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Numerical study on boundary layer flow over the bow of SUBOFF model with turbulent inflow

Published online by Cambridge University Press:  12 November 2025

Fei Zhu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University , Beijing 100084, PR China
Jing-Wei Jiang
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University , Beijing 100084, PR China
Chun-Xiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University , Beijing 100084, PR China State Key Laboratory of Advanced Space Propulsion, Tsinghua University , Beijing 100084, PR China
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University , Beijing 100084, PR China State Key Laboratory of Advanced Space Propulsion, Tsinghua University , Beijing 100084, PR China
*
Corresponding author: Wei-Xi Huang, hwx@tsinghua.edu.cn

Abstract

To investigate the characteristics of a turbulent boundary layer (TBL) over the curved edge of the bow of submarine technology program office (SUBOFF) model, wall-resolved large-eddy simulation is conducted at a Reynolds number of $\mathop {\textit{Re}}\nolimits _L = 1.1 \times {10^6}$ based on the model length and free-stream velocity. Instead of using a trip wire at the bow surface, turbulent inflow is added to the simulation to induce boundary layer transition. The effects of geometric curvature and inflow turbulence intensity (ITI) are examined. With a low ITI level, natural transition takes place at the rear end of the straight section. With higher ITI levels, turbulence emerges immediately and evolves gradually, following a strong favourable-pressure-gradient (FPG) region near the forehead, which is significantly influenced by the large streamwise curvature. Within the FPG region, the root mean square of the wall pressure fluctuation (WPF) decreases rapidly, with the frequency spectra of WPF exhibiting good scalability with outer variables. Moreover, higher turbulence intensity levels lead to larger skin friction, which is related to the development of the TBL. To elucidate the generation mechanism of skin friction, the dynamic decomposition is derived in the curvilinear coordinate system. The mean convection and streamwise pressure gradient make the largest contributions to the local skin friction. Furthermore, an analysis of the energy transfer process based on the Reynolds stress transport equations in the curvilinear coordinate system is presented, highlighting the significant impact of geometric effects, particularly on the production term.

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© The Author(s), 2025. Published by Cambridge University Press

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References

Abarbanel, H.D.I., Katz, R.A., Galib, T., Cembrola, J. & Frison, T.W. 1994 Nonlinear analysis of high-Reynolds-number flows over a buoyant axisymmetric body. Phys. Rev. E 49, 40034018.10.1103/PhysRevE.49.4003CrossRefGoogle Scholar
Abedi, S., Dehghan, A.A., Saeidinezhad, A. & Manshadi, M.D. 2016 Effects of bulbous bow on cross-flow vortex structures around a streamlined submersible body at intermediate pitch maneuver: a numerical investigation. J. Mar. Sci. Appl. 15, 815.10.1007/s11804-016-1338-xCrossRefGoogle Scholar
Alin, N., Bensow, R.E., Fureby, C., Huuva, T. & Svennberg, U. 2010 Current capabilities of DES and LES for submarines at straight course. J. Ship Res. 54 (03), 184196.10.5957/jsr.2010.54.3.184CrossRefGoogle Scholar
Aupoix, B. 2015 Extension of Lysak’s approach to evaluate the wall pressure spectrum for boundary layer flows. Flow Turbul. Combust. 94, 6378.10.1007/s10494-014-9538-4CrossRefGoogle Scholar
Bailly, C. & Juve, D. 1999 A stochastic approach to compute subsonic noise using linearized Euler’s equations. In 5th AIAA/CEAS Aeroacoustics Conference and Exhibit, pp. 1872.Google Scholar
Balin, R. & Jansen, K.E. 2021 Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients. J. Fluid Mech. 918, A14.10.1017/jfm.2021.312CrossRefGoogle Scholar
Bentaleb, Y., Lardeau, S. & Leschziner, M.A. 2012 Large-eddy simulation of turbulent boundary layer separation from a rounded step. J. Turbul. 13 (4), 128.10.1080/14685248.2011.637923CrossRefGoogle Scholar
Blake, W.K. 2017 Mechanics of Flow-Induced Sound and Vibration, vol. 2. Complex Flow-Structure Interactions. Academic Press.Google Scholar
Bouruet-Aubertot, P., Cuypers, Y., Ferron, B., Dausse, D., Ménage, O., Atmadipoera, A.Jaya, I. 2018 Contrasted turbulence intensities in the Indonesian throughflow: a challenge for parameterizing energy dissipation rate. Ocean Dyn. 68, 779800.10.1007/s10236-018-1159-3CrossRefGoogle Scholar
Brethouwer, G. 2022 Turbulent flow in curved channels. J. Fluid Mech. 931, A21.10.1017/jfm.2021.953CrossRefGoogle Scholar
Caiazzo, A., Pargal, S., Wu, H., Sanjosé, M., Yuan, J. & Moreau, S. 2023 On the effect of adverse pressure gradients on wall-pressure statistics in a controlled-diffusion aerofoil turbulent boundary layer. J. Fluid Mech. 960, A17.10.1017/jfm.2023.157CrossRefGoogle Scholar
Chang, Y.-C., Hou, T.Y., Merriman, B. & Osher, S. 1996 A level set formulation of Eulerian interface capturing methods for incompressible fluid flows. J. Comput. Phys. 124 (2), 449464.10.1006/jcph.1996.0072CrossRefGoogle Scholar
Chen, L., Li, C., Wang, J., Hu, G. & Xiao, Y. 2024 A coherence-improved and mass-balanced inflow turbulence generation method for large eddy simulation. J. Comput. Phys. 498, 112706.10.1016/j.jcp.2023.112706CrossRefGoogle Scholar
Chesnakas, C.J. & Simpson, R.L. 1997 Detailed investigation of the three-dimensional separation about a 6 : 1 prolate spheroid. AIAA J. 35 (6), 990999.10.2514/2.208CrossRefGoogle Scholar
Chung, W.T., Mishra, A.A. & Ihme, M. 2022 Interpretable data-driven methods for subgrid-scale closure in LES for transcritical LOX/GCH4 combustion. Combust. Flame 239, 111758.10.1016/j.combustflame.2021.111758CrossRefGoogle Scholar
Drouet, A., Reliquet, G., Bardin, A., Jacquin, E., Gentaz, L. & Alessandrini, B. 2011 Simulation of submarine manoeuvring using Navier–Stokes solver. In International Conference on Computational Methods in Marine Engineering, pp. 301312. CIMNE.Google Scholar
El-Askary, W.A. 2009 Turbulent boundary layer structure of flow over a smooth-curved ramp. Comput. Fluids 38 (9), 17181730.10.1016/j.compfluid.2009.03.004CrossRefGoogle Scholar
Erm, L.P., Jones, M.B. & Henbest, S.M. 2012 Boundary layer trip size selection on streamlined bodies of revolution. In Proceedings of the 18th Australian Fluids Mechanics Conference, pp. 374377.Google Scholar
Farabee, T.M. & Casarella, M.J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A: Fluid Dyn. 3 (10), 24102420.10.1063/1.858179CrossRefGoogle Scholar
Finnicum, D.S. & Hanratty, T.J. 1988 Effect of favorable pressure gradients on turbulent boundary layers. AIChE J. 34 (4), 529540.10.1002/aic.690340402CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73L76.10.1063/1.1516779CrossRefGoogle Scholar
Gargett, A.E. 1999 Velcro measurement of turbulence kinetic energy dissipation rate $arepsilon$ . J. Atmos. Ocean. Technol. 16 (12), 19731993.10.1175/1520-0426(1999)016<1973:VMOTKE>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Goody, M.C. & Simpson, R.L. 2000 Surface pressure fluctuations beneath two-and three-dimensional turbulent boundary layers. AIAA J. 38 (10), 18221831.10.2514/2.863CrossRefGoogle Scholar
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86 (17), 3775.10.1103/PhysRevLett.86.3775CrossRefGoogle ScholarPubMed
Greene, A.D., Hendricks, P.J. & Gregg, M.C. 2015 Using an adcp to estimate turbulent kinetic energy dissipation rate in sheltered coastal waters. J. Atmos. Ocean. Technol. 32 (2), 318333.10.1175/JTECH-D-13-00207.1CrossRefGoogle Scholar
Gross, A., Jagadeesh, C. & Fasel, H. 2012 Numerical investigation of three-dimensional separation on axisymmetric bodies at angle of attack. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, pp. 97.Google Scholar
Gross, A., Kremheller, A. & Fasel, H. 2011 Simulation of flow over suboff bare hull model. In 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, pp. 290.Google Scholar
Groves, N.C., Huang, T.T. & Chang, M.S. 1989 Geometric Characteristics of DARPA SUBOFF Models (DTRC Model Nos. 5470 and 5471). David Taylor Research Center.Google Scholar
Hong, C. 2015 Wall pressure fluctuations in naturally developing boundary layer flows on axisymmetric bodies. Intl J. Mech. Mechatronics Engng 10 (1), 1015.Google Scholar
Hong, C., Shin, K.-K., Jeon, J.-J. & Kim, S.-Y. 2008 Transitional wall pressure fluctuations on axisymmetric bodies. J. Acoust. Soc. Am. 124 (5), 27672773.10.1121/1.2988291CrossRefGoogle ScholarPubMed
Hu, Z.W., Morfey, C.L. & Sandham, N.D. 2006 Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44 (7), 15411549.10.2514/1.17638CrossRefGoogle Scholar
Huang, T. & Liu, H.L. 1994 Measurements of flows over an axisymmetric body with various appendages in a wind tunnel: the darpa suboff experimental program. In Nineteenth Symposium on Naval Hydrodynamics, pp. 321346. National Academy Press.Google Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of the 1988 Summer Program, pp. 193208. Center for Turbulence Research.Google Scholar
Idelsohn, S.R., Gimenez, J.M., Larreteguy, A.E., Nigro, N.M., Sívori, F.M. & Oñate, E. 2024 The P-DNS method for turbulent fluid flows: an overview. Arch. Comput. Meth. Engng 31 (2), 9731021.10.1007/s11831-023-10004-3CrossRefGoogle Scholar
Jasak, H. 1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, University of London and Diploma of Imperial College, London, UK.Google Scholar
Jiménez, J., Hoyas, S., Simens, M.P. & Mizuno, Y. 2010 a Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335360.10.1017/S0022112010001370CrossRefGoogle Scholar
Jiménez, J.M., Hultmark, M. & Smits, A.J. 2010 b The intermediate wake of a body of revolution at high Reynolds numbers. J. Fluid Mech. 659, 516539.10.1017/S0022112010002715CrossRefGoogle Scholar
Jiménez, J.M., Reynolds, R.T. & Smits, A.J. 2010 c The effects of fins on the intermediate wake of a submarine model. J. Fluids Engng 132 (3), 031102.10.1115/1.4001010CrossRefGoogle Scholar
Kachanov, Y.S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411482.10.1146/annurev.fl.26.010194.002211CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421451.10.1017/S0022112089002090CrossRefGoogle Scholar
Kim, J., Park, I.-R., Van, S.-H. & Kim, W.-J. 2003 Calculation of turbulent flows around a submarine for the prediction of hydrodynamic performance. J. Ship Ocean Technol. 7 (4), 1631.Google Scholar
Kim, M., Lim, J., Kim, S., Jee, S., Park, J. & Park, D. 2019 Large-eddy simulation with parabolized stability equations for turbulent transition using OpenFOAM. Comput. Fluids 189, 108117.10.1016/j.compfluid.2019.04.010CrossRefGoogle Scholar
Kumar, P. & Mahesh, K. 2018 Large-eddy simulation of flow over an axisymmetric body of revolution. J. Fluid Mech. 853, 537563.10.1017/jfm.2018.585CrossRefGoogle Scholar
Ladd, D.M. 1990 Control of natural laminar instability waves on an axisymmetric body. AIAA J. 28 (2), 367369.10.2514/3.10399CrossRefGoogle Scholar
Lagraa, B., Labraga, L. & Mazouz, A. 2004 Characterization of low-speed streaks in the near-wall region of a turbulent boundary layer. Eur. J. Mech.-B/Fluids 23 (4), 587599.10.1016/j.euromechflu.2003.12.005CrossRefGoogle Scholar
Lee, I. & Sung, H.J. 2001 Characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step: part I. Time-mean statistics and cross-spectral analyses. Exp. Fluids 30, 262272.10.1007/s003480000172CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2018 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech. 842, 128145.10.1017/jfm.2018.131CrossRefGoogle Scholar
Lee, S., Kim, H.-J., Kwon, O.-S. & Lee, S.-K. 2000 Wall pressure fluctuations and radiated sound from turbulent boundary layer on an axisymmetric body. Acoust. Res. Lett. Online 1 (1), 712.10.1121/1.1314680CrossRefGoogle Scholar
Lee, S.-K. & Jones, M.B. 2020 Surface-pressure pattern of separating flows over inclined slender bodies. Phys. Fluids 32 (9), 095123.10.1063/5.0019098CrossRefGoogle Scholar
Lee, Y.-T., Blake, W. & Farabee, T. 2005 Prediction of wall pressure spectrum using a RANS calculation. In 43rd AIAA Aerospace Sciences Meeting and Exhibit, pp. 802.Google Scholar
Li, F., Zhang, Y. & Shi, X. 1999 Flow noise-transition noise received at the stagnation point of an axisymmetric body. Acta Acust. 24, 536543.Google Scholar
Liu, J., Chu, X. & Zhang, Y. 2021 a Numerical investigation of natural transitions of bow boundary layers over underwater axisymmetric bodies. Phys. Fluids 33 (7), 074101.10.1063/5.0052072CrossRefGoogle Scholar
Liu, J., Liu, J. & Zhang, Y. 2023 a Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies. Phys. Fluids 35 (4), 044107.Google Scholar
Liu, Y., Pan, C. & Liu, J. 2023 b Intermittent behavior of a bypass transition of boundary layers over an axisymmetric body of revolution. Ocean Engng 286, 115689.10.1016/j.oceaneng.2023.115689CrossRefGoogle Scholar
Liu, Y., Pan, C., Zhang, Q. & Liu, J. 2024 Multi-scale characteristics and inter-scale interaction in a transitional boundary layer over an axisymmetric body of revolution. Phys. Fluids 36 (8), 084124.10.1063/5.0220868CrossRefGoogle Scholar
Liu, Y., Zhou, Z., Zhu, L. & Wang, S. 2021 b Numerical investigation of flows around an axisymmetric body of revolution by using reynolds-stress model based hybrid Reynolds-averaged Navier–Stokes/large eddy simulation. Phys. Fluids 33 (8), 085115.10.1063/5.0058016CrossRefGoogle Scholar
Lozano-Durán, A., Hack, M.J.P. & Moin, P. 2018 Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations. Phys. Rev. Fluids 3 (2), 023901.10.1103/PhysRevFluids.3.023901CrossRefGoogle ScholarPubMed
Lungu, A. 2019 DES-based computation of the flow around the DARPA suboff. In IOP Conference Series: Materials Science and Engineering, vol. 591, pp. 012053. IOP Publishing.10.1088/1757-899X/591/1/012053CrossRefGoogle Scholar
Luo, R., Sun, Y., Zhang, H., Zhan, J. & Cai, X. 2019 The vortex and wall fluctuating pressure around submarine sail based on DDES method. In International Conference on Offshore Mechanics and Arctic Engineering, vol. 58776, pp. V002T08A048. American Society of Mechanical Engineers.10.1115/OMAE2019-96018CrossRefGoogle Scholar
Lv, S.-J., Miao, J.-L. & Zhang, X.-W. 2012 Prediction method of hydrodynamic self-noise and design of low noise bow profile for underwater high speed vehicle. J. Hydrodyn. 27 (3), 303310.Google Scholar
Lyu, X., Tang, H., Sun, J., Wu, X. & Chen, X. 2014 Simulation of microbubble resistance reduction on a suboff model. Brodogradnja: Intl J. Naval Archit. Ocean Engng Res. Develop. 65 (2), 2332.Google Scholar
Markesteijn, A.P., Gryazev, V., Karabasov, S.A., Ayupov, R.S., Benderskiy, L.A. & Lyubimov, D.A. 2020 Flow and noise predictions of coaxial jets. AIAA J. 58 (12), 52805293.10.2514/1.J058881CrossRefGoogle Scholar
Markesteijn, A.P. & Karabasov, S.A. 2019 Simulations of co-axial jet flows on graphics processing units: the flow and noise analysis. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 377 (2159), 20190083.10.1098/rsta.2019.0083CrossRefGoogle ScholarPubMed
Miao, X., Li, Y., Pang, F., Xiao, J. & Jia, D. 2020 Experimental investigation on pulsating pressure of a cone-cylinder-hemisphere model under different flow velocities. Phys. Fluids 32 (9), 095106.10.1063/5.0023409CrossRefGoogle Scholar
Moonesun, M., Korol, Y.M., Nikrasov, V.A., Ursalov, A. & Brajhko, A. 2016 a CFD analysis of the bow shapes of submarines. J. Sci. Engng Res. 3 (1), 116.Google Scholar
Moonesun, M., Mahdian, A., Korol, Y.M., Dadkhah, M. & Javadi, M.M. 2016 b Concepts in submarine shape design. Indian J. Geo-Mar. Sci. 45 (1), 100104.Google Scholar
Morse, N. & Mahesh, K. 2021 Large-eddy simulation and streamline coordinate analysis of flow over an axisymmetric hull. J. Fluid Mech. 926, A18.10.1017/jfm.2021.714CrossRefGoogle Scholar
Morse, N. & Mahesh, K. 2023 Tripping effects on model-scale studies of flow over the darpa suboff. J. Fluid Mech. 975, A3.10.1017/jfm.2023.777CrossRefGoogle Scholar
Moser, R.D. & Moin, P. 1987 The effects of curvature in wall-bounded turbulent flows. J. Fluid Mech. 175, 479510.10.1017/S0022112087000491CrossRefGoogle Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62 (3), 183200.10.1023/A:1009995426001CrossRefGoogle Scholar
Osborn, T.R. 1978 Measurements of energy dissipation adjacent to an island. J. Geophys. Res.: Oceans 83 (C6), 29392957.10.1029/JC083iC06p02939CrossRefGoogle Scholar
Osborn, T.R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10 (1), 8389.10.1175/1520-0485(1980)010<0083:EOTLRO>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
O’sullivan, P.L. & Breuer, K.S. 1994 Transient growth in circular pipe flow. I. Linear disturbances. Phys. Fluids 6 (11), 36433651.10.1063/1.868421CrossRefGoogle Scholar
Pantelatos, D.K. & Mathioulakis, D.S. 2004 Experimental flow study over a blunt-nosed axisymmetric body at incidence. J. Fluids Struct. 19 (8), 11031115.10.1016/j.jfluidstructs.2004.07.004CrossRefGoogle Scholar
Pargal, S., Wu, H., Yuan, J. & Moreau, S. 2022 Adverse-pressure-gradient turbulent boundary layer on convex wall. Phys. Fluids 34 (3), 035107.10.1063/5.0083919CrossRefGoogle Scholar
Plasseraud, M., Kumar, P. & Mahesh, K. 2023 Large-eddy simulation of tripping effects on the flow over a 6 : 1 prolate spheroid at angle of attack. J. Fluid Mech. 960, A3.10.1017/jfm.2023.175CrossRefGoogle Scholar
Posa, A. & Balaras, E. 2016 A numerical investigation of the wake of an axisymmetric body with appendages. J. Fluid Mech. 792, 470498.10.1017/jfm.2016.47CrossRefGoogle Scholar
Posa, A. & Balaras, E. 2020 A numerical investigation about the effects of Reynolds number on the flow around an appended axisymmetric body of revolution. J. Fluid Mech. 884, A41.10.1017/jfm.2019.961CrossRefGoogle Scholar
Rajaee, M., Karlsson, S. & Sirovich, L. 1995 On the streak spacing and vortex roll size in a turbulent channel flow. Phys. Fluids 7 (10), 24392443.10.1063/1.868688CrossRefGoogle Scholar
Richmond, M., Chen, H. & Patel, V. 1986 Equations of laminar and turbulent flows in general curvilinear coordinates. Tech. Rep. 300. Iowa Institute of Hydraulic Research.Google Scholar
Saad, T., Cline, D., Stoll, R. & Sutherland, J.C. 2017 Scalable tools for generating synthetic isotropic turbulence with arbitrary spectra. AIAA J. 55 (1), 327331.10.2514/1.J055230CrossRefGoogle Scholar
Saeidinezhad, A., Dehghan, A.A. & Dehghan Manshadi, M. 2020 Boundary layer and surface pressure distribution behavior over a submarine nose model with two different nose shapes. Scientia Iranica 27 (3), 12771289.Google Scholar
Saffman, P.G. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27 (3), 581593.10.1017/S0022112067000552CrossRefGoogle Scholar
Sayadi, T., Hamman, C.W. & Moin, P. 2013 Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480509.10.1017/jfm.2013.142CrossRefGoogle Scholar
Schlichting, H. & Kestin, J. 1961 Boundary Layer Theory. Springer.Google Scholar
Shi, B., Yang, X., Jin, G., He, G. & Wang, S. 2019 Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method. Appl. Maths Mech. 40 (3), 305320.10.1007/s10483-019-2425-6CrossRefGoogle Scholar
Smith, C.R. & Metzler, S.P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.10.1017/S0022112083000634CrossRefGoogle Scholar
Spalart, P.R. & Watmuff, J.H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337371.10.1017/S002211209300120XCrossRefGoogle Scholar
Wei, X., Yan, T., Liu, J., Liu, S., He, B. & Sun, T. 2024 Study on the interaction characteristics of hull-propeller-appendages of autonomous underwater vehicle based on unsteady conditions. Ocean Engng 312, 119087.10.1016/j.oceaneng.2024.119087CrossRefGoogle Scholar
White, F.M. & Majdalani, J. 2006 Viscous Fluid Flow, vol. 3. McGraw-Hill New York.Google Scholar
Witte, U., Brattegard, T., Graf, G. & Springer, B. 1997 Particle capture and deposition by deep-sea sponges from the Norwegian-Greenland sea. Mar. Ecol. Prog. Ser. 154, 241252.10.3354/meps154241CrossRefGoogle Scholar
Wu, X. 2023 New insights into turbulent spots. Annu. Rev. Fluid Mech. 55 (1), 4575.10.1146/annurev-fluid-120720-021813CrossRefGoogle Scholar
Wu, X. & Squires, K.D. 1998 Numerical investigation of the turbulent boundary layer over a bump. J. Fluid Mech. 362, 229271.10.1017/S0022112098008982CrossRefGoogle Scholar
Xia, Q.-J., Huang, W.-X., Xu, C.-X. & Cui, G.-X. 2015 Direct numerical simulation of spatially developing turbulent boundary layers with opposition control. Fluid Dyn. Res. 47 (2), 025503.10.1088/0169-5983/47/2/025503CrossRefGoogle Scholar
Yang, C. & Lohner, R. 2003 Prediction of flows over an axisymmetric body with appendages. In The 8th International Conference on Numerical Ship Hydrodynamics, Busan, Korea, pp. 147160.Google Scholar
Yazici, B.U. 2020 Hydro-acoustic and hydrodynamic optimization of darpa suboff submarine bow form using genetic algorithm. Available at: https://www.caeses.com/blog/2020/hydro-acoustic-and-hydrodynamic-optimization-of-a-submarine-bow-form/.Google Scholar
Yu, M.S., Lv, S.J. & Wu, Y.X. 2002 An acoustic designing method of low noise profile for fore-body of underwater vehicle. J. Hydrodyn. 17, 529537.Google Scholar
Zhao, J.P., Shi, X.H. & Du, X.D. 2008 The pressure distribution rule and its effect on transitional point of a head part of revolution. Comput. Simul. 25, 4245.Google Scholar
Supplementary material: File

Zhu et al. supplementary movie 1

Contours of wall pressure fluctuation over the bow surface: (a) case 1; (b) case 2; (c) case 3.
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Supplementary material: File

Zhu et al. supplementary movie 2

Contours of skin friction fluctuation over the bow surface: (a) case 1; (b) case 2; (c) case 3.
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