Space-Time Resolution for Transitional and Turbulent Flows

  • Tapan K. SenguptaEmail author
  • Pushpender K. Sharma
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 592)


Here, we discuss the space-time requirements for the accurate computations of transitional and turbulent flows. Most of the flows in nature and engineering applications are turbulent. These flows are dominated by scales of various kinds. For the accurate determination of the physics of these flows, we should know the resolution requirements before doing the computations. Understanding how flows transition from a laminar state to a turbulent state is another objective, and studied by tracing the evolution of disturbances under the subject area of instabilities of flows. Receptivity studies of two- and three-dimensional equilibrium flows over a flat-plate, to the wall and free-stream excitations are presented. In receptivity studies boundary layer is excited using deterministic excitations and the response is checked. The transitional and turbulent flows are also dominated by various vortical/ coherent structures. We will discuss some new methods of disturbance tracking and coherent structure detection.


  1. Batchelor, G. K. (1953). The theory of homogeneous turbulence. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  2. Batchelor, G. K. (1969) Computation of the energy spectrum in homogeneous two-dimensional turbulence. Physics of Fluids, 12(12), II–233zbMATHGoogle Scholar
  3. Bhaumik, S., & Sengupta, T. K. (2014). Precursor of transition to turbulence: Spatio-temporal wave front. Physical Review E, 89(4), 043018.CrossRefGoogle Scholar
  4. Bhaumik, S., & Sengupta, T. K. (2015). A new velocity-vorticity formulation for direct numerical simulation of 3D transitional and turbulent flows. Journal of Computational Physics, 284, 230–260.MathSciNetCrossRefGoogle Scholar
  5. Bhumkar, Y. G., & Sengupta, T. K. (2011). Adaptive multi-dimensional filters. Computers and Fluids, 49(1), 128–140.MathSciNetCrossRefGoogle Scholar
  6. Chong, M. S., Perry, A. E., & Cantwell, B. J. (1990). A general classification of three-dimensional flow fields. Physics of Fluids, 2(5), 765–777.MathSciNetCrossRefGoogle Scholar
  7. Doering, C. R., & Gibbon, J. D. (1995). Applied analysis of the Navier–Stokes equations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  8. Fasel, H., & Konzelmann, U. (1990). Non-parallel stability of a flat-plate boundary layer using the complete Navier–Stokes equations. Journal of Fluid Mechanics, 221, 311–347.CrossRefGoogle Scholar
  9. Fjørtoft, R. (1953). On the changes in the spectral distribution of kinetic energy for two-dimensional, non-divergent flow. Tellus, 5(3), 225–230.MathSciNetCrossRefGoogle Scholar
  10. Jeong, J., & Hussain, F. (1995). On the identification of a vortex. Journal of Fluid Mechanics, 285, 69–94.MathSciNetCrossRefGoogle Scholar
  11. Haller, G. (2005). An objective definition of a vortex. Journal of Fluid Mechanics, 525, 1–26.MathSciNetCrossRefGoogle Scholar
  12. Hunt, J. C. R., Wray, A. A. & Moin, P. (1988). Eddies, streams, and convergence zones in turbulent flows. CTR Report Stanford University, (p. 193).Google Scholar
  13. Kachanov, Y. S. (1994). Physical mechanisms of laminar-boundary-layer transition. Annual Review of Fluid Mechanics, 26(1), 411–482.MathSciNetCrossRefGoogle Scholar
  14. Klebanoff, P. S., Tidstrom, K. D., & Sargent, L. M. (1962). The three-dimensional nature of boundary-layer instability. Journal of Fluid Mechanics, 12(1), 1–34.CrossRefGoogle Scholar
  15. Kolmogorov, A. N. (1941). Dissipation of energy in locally isotropic turbulence. Akademiia Nauk SSSR Doklady, 32(1), 16–18.MathSciNetzbMATHGoogle Scholar
  16. Kraichnan, R. H. (1967). Inertial ranges in two-dimensional turbulence. Physics of Fluids, 10(7), 1417–1423.MathSciNetCrossRefGoogle Scholar
  17. Kraichnan, R. H., & Montgomery, D. (1980). Two-dimensional turbulence. Reports on Progress in Physics, 43(5), 547.MathSciNetCrossRefGoogle Scholar
  18. Laufer, J. (1954). The structure of turbulence in fully developed pipe flow. NACA TN, 2954.Google Scholar
  19. Nastrom, G. D., Gage, K. S., & Jasperson, W. H. (1984). Kinetic energy spectrum of large-and mesoscale atmospheric processes. Nature, 310(5972), 36.CrossRefGoogle Scholar
  20. Monin, A. S., & Yaglom, A. M. (1975). Statistical fluid mechanics (Vol. 2). MIT Press, USAGoogle Scholar
  21. Pope, S. B. (2000). Turbulent Flows. Cambridge, UK: Cambridge University Press.Google Scholar
  22. Robinson, S. K. (1991). Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics, 23(1), 601–639.CrossRefGoogle Scholar
  23. Saddoughi, S. G., & Veeravalli, S. V. (1994). Local isotropy in turbulent boundary layers at high Reynolds number. Journal of Fluid Mechanics, 268, 333–372.CrossRefGoogle Scholar
  24. Schlichting, H. (1968). Boundary-layer theory. New York, USA: McGraw-Hill.Google Scholar
  25. Sengupta, T. K. (2012). Instabilities of flows and transition to turbulence. Florida, USA: CRC Press.Google Scholar
  26. Sengupta, T. K. (2013). High accuracy computing methods: Fluid flows and wave phenomena. New York, USA: Cambridge University Press.CrossRefGoogle Scholar
  27. Sengupta, T. K., & Bhaumik, S. (2011). Onset of turbulence from the receptivity stage of fluid flows. Physical Review Letters, 107(15), 154501.CrossRefGoogle Scholar
  28. Sengupta, T. K., Bhaumik, S., & Bhumkar, Y. G. (2011). Direct numerical simulation of two-dimensional wall-bounded turbulent flows from receptivity stage. Physical Review Letters, 107(15), 154501.CrossRefGoogle Scholar
  29. Sengupta, T. K., Bhaumik, S., Singh, V., & Shukl, S. (2009). Nonlinear and nonparallel receptivity of zero-pressure gradient boundary layer. International Journal of Emerging Multidisciplinary Fluid Sciences, 1(1), 19–35.CrossRefGoogle Scholar
  30. Sengupta, T. K., Chattopadhyay, M., Wang, Z. Y., & Yeo, K. S. (2002). By-pass mechanism of transition to turbulence. Journal of Fluids and Structures, 16(1), 15–29.CrossRefGoogle Scholar
  31. Sengupta, T. K., De, S., & Sarkar, S. (2003). Vortex-induced instability of an incompressible wall-bounded shear layer. Journal of Fluid Mechanics, 493, 277–286.MathSciNetCrossRefGoogle Scholar
  32. Sengupta, T. K., Dipankar, A., & Rao, A. K. (2007). Computation of the energy spectrum in homogeneous two-dimensional turbulence. Journal of Computational Physics, 220(2), 654–677.CrossRefGoogle Scholar
  33. Sengupta, T. K., Sharma, N., & Sengupta, A. (2018a). Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor–Green vortex problem. Physics of Fluids, 30(5), 054105.Google Scholar
  34. Sengupta, A., Suman, V. K., Sengupta, T. K., & Bhaumik, S. (2018b). An enstrophy-based linear and nonlinear receptivity theory. Physics of Fluids, 30(5), 054105.Google Scholar
  35. Sengupta, T. K., Rajpoot, M. K., & Bhumkar, Y. G. (2011). Space-time discretizing optimal DRP schemes for flow and wave propagation problems. Computers and Fluids, 47(1), 144–154.MathSciNetCrossRefGoogle Scholar
  36. Sengupta, T. K., Rao, A. K., & Venkatasubbaiah, K. (2006). Spatiotemporal growing wave fronts in spatially stable boundary layers. Physical Review Letters, 96(22), 224504.CrossRefGoogle Scholar
  37. Sharma, P., Sengupta, T. K., & Bhaumik, S. (2018). Three-dimensional transition of zero pressure gradient boundary layer by impulsively and nonimpulsively started harmonic wall excitation. Physical Review E, 98, 053106.CrossRefGoogle Scholar
  38. Smith, C. R., Walker, J. D. A., Haidari, A. H., & Sobrun, U. (1991). On the dynamics of near-wall turbulence. Philosophical Transactions of the Royal Society A, 336(1641), 131–175.zbMATHGoogle Scholar
  39. Suman, V. K., Siva Viknesh, S., Tekriwal, M. K., Bhaumik, S., & Sengupta, T. K. (2019). Grid sensitivity and role of error in computing a lid-driven cavity problem. Physical Review E, 99, 013305.Google Scholar
  40. Tennekes, H., & Lumley, J. L. (1972). A first course in turbulence. Cambridge: MIT Press.zbMATHGoogle Scholar
  41. Zhou, J., Adrian, R. J., Balachandar, S., & Kendall, T. M. (1999). Mechanisms for generating coherent packets of hairpin vortices in channel flow. Journal of Fluid Mechanics, 387, 353–396.MathSciNetCrossRefGoogle Scholar

Copyright information

© CISM International Centre for Mechanical Sciences 2019

Authors and Affiliations

  1. 1.Department of Aerospace Engineering, High Performance Computing LaboratoryI. I. T. KanpurKanpurIndia

Personalised recommendations