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  • Open Access

Momentum decomposition of the pressure field

Taihang Zhu1,2,*, Chao Xia1,3, Jiabin Pang1, Olivier Cadot4, and Jonathan F. Morrison2

  • *Contact author: taihang_zhu@tongji.edu.cn
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Phys. Rev. Fluids 11, 044608 – Published 24 April, 2026

DOI: https://doi.org/10.1103/bbyr-wqyv

Abstract

The generative mechanism of the pressure field is fundamental in turbulence research and flow control, especially when subject to turbulent separation at high Reynolds numbers. To this end, we propose a physics-based framework—momentum decomposition of the pressure field—which uses the momentum equations to decompose the spatial pressure gradient into quantifiable momentum budgets. Each momentum budget corresponds to a distinct physical mechanism, enabling a rigorous decomposition and quantitative evaluation of the inherent mechanisms governing pressure generation. Incorporating results of a direct numerical simulation of laminar cylinder flow, this method is first demonstrated, after which the three-dimensional large eddy simulation results of a complex turbulent bluff body wake at ReD=1.88×105 are analyzed with a comparison of flow control. In the near wake, the bulk of low pressure originates from the streamwise convection of the centripetal flow outside the wake, which manifests as a streamline curvature effect from the term u¯∂v¯/∂x, while the pressure variation inside the wake receives main contributions from Reynolds stresses. Under flow control, due to the streamline curvature modification near the base edge, the pulsed jet produces favorable pressure gradients from the mean flow term u¯∂v¯/∂x contributing to the bulk of base-pressure recovery. Overall, the proposed framework provides a fundamental flow diagnostic tool and a rigorous foundation for designing and analyzing flow control strategies, since pressure control can be rationally linked to the momentum budgets manipulation, generally applicable to flow regimes governed by the Navier-Stokes equations.

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References (48)

  1. G. Kirchhoff, Zur theorie freier flüssigkeitsstrahlen, J. Angew. Math. 1869, 289 (1869).
  2. D. Riabouchinsky, On steady fluid motions with free surfaces, Proc. Lond. Math. Soc. s2-19, 206 (1921).
  3. T. Y. T. Wu, Cavity and wake flows, Annu. Rev. Fluid Mech. 4, 243 (1972).
  4. V. V. Sychev, Asymptotic theory of separation flows, Fluid Dyn. 17, 179 (1982).
  5. A. Roshko, Perspectives on bluff body aerodynamics, J. Wind Eng. Ind. Aerodyn. 49, 79 (1993).
  6. S. Balachandar, R. Mittal, and F. M. Najjar, Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies, J. Fluid Mech. 351, 167 (1997).
  7. J. L. Lumley, Stochastic Tools in Turbulence (Academic Press, New York, 1970).
  8. P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5 (2010).
  9. O. T. Schmidt, A. Towne, G. Rigas, T. Colonius, and G. A. Brès, Spectral analysis of jet turbulence, J. Fluid Mech. 855, 953 (2018).
  10. A. Towne, O. T. Schmidt, and T. Colonius, Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis, J. Fluid Mech. 847, 821 (2018).
  11. B. R. S. Freeman, R. J. Martinuzzi, and A. Hemmati, Exploring the influence of span-wise boundary conditions on the wake of a thin flat plate using Fourier-averaged Navier–Stokes equations, Int. J. Heat Fluid Flow 103, 109176 (2023).
  12. B. R. S. Freeman, R. J. Martinuzzi, and A. Hemmati, Momentum analysis of complex time-periodic flows, J. Fluid Mech. 979, A50 (2024).
  13. M. Grandemange, M. Gohlke, and O. Cadot, Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability, J. Fluid Mech. 722, 51 (2013).
  14. H. Choi, J. Lee, and H. Park, Aerodynamics of heavy vehicles, Annu. Rev. Fluid Mech. 46, 441 (2014).
  15. G. Rigas, A. S. Morgans, R. D. Brackston, and J. F. Morrison, Diffusive dynamics and stochastic models of turbulent axisymmetric wakes, J. Fluid Mech. 778, R2 (2015).
  16. G. Pavia, M. Varney, M. Passmore, and M. Almond, Three dimensional structure of the unsteady wake of an axisymmetric body, Phys. Fluids 31, 025113 (2019).
  17. L. Dalla Longa, O. Evstafyeva, and A. S. Morgans, Simulations of the bi-modal wake past three-dimensional blunt bluff bodies, J. Fluid Mech. 866, 791 (2019).
  18. Y. Fan, C. Xia, S. Chu, Z. Yang, and O. Cadot, Experimental and numerical analysis of the bi-stable turbulent wake of a rectangular flat-backed bluff body, Phys. Fluids 32, 10511 (2020).
  19. K. He, G. Minelli, X. Su, G. Gao, and S. Krajnović, On state instability of the bi-stable flow past a notchback bluff body, J. Fluid Mech. 931, R6 (2022).
  20. V. Gentile, F. F. J. Schrijer, B. W. Van Oudheusden, and F. Scarano, Low-frequency behavior of the turbulent axisymmetric near-wake, Phys. Fluids 28, 065102 (2016).
  21. T. Zhu and J. F. Morrison, Simulation of the turbulent axisymmetric bluff body wake with pulsed jet forcing, Phys. Rev. Fluids 6, 124604 (2021).
  22. M. Grandemange, M. Gohlke, and O. Cadot, Bi-stability in the turbulent wake past parallelepiped bodies with various aspect ratios and wall effects, Phys. Fluids 25, 095103 (2013).
  23. R. D. Brackston, J. M. García de la Cruz, A. Wynn, G. Rigas, and J. F. Morrison, Stochastic modelling and feedback control of bistability in a turbulent bluff body wake, J. Fluid Mech. 802, 726 (2016).
  24. T. Zhu, G. Rigas, and J. F. Morrison, Near wake coherent structures of a turbulent axisymmetric bluff body wake, Int. J. Heat Fluid Flow 112, 109668 (2025).
  25. G. Rigas, L. Esclapez, and L. Magri, Symmetry breaking in 3D wakes, in Proceedings of the Summer Program, Center for Turbulence Research (Stanford University, Stanford, 2016).
  26. H. Choi, W.-P. Jeon, and J. Kim, Control of flow over a bluff body, Annu. Rev. Fluid Mech. 40, 113 (2008).
  27. M. C. Thompson, T. Leweke, and K. Hourigan, Bluff bodies and wake–wall interactions, Annu. Rev. Fluid Mech. 53, 347 (2021).
  28. A. R. Oxlade, J. F. Morrison, A. Qubain, and G. Rigas, High-frequency forcing of a turbulent axisymmetric wake, J. Fluid Mech. 770, 305 (2015).
  29. D. Barros, J. Borée, B. R. Noack, A. Spohn, and T. Ruiz, Bluff body drag manipulation using pulsed jets and Coanda effect, J. Fluid Mech. 805, 422 (2016).
  30. Y. Haffner, J. Borée, A. Spohn, and T. Castelain, Unsteady Coanda effect and drag reduction for a turbulent wake, J. Fluid Mech. 899, A36 (2020).
  31. D. Fan, B. Zhang, Y. Zhou, and B. R. Noack, Optimization and sensitivity analysis of active drag reduction of a square-back Ahmed body using machine learning control, Phys. Fluids 32, 125117 (2020).
  32. T. Shaqarin, P. Oswald, B. R. Noack, and R. Semaan, Drag reduction of a D-shaped bluff-body using linear parameter varying control, Phys. Fluids 33, 077108 (2021).
  33. Y. Haffner, T. Castelain, J. Borée, and A. Spohn, Manipulation of three-dimensional asymmetries of a turbulent wake for drag reduction, J. Fluid Mech. 912, A6 (2021).
  34. B. F. Zhang, D. W. Fan, and Y. Zhou, Artificial intelligence control of a low-drag Ahmed body using distributed jet arrays, J. Fluid Mech. 963, A3 (2023).
  35. T. J. Lambert, B. Vukasinovic, and A. Glezer, Aerodynamic flow control of axisymmetric bluff body by coupled wake interactions, AIAA J. 56, 2992 (2018).
  36. T. J. Lambert, B. Vukasinovic, and A. Glezer, A freely yawing axisymmetric bluff body controlled by near-wake flow coupling, J. Fluid Mech. 863, 1123 (2019).
  37. T. J. Lambert, B. Vukasinovic, and A. Glezer, Fluidic control of a precessing axisymmetric body by near-wake coupling, Phys. Rev. Fluids 9, 053904 (2024).
  38. A. Canova, T. Zhu, and J. F. Morrison, Control of a bluff body wake using travelling jets, Int. J. Heat Fluid Flow 110, 109605 (2024).
  39. G. Rigas, A. R. Oxlade, A. S. Morgans, and J. F. Morrison, Low-dimensional dynamics of a turbulent axisymmetric wake, J. Fluid Mech. 755, R5 (2014).
  40. P. M. Nadge and R. N. Govardhan, High Reynolds number flow over a backward-facing step: Structure of the mean separation bubble, Exp. Fluids 55, 1657 (2014).
  41. B. Podvin, S. Pellerin, Y. Fraigneau, G. Bonnavion, and O. Cadot, Low-order modelling of the wake dynamics of an Ahmed body, J. Fluid Mech. 927, R6 (2021).
  42. C. Zhang, Mechanisms for aerodynamic force generation and flight stability in insects, Ph.D. thesis, Johns Hopkins University, 2015.
  43. K. Menon and R. Mittal, On the initiation and sustenance of flow-induced vibration of cylinders: Insights from force partitioning, J. Fluid Mech. 907, A37 (2021).
  44. S. Prakhar, J.-H. Seo, and R. Mittal, Modal force partitioning–a method for determining the aerodynamic loads for decomposed flow modes with application to aeroacoustic noise, J. Fluid Mech. 1013, A7 (2025).
  45. P. Bradshaw and Y. M. Koh, A note on Poisson's equation for pressure in a turbulent flow, Phys. Fluids 24, 777 (1981).
  46. T. Zhu, Y. Pan, and J. Morrison, Numerical simulation of the pressure characteristics of the pulsed jet actuator, Aeronaut. J. 128, 896 (2024).
  47. S. Davoust, L. Jacquin, and B. Leclaire, Dynamics of m=0 and m=1 modes and of streamwise vortices in a turbulent axisymmetric mixing layer, J. Fluid Mech. 709, 408 (2012).
  48. T. Zhu, The turbulent axisymmetric bluff body wake: Analysis and control through experiment and simulation, Ph.D. thesis, Imperial College London, 2023.

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Phys. Rev. Fluids 11, 044608– Published 24 April, 2026
  • Received 30 May 2025
  • Accepted 1 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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