Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow

H. Kalisch

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 2, page 77-82
  • ISSN: 0973-5348

Abstract

top
Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.

How to cite

top

Kalisch, H.. "Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow." Mathematical Modelling of Natural Phenomena 7.2 (2012): 77-82. <http://eudml.org/doc/222414>.

@article{Kalisch2012,
abstract = {Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.},
author = {Kalisch, H.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {inviscid channel flow; hodograph transform; maximum principle; steady flow},
language = {eng},
month = {2},
number = {2},
pages = {77-82},
publisher = {EDP Sciences},
title = {Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow},
url = {http://eudml.org/doc/222414},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Kalisch, H.
TI - Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/2//
PB - EDP Sciences
VL - 7
IS - 2
SP - 77
EP - 82
AB - Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
LA - eng
KW - inviscid channel flow; hodograph transform; maximum principle; steady flow
UR - http://eudml.org/doc/222414
ER -

References

top
  1. M. Bjørkavåg, H. Kalisch. Wave breaking in Boussinesq models for undular bores. Phys. Lett. A, 375 (2011), 157–1578.  
  2. A. Constantin, M. Ehrnström, E. Wahlén. Symmetry of steady periodic gravity water waves with vorticity. Duke Math. J., 140 (2007), 591–603.  
  3. A. Constantin, W. Strauss. Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math., 57 (2004), 481–527.  
  4. W. Craig. Non-existence of solitary water waves in three dimensions. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 360 (2002), 2127–2135.  
  5. P.G. Drazin, W.H. Reid. Hydrodynamic stability. Cambridge University Press, Cambridge, 2004.  
  6. M.-L. Dubreil-Jacotin. Sur la détermination rigoureuse des ondes permanentes périodiques d’ampleur finie. J. Math. Pures Appl., 13 (1934), 217–291.  
  7. M.-L. Dubreil-Jacotin. Sur les théorèmes d’existence relatifs aux ondes permanentes périodiques ’a deux dimensions dans les liquides hétérogènes. J. Math. Pures Appl., 16 (1937), 43–67.  
  8. M. Ehrnström. A note on surface profiles for symmetric gravity waves with vorticity. J. Nonlinear Math. Phys., 13 (2006), 1–8.  
  9. M. Ehrnström. Uniqueness for steady periodic water waves with vorticity. Int. Math. Res. Not., 2005 (2005), 3721–3726.  
  10. L.E. Fraenkel. On Kelvin-Stuart vortices in a viscous fluid. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 366 (2008), 2717–2728.  
  11. S. Friedlander, W. Strauss, M. Vishik. Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré Anal. Non Linéaire, 14 (1997), 187–209.  
  12. D. Gilbarg, N.S. Trudinger. Elliptic partial differential equations of second order. Grundlehren der Mathematischen Wissenschaften 224, Springer, Berlin-New York, 1977.  
  13. O. Goubet. A relation between the pressure gradient and the flux for the general channel flow problem. Appl. Math. Optim., 34 (1996), 361–365.  
  14. B. Hof, C.W.H. van Doorne, J. Westerweel, F.T.M. Nieuwstadt, H. Faisst, B. Eckhardt, H. Wedin, R.R. Kerswell, F. Waleffe. Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow. Science, 10 (2004), 1594–1598.  
  15. V.M Hur, Z. Lin. Unstable surface waves in running water. Comm. Math. Phys., 282 (2008), 733–796.  
  16. N.H. Ibragimov, R Aitbayev, R.N. Ibragimov. Three-dimensional nonlinear rotating surface waves in channels of variable depth in the presence of formation of a small perturbation of atmospheric pressure across the channel. Commun. Nonlinear Sci. and Numer. Simul., 14 (2009), 3811–3820.  
  17. R.N. Ibragimov, D.E. Pelinovsky. Three-dimensional gravity waves in a channel of variable depth. Commun. Nonlinear Sci. and Numer. Simul., 13 (2008), 2104–2113.  
  18. H. Kalisch. Periodic traveling water waves with isobaric streamlines. J. Nonlinear Math. Phys., 11 (2004), 461–471.  
  19. H. Kalisch. A uniqueness result for periodic traveling waves in water of finite depth. Nonlinear Anal., 58 (2004), 779–785.  
  20. W. Thomson. On disturbing infinity in Lord Rayleigh’s solution for waves in a plane vortex stratum. Nature, 23 (1880), 45–46.  
  21. H. Lamb. Hydrodynamics. Cambridge University Press, London, 1924.  
  22. P. Moin, J. Kim. Numerical investigation of turbulent channel flow. J. Fluid Mech., 118 (1982), 341–377.  
  23. A.E. Trefethen, L.N. Trefethen, P.J. Schmid. Spectra and pseudospectra for pipe Poiseuille flow. Comput. Methods Appl. Mech. Engrg., 175 (1999), 413–420.  
  24. E. Wahlén. Steady water waves with a critical layer. J. Differential Equations, 246 (2009), 2468–2483.  
  25. F. Waleffe. Homotopy of exact coherent structures in plane shear flows. Phys. Fluids, 15 (2003), 1517–1534.  
  26. P.O. Åsén, G. Kreiss. On a rigorous resolvent estimate for plane Couette flow. J. Math. Fluid Mech., 9 (2007), 153–180.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.