Abstract
The equations of motion for an incompressible Newtonian fluid are given in Sect. 8.11.1.
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References
H. Bhatia, G. Norgard, V. Pascucci, and P.T. Bremer, The Helmholtz-Hodge decomposition - a survey. IEEE Trans. Vis. Comput. Graph. 19 (8), 1386–1404 (2013). https://doi.org/10.1109/TVCG.2012.316. ISSN 1077-2626
L. Cavaleri, J.-H.G.M. Alves, F. Ardhuin, A. Babanin, M. Banner, K. Belibassakis, M. Benoit, M. Donelan, J. Groeneweg, T.H.C. Herbers, P. Hwang, P.A.E.M. Janssen, T. Janssen, I.V. Lavrenov, R. Magne, J. Monbaliu, M. Onorato, V. Polnikov, D. Resio, W.E. Rogers, A. Sheremet, J. McKee Smith, H.L. Tolman, G. van Vledder, J. Wolf, I. Young, Wave modelling - the state of the art. Prog. Oceanogr. 75 (4), 603–674 (2007). https://doi.org/10.1016/j.pocean.2007.05.005. http://www.sciencedirect.com/science/article/pii/S0079661107001206. ISSN 0079-6611
T. Cebeci, J. Cousteix, Modeling and Computation of Boundary-layer Flows, 2nd edn. (Springer, New York, 2005)
R.C.V. Coelho, M. Mendoza, M.M. Doria, H.J. Herrmann, Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene. Phys Rev B 96, 184307 (2017). https://doi.org/10.1103/PhysRevB.96.184307. https://link.aps.org/doi/10.1103/PhysRevB.96.184307
P.G. Drazin, W.H. Reid, Hydrodynamic Stability, 2nd edn. (Cambridge University Press, Cambridge, 2004)
B. Eckhardt, T.M. Schneider, B. Hof, J. Westerweel, Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447–468 (2007)
J. Ellenberger, P.J. Klijn, M. Tels, J. Vleggaar, Construction and performance of a cone-and-plate rheogoniometer with air bearings. J. Phys. E Sci. Instrum. 9, 763–765 (1976)
G. Eyink, U. Frisch, R. Moreau, A. Sobolevski, Euler equations: 250 years on, proceedings of an international conference. Physica D 237 (14–17), 1825–2250 (2008)
R.D. Gregory, Helmholtz’s theorem when the domain is infinite and when the field has singular points. Q. J. Mech. Appl. Math. 49, 439–450 (1996)
M.H. Holmes, Introduction to Numerical Methods in Differential Equations. Texts in Applied Mathematics, vol. 52 (Springer, New York, 2005)
P. Iskyan, Cloud formation over Breckenridge, Colorado (2019), https://www.facebook.com/piskyan/media_set?set=a.1777219625455&type=3. Accessed 10 Jan 2019
D.D. Joseph, Potential flow of viscous fluids: Historical notes. Int. J. Multiphase Flow 32, 285–310 (2006)
S. Kavosi, Kelvin-Helmholtz Instability at Earth’s magnetopause: THEMIS Observations and OpenGGCM Simulations, PhD thesis, University of New Hampshire (2015)
C. Kunkle, Velocity field in a pipe, in Millersville University Physics: Experiment of the Month (2008). https://www.millersville.edu/physics/experiments/067/index.php
H.G. Lee, J. Kim, Two-dimensional Kelvin–Helmholtz instabilities of multi-component fluids. Eur. J. Mech. B Fluids 49, 77–88 (2015). https://doi.org/10.1016/j.euromechflu.2014.08.001. http://www.sciencedirect.com/science/article/pii/S0997754614001319. ISSN 0997-7546
Y.K. Leong, Y.L. Yeow, Obtaining the shear stress shear rate relationship and yield stress of liquid foods from couette viscometry data. Rheol. Acta 42, 365–371 (2003)
B.W. Levin, M.A. Nosov, Physics of Tsunamis (Springer, New York, 2016)
S. Morris, Boeing 777-236/ER aircraft, in AirTeamImages (2006)
T. Mullin, Experimental studies of transition to turbulence in a pipe. Annu. Rev. Fluid Mech. 43 (1), 1–24 (2011). https://doi.org/10.1146/annurev-fluid-122109-160652
A. Paquier, F. Moisy, M. Rabaud, Viscosity effects in wind wave generation. Phys. Rev. Fluids 1, 083901 (2016). https://doi.org/10.1103/PhysRevFluids.1.083901. https://link.aps.org/doi/10.1103/PhysRevFluids.1.083901
Y.M. Shtemler, M. Mond, V. Cherniavskii, E. Golbraikh, Y. Nissim, An asymptotic model for the Kelvin–Helmholtz and Miles mechanisms of water wave generation by wind. Phys. Fluids 20 (9), 094106 (2008). https://doi.org/10.1063/1.2980350
S. Taneda, Oscillation of the wake behind a flat plate parallel to the flow. J. Phys. Soc. Jpn. 13 (4), 418–425 (1958). https://doi.org/10.1143/JPSJ.13.418
S.A. Thorpe, A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32 (4), 693–704 (1968). https://doi.org/10.1017/S0022112068000972
N. Tillmark, P.H. Alfredsson, Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102 (1992)
H. van Haren, L. Gostiaux, E. Morozov, R. Tarakanov, Extremely long Kelvin-Helmholtz billow trains in the Romanche Fracture Zone. Geophys. Res. Lett. 41 (23), 8445–8451 (2014). https://doi.org/10.1002/2014GL062421. ISSN 1944-8007
H.F. Weinberger, A First Course in Partial Differential Equations: with Complex Variables and Transform Methods (Dover, New York, 1995)
A.P. Willis, J. Peixinho, R.R. Kerswell, T. Mullin, Experimental and theoretical progress in pipe flow transition. Philos. Trans. A Math. Phys. Eng. Sci. 366 (1876), 2671– 2684 (2008). https://doi.org/10.1098/rsta.2008.0063. http://rsta.royalsocietypublishing.org/content/366/1876/2671. ISSN 1364-503X
N. Zahibo, E. Pelinovsky, T. Talipova, A. Kozelkov, A. Kurkin, Analytical and numerical study of nonlinear effects at tsunami modeling. Appl. Math. Comput. 174 (2), 795–809 (2006). https://doi.org/10.1016/j.amc.2005.05.014. http://www.sciencedirect.com/science/article/pii/S0096300305005102. ISSN 0096-3003
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Holmes, M.H. (2019). Newtonian Fluids. In: Introduction to the Foundations of Applied Mathematics. Texts in Applied Mathematics, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-030-24261-9_9
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