Books
2.Waves and Mean Flows
Second edition in paperback to appear April 2014!!
Appeared first in summer 2009 in the series Cambridge Monographs on Mechanics,
Cambridge University Press.
Sneak preview: table of contents.
1. A Brief Introduction to Classical, Statistical, and Quantum Mechanics
Courant Lecture Notes Series vol. 13, American Mathematical Society, 2006.
Hundred most frequent words in this book (amazon):
action again along amplitude between called canonical case change classical conditions conservation consider constant continuous coordinates corresponds density depend derivatives different discrete does dt dx el energy equal equation example finite first fixed follows form frequency function functional general given hamiltonian however implies initial instance integral large law line macrostate mass matrix means measurement mechanics now number operator particle path phase point potential principle probability problem quantum rays satisfies second see shows simple small solution space state statistical steps sum switch system temperature terms theorem theory therefore time trajectory transform two use value variables variations vector velocity wave yields zero
Articles
44. Xie, JH, Bühler, O. 2018
Exact third-order structure functions for two-dimensional turbulence
Journal of Fluid Mechanics, in press
43. Thomas, J., Bühler, O., Smith, K.S. 2018
Wave-induced mean flows in rotating shallow water with uniform potential vorticity
Journal of Fluid Mechanics, 839, 408-429
42. Thomas, J., Smith, K.S., Bühler, O., 2017
Near-inertial wave dispersion by geostrophic flows
Journal of Fluid Mechanics, 817, 406-438
41. Bühler, O., Kuang, M., Tabak, E., 2017
Anisotropic Helmholtz and wave-vortex decomposition of one-dimensional ship-track data.
Journal of Fluid Mechanics, 815, 361-387
40. Callies, J., Bühler, O., Ferrari, R. 2016
The dynamics of mesoscale winds in the upper troposphere and lower stratosphere
Journal of the Atmospheric Sciences, 73, 12 ,4853-4872
39. Walsh, S., Bühler, O., Shatah, J., Walsh, S., Zeng, C., 2016
On the wind generation of water waves
Archive for Rational Mechanics and Analysis, 222: 827-878
38. Bühler, O., Guo, Y., 2016
Particle dispersion by nonlinearly damped random waves
Journal of Fluid Mechanics, 786, 332-347
37. Wei, C., Bühler, O., Tabak, E., 2015
Evolution of Tsunami-induced internal acoustic-gravity waves
Journal of the Atmospheric Sciences, 72, 2303-2317
36. Danioux, E., Vanneste, J., Bühler, O., 2015
On the concentration of near-inertial waves in anti-cyclones.
Journal of Fluid Mechanics, 773, R2
35. Cohen, N., Gerber, E., Bühler, O., 2014
What drives the Brewer-Dobson circulation?
Journal of the Atmospheric Sciences, 71, 10, 3837-3855
34. Callies, J., Ferrari, R., Bühler, O., 2014
Transition from geostrophic turbulence to inertia-gravity waves in
the atmospheric energy spectrum.
Proc. Nat. Acad. Sciences, 111.48 (2014): 17033-17038
33. Bühler, O., Callies, J., Ferrari, R., 2014
Wave-vortex decomposition of one-dimensional ship-track data.
Journal of Fluid Mechanics, 756, 1007-1026.
32. Guo, Y., Bühler, O., 2014
Wave-vortex interactions in the nonlinear Schrödinger equation
Physics of Fluids, 26, 027105
31. Bühler, O., 2014
A gentle stroll through EP flux theory
European Journal of Mechanics - B/Fluids, 47, 12-15
30. Cohen, N., Gerber, E., Bühler, O., 2013
Compensation between resolved and unresolved wave driving in the stratosphere: implications for downward control
Journal of the Atmospheric Sciences, 70, 12, 3780-3798
29. Walsh, S., Bühler, O., Shatah, J., 2013
Steady water waves in the presence of wind
SIAM Journal on Mathematical Analysis, 45, 4, 2182-2227
28. Bühler, O., Grisouard, N., Holmes–Cerfon, M., 2013
Strong particle dispersion by weakly dissipative random internal waves.
Journal of Fluid Mechanics, 719, R4
27. Grisouard, N., Bühler, O., 2012.
Forcing of oceanic mean flows by dissipating internal tides
Journal of Fluid Mechanics, 708, 250-278
26.Vanneste, J., Bühler, O., 2011.
Streaming by leaky surface acoustic waves
Proc. Royal Society A, 467, 1179-1800
25. Bühler, O., Holmes–Cerfon, M., 2011
Decay of an internal tide due to random topography in the ocean.
Journal of Fluid Mechanics, 678, 271-293.
24. Holmes–Cerfon, M., Bühler, O., Ferrari, R., 2011
Particle dispersion by random waves in the rotating Boussinesq system.
Journal of Fluid Mechanics, 670, 150-175
23. Bühler, O, 2010
Wave-vortex interactions in fluids and superfluids
Annual Review of Fluid Mechanics, 42, 205-228.
22. Bühler, O., Holmes–Cerfon, M., 2009
Particle dispersion by random waves in rotating shallow water.
Journal of Fluid Mechanics, 638, 5-26.
21. Muller, C., Bühler, O., 2009
Saturation of the internal tides and induced mixing in the abyssal ocean.
Journal of Physical Oceanography, 39, 2077-2096.
20. Barreiro, A., Bühler, O., 2008
Longshore current dislocation on barred beaches.
Journal of Geophysical Research - Oceans, 113, C12004.
19. Bühler, O, 2008
Wave-vortex interactions.
Fronts, waves and vortices in geophysics, ed. J.B. Flor, Springer,
Lecture notes in physics, in press
18. Hasha, A., Bühler, O., & Scinocca, J.F, 2008
Gravity wave refraction by three-dimensionally varying winds and the global transport of angular momentum.
Journal of the Atmospheric Sciences, 65, 2892-2906.
17. Bühler, O., Muller, C., 2007
Instability and focusing of internal tides in the deep ocean.
Journal of Fluid Mechanics, 588, 1-28.
16. Bühler, O. 2007
Large deviation theory and extreme waves file
`Aha Huliko`a proceedings 2007
15. Oliver, M., Bühler, O., 2007
Transparent boundary conditions as dissipative subgrid closures for the spectral representation of scalar advection by shear flows.
Journal of Mathematical Physics, 48, 065502, 26pp.
14. Bühler, O., 2007
Impulsive fluid forcing and water strider locomotion.
Journal of Fluid Mechanics, 573, 211-236
13. Bühler, O., McIntyre, M. E., 2005
Wave capture and wave–vortex duality.
Journal of Fluid Mechanics, 534, 67-95.
12. Bühler, O., 2005
Wave-mean interaction theory
Nonlinear Waves in Fluids, ed. R. Grimshaw, Springer CISM 483, 95-133
11. Bühler, O., McIntyre, M. E., 2003
Remote recoil: a new wave–mean interaction effect.
Journal of Fluid Mechanics, 492, 207-230.
10. Bühler, O., 2003
Equatorward propagation of inertia–gravity waves due to steady and intermittent sources.
Journal of the Atmospheric Sciences, 60, 1410-1419.
A short paper motivated by reading about some conceptual issues when interpreting potential energy spectra in the atmosphere. Here it is pointed out that meridional propagation alone leads to non-uniform energy spectra due to the variation of the Coriolis parameter with latitude.
9. Bühler, O., 2002
Statistical mechanics of strong and weak point vortices in a cylinder.
Physics of Fluids, 14, 2139-2149. animations
Onsager made a famous analogy between the emergence of strong vortices in turbulence and negative temperature states in the statistical mechanics of point vortices, which predicts clumping together of like-signed vortices. This paper picks up on a detail of Onsager’s statement that is usually ignored, namely that strong vortices (as measured in terms of their circulation) should then be more clumped together than weak ones. The paper combines direct numerical simulations of the point vortex system with Monte-Carlo evaluations of the relevant integrals of the statistical mechanics and after some tricky details remarkably good agreement is found.
8. Bühler, O., Jacobson, T. E., 2001
Wave-driven currents and vortex dynamics on barred beaches.
Journal of Fluid Mechanics, 449, 313-339.
The outcome of a very enjoyable summer project from the 2000 GFD school in Woods Hole. I had attended the same school as a student in 1993 and this was the first time I was able to return. At that time the understanding of longshore currents driven by the breaking of obliquely incident water waves was almost entirely based on Longuet-Higgins’s famous papers from the 1970s. Crucial to those papers was a homogeneous wave field in the alongshore direction, which made averaging in that direction a natural step to take. However, when the waves are not homogeneous then there is a strong generation of extra vorticity that is missed by the earlier theory. This was one of the early papers pointing out the importance of the vortex dynamics that ensues, which can have unexpected outcomes for the current structure, especially on barred beaches. It was great fun working out this theory and I am glad that we were able to show it to Longuet-Higgins in person, who was very kind and positive about this new development.
7. Bühler, O., 2000
On the vorticity transport due to dissipating or breaking waves in shallow-water flow.
Journal of Fluid Mechanics, 407, 235-263.
In 1999 I left Cambridge and moved to St Andrews, where I spent more time thinking about two-dimensional vortex dynamics and dissipative wave-vortex interactions. Wave breaking is an important form of wave dissipation, but the lack of smooth solutions makes it harder to derive a clear theory for it. Here this was achieved for the shallow-water system, with discontinuous shocks standing in for true wave breaking. I wrote a finite-volume code for the dynamics and was able to make theory and simulations agree. The most important take-home message was that the local conservation of mass and momentum were crucial to get the correct vorticity generation. This is trivial mathematically, but can be a challenge for a numerical simulation.
6. Bühler, O., McIntyre, M. E., 1999
On shear-generated gravity waves that reach the mesosphere.
Part ii: wave propagation
Journal of the Atmospheric Sciences, 56, 3764-3773.
The second part of this study investigated the subsequent propagation of the emitted internal waves through a sheared atmosphere using ray tracing. The strongest effects are due to wave reflection and wave breaking, but radiative damping and viscosity were also included.
5. Bühler, O., McIntyre, M. E., & Scinocca, J. F., 1999
On shear-generated gravity waves that reach the mesosphere.
Part i: wave generation
Journal of the Atmospheric Sciences, 56, 3749-3763.
PhD thesis work on the re-radiation of internal gravity waves from 3d patches of mixed fluid in the lower stratosphere. The pancake-shaped patches are envisaged to stem from prior episodes of clear-air turbulence and they collapse whilst emitting internal waves. Most of this was simple linear wave theory, but we did compare to nonlinear simulations in 2d. There is a nice definition of a complex wave amplitude function in this paper, which helps a lot in describing the wave field, and the exact 2d pseudomomentum diagnostic equation seems to have been new as well.
4. Bühler, O. Haynes P.H., 1999
Constraints on the mean mass transport across potential vorticity contours.
Journal of the Atmospheric Sciences, 56, 942-947.
An outgrowth from the paper below, giving a better and simpler dynamical underpinning for the bounds on the mass flux.
3. Mo, R., Bühler, O., & McIntyre, M. E., 1998
Permeability of the stratospheric vortex edge: on the mean mass flux due to thermally dissipating, steady, non-breaking Rossby waves.
Quarterly Journal of the Royal Meteorological Society, 124, 2129-2148.
A paper on the question as to how permeable the sloping edge of the stratospheric polar vortex is to lateral mass fluxes, which are under tight dynamical constraints due to angular momentum conservation and related effects. There had been some statements in the chemical literature that such permeability could be very strong and hence make the vortex a very leaky vessel indeed. In contrast, this paper argued for some pretty restrictive upper bounds on such lateral mass flux.
2. Bühler, O., McIntyre, M. E., 1998
On non-dissipative wave–mean interactions in the atmosphere or oceans.
Journal of Fluid Mechanics, 354, 301-343.
This paper contains the main theoretical results from my PhD thesis, which I defended in 1996. In those days it was possible to publish your thesis work more slowly than today, perhaps! In hindsight, this very long paper should have been split into two papers dealing with the 2d shallow water and the 3d Boussinesq equations separately; that would have been more readable.
The main content of the paper was to show that the traditional link between wave dissipation and irreversible forcing of a mean flow was limited to simple geometries involving zonal averaging and, therefore, a zonally symmetric mean flow. In any more localized situation, e.g. one involving a compactly supported wave packet, this is no longer the case. This result was somewhat new at the time, though the amazing but under-appreciated JFM paper by Bretherton from1969 had nearly gotten there decades before. The paper also presents some modest extensions of the formalism of generalized Lagrangian-mean theory invented by Andrew & McIntyre in the 1970s.
1. Bühler, O., 1998
A shallow-water model that prevents nonlinear steepening of gravity waves.
Journal of the Atmospheric Sciences, 55, 2884-2891.
My first paper, which was rejected three times before it got accepted. That taught me a lot about the process! The paper describes a simple modification of the shallow-water equations that eliminates the shock formation of gravity waves in that system, which is really just a two-dimensional gas dynamics system whose sound waves are the gravity waves. Riemann variables are used to determine the unique equation of state that eliminates wave steepening and shock formation for simple waves. Amusingly, this corresponds to an ideal gas with uniform entropy and ratio of specific heats equal to minus one.. The modified system is easy to integrate and behaves very well. It allowed the study of weak non-dissipative wave-vortex interactions over long time scales, which was not possible with the unmodified equations.
Dissertations
2. PhD, 1996 (supervised by Prof. Michael E. McIntyre):
Waves and Balanced Mean Flows in the Atmosphere.
180pages. Cambridge University.
1. Diplom, 1992 (supervised by Prof. Ingo Müller):
Randbedingungen in verdünnten Gasen. Einfluß von Inertialkräften auf Spannung und Wärmefluß.
(Boundary Conditions in Rarefied Gases. Influence of Inertial Forces on Stress and Heat flux.)
76pages. Technische Universität Berlin.
Provides between two covers a rapid introduction to particle mechanics, dispersive waves, statistical mechanics, and elementary quantum mechanics aimed at advanced undergraduates and beginning graduate students. Focuses on mathematical techniques (e.g. Hamilton–Jacobi theory and path integrals) that provide links between seemingly unrelated material.