanwise oscillations given to the wall. The authors used direct numerical simulations for their study63. The 5th paper titled ‘Application of neural networks to turbulence control for drag reduction’ discusses about application of neural networks for getting drag reduction in turbulent flows in channels using the blowing/suction method and optimizing the process64. The 6th paper titled ‘Issues in active flow control: theory, control, simulation, and experiment’ deals with the present status of active flow control techniques. It discusses selective issues related to this domain65. The 7th publication titled ‘Drag reduction in wall-bounded turbulence via a transverse travelling wave’ focuses on obtaining drag reduction in wall-bounded flows by making use of travelling waves by suppressing the turbulence production66. The 8th publication titled ‘Optimal control of vortex shedding using low order models part 1 open loop model development’ discusses the problem involving vortex shedding behind a cylinder and how to reduce drag by suction/blowing methods67. The 9th paper titled ‘Numerical simulation of active separation control by a synthetic jet’ discusses making use of numerical simulations for reduced separation of the boundary layer by using synthetic jets. Both direct numerical simulations as well as large eddy simulations were used in this study68. The 10th paper titled ‘The effect of bubbles on the wall drag in a turbulent channel flow’ discusses the effect of the introduction of bubbles near the wall of the channel on drag reduction. Direct numerical simulations were used for this purpose69.
Table 6 Top ten most cited published works
Paper | DOI | Total Citations | Citations per year | Normalized citations |
CHOI H, 1994, J FLUID MECH | 10.1017/S0022112094000431 | 497 | 16.57 | 1.00 |
BEWLEY TR, 2001, J FLUID MECH | 10.1017/S0022112001005821 | 285 | 12.39 | 3.87 |
RAVINDRAN SS, 2000, INT J NUMER METH FL | https://doi.org/10.1002/1097-0363(20001115)34:5%3C425::AID-FLD67%3E3.0.CO;2-W | 275 | 11.46 | 3.00 |
QUADRIO M, 2004, J FLUID MECH | 10.1017/S0022112004001855 | 241 | 12.05 | 3.64 |
LEE C, 1997, PHYS FLUIDS | 10.1063/1.869290 | 193 | 7.15 | 1.83 |
COLLIS SS, 2004, PROG AEROSP SCI | 10.1016/j.paerosci.2004.06.001 | 178 | 8.90 | 2.69 |
DU YQ, 2002, J FLUID MECH | 10.1017/S0022112001007613 | 153 | 6.95 | 2.98 |
GRAHAM WR, 1999, INT J NUMER METH ENG | https://doi.org/10.1016/S0045-7930(02)00007-5 | 150 | 6.00 | 1.80 |
DANDOIS J, 2007, J FLUID MECH | 10.1017/S0022112006003995 | 143 | 8.41 | 4.85 |
LU JC, 2005, PHYS FLUIDS | 10.1063/1.2033547 | 135 | 7.11 | 4.08 |
3.6 Keyword Co-occurrence and Co-citation Networks
3.6.1 Keyword Co-occurrence Network
A keyword concurrence network is a way of showing the frequency of appearance of different keywords together in a group of published works. It is done graphically as shown in Fig. 11 where nodes represent keywords and link connecting the nodes indicates the co-occurrence of keywords and the thickens of the line connecting the two keywords is an indicator of the frequency of the co-occurrence of the connected keywords by that line. The thicker the connecting line between two keywords (nodes), the more the frequency of the co-occurrence of those 2 keywords. Figure 11 shows four clusters in the keyword co-occurrence network. 1st cluster (blue) has 51 nodes with each node representing a keyword and the most important keywords in this node are turbulent, drag, reduction, channel, wall, boundary, oscillations, microbubbles, blowing, motion, suction, injection etc., it clearly shows that the first cluster shows different drag reduction techniques used for turbulent channel flows, with while the 2nd cluster (purple) has 24 nodes. The most important keywords in this cluster are flow and control with a strong co-occurrence of these two words, other significant keywords are numerical, active, model, unsteady, transition etc. The co-occurrence of these keywords indicates that research work in this domain is focused on obtaining drag reduction by using active agents in turbulent channel flows using numerical simulations such as direct numerical simulations, large eddy simulation etc. The third cluster (Red) has important keywords like cylinder, circular, step, investigation, aerodynamic etc. which shows it discusses about use of different geometries during the study of drag reduction70–72. The fourth cluster has keywords heat, transfer and enhancement which shows this cluster deals with heat transfer involved in some cases involving drag reduction.
3.6.2 Keyword Co-citation Network
Co-citation networks can be of great help in understanding the scholarly structure of a particular area of research as these networks give significant information related to research papers published for a given domain and most significant authors related to that research and co-citation networks can also help in tracking the growth in that field of research with time and also help in identifying new themes of research related to the domain. Nodes represent the publications and the thickness of the lines linking any two publications tells about the frequency of the two publications that have been cited together. In Fig. 12, we can observe a strong co-citation relation between the following pair of publications:
Red cluster: (Choi H, 1994) and (Fukagata K, 2002)
Red cluster: (Choi H, 1994) and (Kim J, 1987)
Blue cluster: (Jung W.J, 1992) and (Quadrio M, 2004)
Blue cluster: (Quadrio M, 2004) and (Quadrio M, 2009)
Blue cluster: (Jung W.J, 1992) and (Baron A, 1995)
3.7 Thematic and Trend Analysis
3.7.1 Thematic Evolution
Figure 13 shows the evolution of this theme that is how research in the field of drag reduction using CFD using active drag reduction methods has evolved from the year 1984 till the date of collection of this data. Four time periods have been shown in the figure. The first period is from 1984 to 2004 and it can be observed that during this period, research was in earlier stages using CFD for drag reduction in pipe/channel flows using active techniques. The main keywords during this period were turbulent boundary layer control, drag reduction, channel flow, pipe, direct numerical simulation and turbulent flow. Researchers were making use of the limited computational resources at their disposal to apply numerical methods to solve turbulent flow-related problems. The second period was from 2005 to 2014, during this time the main keywords for research were channel, simulation, Navier-Stokes equations, incompressible flow and direct numerical simulations. This clearly shows that with the advancement of technology and the availability of commercial and open source CFD packages73, more researchers started showing interest in this domain of research. The use of simulation techniques like Reynolds Averaged Navier-Stokes equations (RANS) which used less computational resources and gave decent results for some of the turbulent flow-related problems was made. The third period from 2015 to 2020 shows new words like turbulence models, heat transfer and some common themes from previous time zones like direct numerical simulations, drag reduction etc. The fourth period from 2021 till the date of collection of this data shows some new keywords like neural network, suppression, design etc. in addition to the previous keywords which shows that researchers are making use of artificial intelligence and neural networks to solve turbulent flow-related problems.
3.7.2 Thematic Map
Thematic maps are a way of visually showing the importance of various themes. It is a plot showing relevance degree (centrality) along the x-axis (it shows how well a theme is connected to other themes in the domain of research) and development degree (density) along its y-axis (it shows the development level of a given theme). If the density of the theme is more it means it is more developed and a lot of research work has already been done using that theme. Thematic maps are usually shown in four quadrants:
1st quadrant (Upper right quadrant): It shows Motor themes, these are the most important types of themes and a lot of research work has already been done using these themes over the past few years. Motor themes have high values of relevance degree as well as development degree. Figure 14 shows that Motor themes are turbulent channel flows, boundary layers, heat transfer etc.
2nd quadrant (Upper left quadrant): It shows Niche themes: Niche themes have a high development degree but low relevance value which means these may be emerging or new themes or are some focussed themes. Figure 14 shows that Niche themes are reinforcement learning, deep reinforcement learning, wall motion etc. It clearly shows that the use of deep learning and machine learning are new and emerging themes related to research in the study of turbulent flows and drag reduction.
3rd quadrant (Lower left quadrant): It shows Emerging/Declining themes which have lower relevance value as well as lower development degree as compared to all other themes. These show those themes which are emerging these days or which are fading away with time. Figure 14 shows that neural network is in trend these days and emerging theme for research in the domain of turbulent flows and drag reduction. Other themes such as passive control, turbulence control and wall-bounded flows can be seen in the figure out of which passive control has the lowest development degree as well as relevance value.
4th quadrant (Lower right quadrant): It shows Basic themes which have relatively lower development value but high relevance degree but low development degree and these themes are considered as basic or fundamental themes in a given research domain. These are the foundations of the entire research work in the given domain. Figure 14 shows drag reduction, flow control, numerical investigation, friction drag, and turbulent drag are some of the basic themes and all research in other themes builds on these topics.
3.7.3 Trend Topics
Figure 15 shows the plot for trend topics which are shown in single-quadrant mode (showing all trend topics in the same quadrant) where circles represent the topics and the frequency of topics is shown by the size of the circle, the bigger the circle more frequent is the appearance of the that topic in the data set. The lines passing through circles represent the popularity of the topics over a duration of time. In trend topic plot if a topic is repeated multiple times over some time that shows that the topic is one of the key topics in that field of research. Figure 15 shows that trend topics in the field of using numerical techniques for active drag reduction in turbulent channel flows in pipes or channels are reinforcement learning and deep reinforcement which shows that artificial intelligence, neural networks, machine learning and deep learning techniques are being used in 2023 for turbulent flows. Other trend topics in recent years are synthetic jets, wall-bounded turbulence, heat transfer, spanwise travelling waves etc.
Figure 16 displays a word cloud for the top 100 keywords. It can be seen from this figure that the most significant keywords are turbulent flows/turbulence, numerical simulations, drag, active control, flow control, skin friction, large eddy simulation, boundary layer, and near-wall turbulence, which indicates that research in the area of drag reduction in turbulent flows in channel or pipe using active methods involves modifying the flow in the boundary layer in one way or the other. Also, the large eddy simulation method is the more preferred method of carrying out this study as compared to direct numerical simulation (DNS) or Reynolds Averaged Navier-Stokes (RANS) modelling techniques as computational facilities may not be available with some of the authors needed for DNS and as RANS modelling usually is not able to provide a complete picture of turbulence so authors prefer LES which needs lesser resources as compared to DNS but more than that needed for RANS and LES can provide some insights into the mechanism involved in most of the cases involving turbulent flows.