Hostname: page-component-857557d7f7-v2cwp Total loading time: 0 Render date: 2025-12-06T11:10:10.266Z Has data issue: false hasContentIssue false
  • English
  • Français

On the pressure field, nuclei dynamics and their relation to cavitation inception in a turbulent shear layer

Published online by Cambridge University Press:  04 July 2023

Karuna Agarwal Open the ORCID record for Karuna Agarwal [Opens in a new window] ,
Omri Ram ,
Yuhui Lu  and
Joseph Katz Open the ORCID record for Joseph Katz [Opens in a new window]
Karuna Agarwal
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Omri Ram
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel
Yuhui Lu
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Joseph Katz*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: katz@jhu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Cavitation inception in the turbulent shear layer developing behind a backward-facing step occurs at multiple points along quasi-streamwise vortices (QSVs), at a rate that increases with the Reynolds number (Re). This study investigates the evolution of the unsteady pressure field and the distribution of nuclei within and around the QSVs. The time-resolved volumetric velocity in the non-cavitating flow is measured using tomographic particle tracking, and the pressure is determined by spatial integration of the material acceleration. Analysis in Eulerian and Lagrangian reference frames reveals that the pressure is lower, and its minima last longer within the QSVs compared with the surrounding flow. The intermittent low pressure regions, whose sizes and shapes are consistent with those of the cavities, are likely to be preceded by axial vortex stretching and followed by contraction. Such phenomena have been observed before in simulations of stretched vortex elements. For the same axial straining, the pressure minima last longer with increasing Re, a trend elucidated in terms of viscous diffusion of the stretched vortex core. The impact of nuclei availability is studied under ‘natural’ and controlled seeding. Owing to differences in the saturation level of non-condensable gas, the microbubble concentration in the shear layer decreases with increasing Re, in contrast to the rate of cavitation events. Minor differences in entrainment rate into the shear layer also do not explain the substantial Re effects on cavitation inception. Hence, the Re scaling of inception appears to be dominated by trends of the pressure field.

JFM classification

Drops and Bubbles: Cavitation Turbulent Flows: Shear layer turbulence Vortex Flows: Vortex dynamics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 966 , 10 July 2023 , A31
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abid, M., Andreotti, B., Douady, S. & Nore, C. 2002 Oscillating structures in a stretched-compressed vortex. J. Fluid Mech. 450, 207–233.Google Scholar
Agarwal, K., Ram, O., Wang, J., Lu, Y. & Katz, J. 2021 Reconstructing velocity and pressure from noisy sparse particle tracks using constrained cost minimization. Exp. Fluids 62, 75.CrossRefGoogle Scholar
Allan, E.S.C., Barbaca, L., Russell, P.S., Venning, J.A., Pearce, B.W. & Brandner, P.A. 2022 The influence of nucleation on cavitation inception in turbulent shear layers. In Proceedings of the 34th Symposium on Naval Hydrodynamics, Washington, DC, USA. US Office of Naval Research and The George Washington University.CrossRefGoogle Scholar
Arakeri, V.H. & Acosta, A.J. 1973 Viscous effects in the inception of cavitation on axisymmetric bodies. J. Fluids Engng 95 (4), 519–527.CrossRefGoogle Scholar
Arndt, R.A. & Keller, A. 1992 Water quality effects on cavitation inception in a trailing vortex. J. Fluids Engng 114 (3), 430–438.CrossRefGoogle Scholar
Arndt, R.E. 1981 Cavitation in fluid machinery and hydraulic structures. Annu. Rev. Fluid Mech. 13 (1), 273–326.CrossRefGoogle Scholar
Arndt, R.E. 2002 Cavitation in vortical flows. Annu. Rev. Fluid Mech. 34 (1), 143–175.CrossRefGoogle Scholar
Arndt, R.E. & Maines, B.H. 2000 Nucleation and bubble dynamics in vortical flows. J. Fluids Engng 122 (3), 488–493.CrossRefGoogle Scholar
Arndt, R.E.A., Arakeri, V.H. & Higuchi, H. 1991 Some observations of tip-vortex cavitation. J. Fluid Mech. 229, 269–289.CrossRefGoogle Scholar
Ashurst, W.T., Kerstein, A.R., Kerr, R.M. & Gibson, C.H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 2343–2353.CrossRefGoogle Scholar
Azijli, I., Sciacchitano, A., Ragni, D., Palha, A. & Dwight, R.P. 2016 A posteriori uncertainty quantification of PIV-based pressure data. Exp. Fluids 57, 1–15.CrossRefGoogle Scholar
Bappy, M., Carrica, P.M. & Buscaglia, G.C. 2019 Lagrangian statistics of pressure fluctuation events in homogeneous isotropic turbulence. Phys. Fluids 31 (8), 085111.CrossRefGoogle Scholar
Bappy, M.H., Carrica, P.M., Vela-Martín, A., Freire, L.S. & Buscaglia, G.C. 2020 Pressure statistics of gas nuclei in homogeneous isotropic turbulence with an application to cavitation inception. Phys. Fluids 32 (9), 095107.CrossRefGoogle Scholar
Barbaca, L., Venning, J.A., Russell, P.S., Russell, E.S., Pearce, B.W. & Brandner, P.A. 2020 Dynamics of cavitation inception in high Reynolds number shear flow. In Proceedings of the 33nd Symposium on Naval Hydrodynamics, Osaka, Japan. US Office of Naval Research and Osaka University.Google Scholar
Batchelor, G. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20 (4), 645–658.CrossRefGoogle Scholar
Batchelor, G. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Bell, J.H. & Mehta, R.D. 1992 Measurements of the streamwise vortical structures in a plane mixing layer. J. Fluid Mech. 239, 213–248.CrossRefGoogle Scholar
Berg, S., et al. 2019 Ilastik: interactive machine learning for (bio) image analysis. Nat. Meth. 16 (12), 1226–1232.CrossRefGoogle ScholarPubMed
Bernal, L.P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.CrossRefGoogle Scholar
Bhatt, A., Ganesh, H. & Ceccio, S.L. 2021 Cavitating flow behind a backward facing step. Intl J. Multiphase Flow 139, 103584.CrossRefGoogle Scholar
Billet, M.L. 1985 Cavitation nuclei measurements-a review. In Cavitation and Multiphase Flow Forum 1985, vol. 23, pp. 31–38.Google Scholar
Brandao, F.L. & Mahesh, K. 2022 Large-eddy simulation of cavitation inception in a shear flow. Intl J. Multiphase Flow 146, 103865.CrossRefGoogle Scholar
Brennen, C.E. 2014 Cavitation and Bubble Dynamics. Cambridge University Press.Google Scholar
Brown, G.L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.CrossRefGoogle Scholar
Brown, G.L. & Roshko, A. 2012 Turbulent shear layers and wakes. J. Turbul. 13, 51.CrossRefGoogle Scholar
Buaria, D., Bodenschatz, E. & Pumir, A. 2020 Vortex stretching and enstrophy production in high Reynolds number turbulence. Phys. Rev. Fluids 5 (10), 104602.CrossRefGoogle Scholar
Chang, N.A., Choi, J., Yakushiji, R. & Ceccio, S.L. 2012 Cavitation inception during the interaction of a pair of counter-rotating vortices. Phys. Fluids 24 (1), 014107.CrossRefGoogle Scholar
Charonko, J.J., King, C.V., Smith, B.L. & Vlachos, P.P. 2010 Assessment of pressure field calculations from particle image velocimetry measurements. Meas. Sci. Technol. 21 (10), 105401.CrossRefGoogle Scholar
Choi, J. & Ceccio, S.L. 2007 Dynamics and noise emission of vortex cavitation bubbles. J. Fluid Mech. 575, 1–26.CrossRefGoogle Scholar
Choi, J., Hsiao, C.T., Chahine, G. & Ceccio, S. 2009 Growth, oscillation and collapse of vortex cavitation bubbles. J. Fluid Mech. 624, 255–279.CrossRefGoogle Scholar
Clift, R., Grace, J.R. & Weber, M.E. 2005 Bubbles, Drops, and Particles. Dover.Google Scholar
Crow, S.C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8 (12), 2172–2179.CrossRefGoogle Scholar
Dabiri, J.O., Bose, S., Gemmell, B.J., Colin, S.P. & Costello, J.H. 2014 An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements. J.Exp. Biol. 217 (3), 331–336.Google ScholarPubMed
d'Agostino, L. & Acosta, A.J. 1991 A cavitation susceptibility meter with optical cavitation monitoring. Part 2. Experimental apparatus and results. J. Fluids Engng 113 (2), 270–277.CrossRefGoogle Scholar
De Chizelle, Y.K., Ceccio, S.L. & Brennen, C.E. 1995 Observations and scaling of travelling bubble cavitation. J. Fluid Mech. 293, 99–126.CrossRefGoogle Scholar
Driver, D.M., Seegmiller, H.L. & Marvin, J.G. 1987 Time-dependent behavior of a reattaching shear layer. AIAA J. 25 (7), 914–919.CrossRefGoogle Scholar
Eaton, J.K. 1980 Turbulent Flow Reattachment: An Experimental Study of the Flow and Structure behind a Backward-facing Step. Stanford University.Google Scholar
Eaton, J.K. & Johnston, J.P. 1982 Low frequency unsteadiness of a reattaching turbulent shear layer. In Turbulent Shear Flows 3, pp. 162–170. Springer.CrossRefGoogle Scholar
Elsinga, G.E., Scarano, F., Wieneke, B. & Van Oudheusden, B.W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41 (6), 933–947.CrossRefGoogle Scholar
Gao, J., Guildenbecher, D.R., Reu, P.L. & Chen, J. 2013 Uncertainty characterization of particle depth measurement using digital in-line holography and the hybrid method. Opt. Express 21 (22), 26432–26449.CrossRefGoogle ScholarPubMed
George, W.K., Beuther, P.D. & Arndt, R.E. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155–191.CrossRefGoogle Scholar
Ghaemi, S., Ragni, D. & Scarano, F. 2012 PIV-based pressure fluctuations in the turbulent boundary layer. Exp. Fluids 53 (6), 1823–1840.CrossRefGoogle Scholar
Ghaemi, S. & Scarano, F. 2013 Turbulent structure of high-amplitude pressure peaks within the turbulent boundary layer. J. Fluid Mech. 735, 381–426.CrossRefGoogle Scholar
Gopalan, S. & Katz, J. 2000 Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 12 (4), 895–911.CrossRefGoogle Scholar
Gopalan, S., Katz, J. & Knio, O. 1999 The flow structure in the near field of jets and its effect on cavitation inception. J. Fluid Mech. 398, 1–43.CrossRefGoogle Scholar
Green, S.I. & Acosta, A.J. 1991 Unsteady flow in trailing vortices. J. Fluid Mech. 227, 107–134.CrossRefGoogle Scholar
Ho, T.K. 1995 Random decision forests. In Proceedings of 3rd International Conference on Document Analysis and Recognition, Montreal, QC, Canada, vol. 1, pp. 278–282. IEEE.Google Scholar
Huang, M.J. 1996 Correlations of vorticity and material line elements with strain in decaying turbulence. Phys. Fluids 8 (8), 2203–2214.CrossRefGoogle Scholar
Hudy, L.M., Naguib, A. & Humphreys, W.M. 2007 Stochastic estimation of a separated-flow field using wall-pressure-array measurements. Phys. Fluids 19 (2), 024103.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285 (1), 69–94.CrossRefGoogle Scholar
Jeon, Y.J., Gomit, G., Earl, T., Chatellier, L. & David, L. 2018 Sequential least-square reconstruction of instantaneous pressure field around a body from TR-PIV. Exp. Fluids 59, 27.CrossRefGoogle Scholar
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319–336.CrossRefGoogle Scholar
Jovic, S. & Driver, D. 1995 Reynolds number effect on the skin friction in separated flows behind a backward-facing step. Exp. Fluids 18 (6), 464–467.CrossRefGoogle Scholar
Katz, J. & O'Hern, T.J. 1986 Cavitation in large scale shear flows. J. Fluids Engng 108, 373.CrossRefGoogle Scholar
Katz, J. & Sheng, J. 2010 Applications of holography in fluid mechanics and particle dynamics. Annu. Rev. Fluid Mech. 42 (1), 531–555.CrossRefGoogle Scholar
Kelvin, L. 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Khoo, M.T., Venning, J.A., Pearce, B.W., Takahashi, K., Mori, T. & Brandner, P.A. 2020 Natural nuclei population dynamics in cavitation tunnels. Exp. Fluids 61, 34.CrossRefGoogle Scholar
Kostas, J., Soria, J. & Chong, M. 2002 Particle image velocimetry measurements of a backward-facing step flow. Exp. Fluids 33 (6), 838–853.CrossRefGoogle Scholar
Lasheras, J.C. & 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.CrossRefGoogle Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.CrossRefGoogle 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 (3), 262–272.CrossRefGoogle Scholar
Lee, T.C., Kashyap, R.L. & Chu, C.N. 1994 Building skeleton models via 3-D medial surface axis thinning algorithms. CVGIP: Graph. Models Image Process. 56 (6), 462–478.Google Scholar
Lima Pereira, L.T., Ragni, D., Avallone, F. & Scarano, F. 2020 Pressure fluctuations from large-scale PIV over a serrated trailing edge. Exp. Fluids 61, 71.CrossRefGoogle Scholar
Ling, H., Katz, J., Fu, M. & Hultmark, M. 2017 Effect of Reynolds number and saturation level on gas diffusion in and out of a superhydrophobic surface. Phys. Rev. Fluids 2 (12), 124005.CrossRefGoogle Scholar
Ling, H., Srinivasan, S., Golovin, K., Mckinley, G.H., Tuteja, A. & Katz, J. 2016 High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670–703.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
Liu, X. & Katz, J. 2006 Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41 (2), 227–240.CrossRefGoogle Scholar
Liu, X. & Katz, J. 2013 Vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. J. Fluid Mech. 728, 417–457.CrossRefGoogle Scholar
Liu, X. & Moreto, J.R. 2020 Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method. Meas. Sci. Technol. 31 (5), 055301.CrossRefGoogle Scholar
Liu, Z., Sato, K. & Brennen, C.E. 1993 Cavitation nuclei population dynamics in a water tunnel. In ASME, vol. 153, pp. 119–124.Google Scholar
Lloyd, S. 1982 Least squares quantization in PCM. IEEE Trans. Inf. Theory 28 (2), 129–137.CrossRefGoogle Scholar
Lu, Y., Ram, O., Jose, J., Agarwal, K. & Katz, J. 2021 A water tunnel with inline cyclone separator for removing freestream bubble. In Proceedings of the 11th International Symposium on Cavitation, Daejon, Korea. Available at: http://cav2021.org/wp-content/uploads/2021/07/P00125_optimize-3.pdf.Google Scholar
Lund, T.S. & Rogers, M.M. 1994 An improved measure of strain state probability in turbulent flows. Phys. Fluids 6 (5), 1838–1847.CrossRefGoogle Scholar
Lundgren, T.S. & Ashurst, W.T. 1989 Area-varying waves on curved vortex tubes with application to vortex breakdown. J. Fluid Mech. 200, 283–307.CrossRefGoogle Scholar
Maurice, G., Machicoane, N., Barre, S. & Djeridi, H. 2021 Coupled x-ray high-speed imaging and pressure measurements in a cavitating backward facing step flow. Phys. Rev. Fluids 6 (4), 044311.CrossRefGoogle Scholar
McCormick, B.W. 1962 On cavitation produced by a vortex trailing form a lifting surface. J. Basic Engng Trans. 84 (3), 369.CrossRefGoogle Scholar
Melander, M.V. & Hussain, F. 1994 Core dynamics on a vortex column. Fluid Dyn. Res. 13, 1.CrossRefGoogle Scholar
Meyer, F. 1994 Topographic distance and watershed lines. Signal Process. 38, 113–125.CrossRefGoogle Scholar
Moet, H., Laporte, F., Chevalier, G. & Poinsot, T. 2005 Wave propagation in vortices and vortex bursting. Phys. Fluids 17 (5), 054109.CrossRefGoogle Scholar
Moisy, F., Voth, G. & Bodenschatz, E. 2000 Using cavitation as a probe of low-pressure filaments in turbulence. In Vortex Structure and Dynamics, pp. 263–274. Springer.CrossRefGoogle Scholar
Nadge, P.M. & Govardhan, R.N. 2014 High Reynolds number flow over a backward-facing step: structure of the mean separation bubble. Exp. Fluids 55, 1657.CrossRefGoogle Scholar
O'Hern, T.J. 1990 An experimental investigation of turbulent shear flow cavitation. J. Fluid Mech. 215, 365–391.CrossRefGoogle Scholar
Oldenziel, D. 1982 A new instrument in cavitation research: the cavitation susceptibility. Trans. ASME J. Fluids Engng 104, 136–142.CrossRefGoogle Scholar
Ooi, K. & Acosta, A. 1984 The utilization of specially tailored air bubbles as static pressure sensors in a jet. J. Fluids Engng 106 (4), 459–465.CrossRefGoogle Scholar
Ooi, K.K. 1985 Scale effects on cavitation inception in submerged water jets: a new look. J. Fluid Mech. 151, 367–390.CrossRefGoogle Scholar
Otsu, N.A. 1979 Threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9, 62–66.CrossRefGoogle Scholar
Pennings, P.C., Westerweel, J. & van Terwisga, T.J.C. 2015 Flow field measurement around vortex cavitation. Exp. Fluids 56, 206.CrossRefGoogle Scholar
Pradeep, D.S. & Hussain, F. 2001 Core dynamics of a strained vortex: instability and transition. J. Fluid Mech. 447, 247–285.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent flows. Cambridge University Press.CrossRefGoogle Scholar
Ram, O., Agarwal, K. & Katz, J. 2020 On the mechanisms that sustain the inception of attached cavitation. J. Fluid Mech. 901, R4.CrossRefGoogle Scholar
Ran, B. & Katz, J. 1991 The response of microscopic bubbles to sudden changes in the ambient pressure. J. Fluid Mech. 224, 91–115.CrossRefGoogle Scholar
Ran, B. & Katz, J. 1994 Pressure fluctuations and their effect on cavitation inception within water jets. J. Fluid Mech. 262, 223–263.CrossRefGoogle Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11 (1), 67–94.CrossRefGoogle Scholar
Rogers, M.M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.CrossRefGoogle Scholar
Rousseeuw, P.J. 1987 Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65.CrossRefGoogle Scholar
Schanz, D., Gesemann, S. & Schröder, A. 2016 Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57, 70.CrossRefGoogle Scholar
Schneiders, J.F. & Scarano, F. 2016 Dense velocity reconstruction from tomographic PTV with material derivatives. Exp. Fluids 57, 139.CrossRefGoogle Scholar
Sene, K., Hunt, J. & Thomas, N. 1994 The role of coherent structures in bubble transport by turbulent shear flows. J. Fluid Mech. 259, 219–240.CrossRefGoogle Scholar
Shen, Y.T., Gowing, S. & Jessup, S. 2009 Tip vortex cavitation inception scaling for high Reynolds number applications. J. Fluids Engng 131, 7.CrossRefGoogle Scholar
Sheng, J., Malkiel, E. & Katz, J. 2006 Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl. Opt. 45 (16), 3893–3901.CrossRefGoogle ScholarPubMed
Smits, A.J., McKeon, B.J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Spazzini, P.G., Iuso, G., Onorato, M., Zurlo, N. & Di Cicca, G.M. 2001 Unsteady behavior of back-facing step flow. Exp. Fluids 30 (5), 551–561.CrossRefGoogle Scholar
Spelt, P. & Biesheuvel, A. 1997 On the motion of gas bubbles in homogeneous isotropic turbulence. J. Fluid Mech. 336, 221–244.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1995 Drag and lift forces on microscopic bubbles entrained by a vortex. Phys. Fluids 7 (2), 389–399.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1999 Effect of entrained bubbles on the structure of vortex rings. J. Fluid Mech. 397, 171–202.CrossRefGoogle Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A-Math. Phys. Sci. 164 (919), 476–490.CrossRefGoogle Scholar
Toshiyuki Matsumi, C., José da Silva, W., Kurt Schneider, F., Miguel Maia, J., Morales, R.E.M. & Araújo Filho, W.D. 2018 Micropipette-based microfluidic device for monodisperse microbubbles generation. Micromachines 9(8), 387.CrossRefGoogle ScholarPubMed
Tsinober, A., Kit, E. & Dracos, T. 1992 Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169–192.CrossRefGoogle Scholar
Tsuji, Y., Fransson, J.H., Alfredsson, P.H. & Johansson, A.V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 1–40.CrossRefGoogle Scholar
Tsuji, Y. & Ishihara, T. 2003 Similarity scaling of pressure fluctuation in turbulence. Phys. Rev. E 68 (2), 026309.CrossRefGoogle ScholarPubMed
van der Maaten, L.J.P. & Hinton, G.E. 2008 Visualizing data using t-SNE. J. Machine Learning Res. 9, 2579–2605.Google Scholar
van Gent, P.L., Michaelis, D., van Oudheusden, B.W., Weiss, PÉ, de Kat, R., Laskari, A. & Schrijer, F.F.J. 2017 Comparative assessment of pressure field reconstructions from particle image velocimetry measurements and Lagrangian particle tracking. Exp. Fluids 58, 33.CrossRefGoogle Scholar
van Oudheusden, B.W., Scarano, F., Roosenboom, E.W., Casimiri, E.W. & Souverein, L.J. 2007 Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43 (2), 153–162.CrossRefGoogle Scholar
Van Rijsbergen, C.J. 1979 Information Retrieval, 2nd edn. Butterworth-Heinemann.Google Scholar
Verzicco, R. & Jimenez, J. 1999 On the survival of strong vortex filaments in ‘model’ turbulence. J. Fluid Mech. 394, 261–279.CrossRefGoogle Scholar
Verzicco, R., Jiménez, J. & Orlandi, P. 1995 On steady columnar vortices under local compression. J. Fluid Mech. 299, 367–388.CrossRefGoogle Scholar
Villegas, A. & Diez, F.J. 2014 Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved PIV. Exp. Fluids 55, 1697.CrossRefGoogle Scholar
Wang, J., Zhang, C. & Katz, J. 2019 GPU-based, parallel-line, omni-directional integration of measured pressure gradient field to obtain the 3D pressure distribution. Exp. Fluids 60, 58.CrossRefGoogle Scholar
Wee, D., Yi, T., Annaswamy, A. & Ghoniem, A.F. 2004 Self-sustained oscillations and vortex shedding in backward-facing step flows: simulation and linear instability analysis. Phys. Fluids 16 (9), 3361–3373.CrossRefGoogle Scholar
Widnall, S.E. 1975 The structure and dynamics of vortex filaments. Annu. Rev. Fluid Mech. 7 (1), 141–165.CrossRefGoogle Scholar
Zhang, C., Wang, J., Blake, W. & Katz, J. 2017 Deformation of a compliant wall in a turbulent channel flow. J. Fluid Mech. 823, 345–390.CrossRefGoogle Scholar