Articles
56. Shavit, M., Shatah, J., Bühler, O., 2024
Sign-indefinite invariants shape turbulent cascades
Physical Review Letters, PhysRevLett.133.014001
55. Bühler, O., 2024
Random walk model for dual cascades in wave turbulence
Physical Review E, 109, 055102
54. Boury, S, Bühler, O., Shatah J., 2023
Fast-slow wave transitions induced by a random mean flow
Physical Review E, 108, 055101
53. Dù, R.S., Bühler, O., 2023
The impact of frequency bandwidth on a one-dimensional model for dispersive wave turbulence
Journal of Nonlinear Science, 33:81
52. Dong, W., Bühler, O., Smith, K.S., 2023
Geostrophic eddies spread near-inertial wave energy to high frequencies
Journal of Physical Oceanography, 53, 1311-1322
51. Maitland-Davies, C., Bühler, O. 2023
Two-way wave-vortex interactions in a Lagrangian-mean shallow water model
Journal of Fluid Mechanics, 954, A1-1
50. Wang, H., Bühler, O. 2021
Anisotropic statistics of Lagrangian structure functions and Helmholtz decomposition
Journal of Physical Oceanography, 51, 1375-1393.
49. Dong, W., Bühler, O., Smith, K.S., 2020
Frequency diffusion of waves by unsteady flows
Journal of Fluid Mechanics, 905, R3
48. Dong, W., Bühler, O., Smith, K.S., 2020
Mean flows induced by inertia–gravity waves in a vertically confined domain
Journal of Fluid Mechanics, 890, A6
47. Wang, H., Bühler, O. 2020
Ageostrophic corrections for power spectra and wave–vortex decomposition
Journal of Fluid Mechanics, 882, A16.
46. Xie, JH, Bühler, O. 2019
Third-order structure functions for isotropic turbulence with bidirectional energy transfer
Journal of Fluid Mechanics, 877, R3.
45. Xie, JH, Bühler, O. 2019
Two-dimensional isotropic inertia–gravity wave turbulence
Journal of Fluid Mechanics, 872, 752-783.
44. Xie, JH, Bühler, O. 2018
Exact third-order structure functions for two-dimensional turbulence
Journal of Fluid Mechanics, 851, 672-686.
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.
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
`Aha Huliko`a proceedings 2007. file
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.
Culmination of a decade’s worth of thinking, on and off 🙂 The results in this paper greatly extend BM23 whilst making the theory easier to follow, a win-win.
The main topic is the three-dimensional propagation of internal wave packets and their interactions with a mean flow. The peculiar role of the pseudomomentum curl is brought out more clearly than before, and it is shown how the intrinsic wave propagation is vital for the wave–mean interactions. Internal waves slow down when their spatial scale decreases (at fixed intrinsic frequency) and the `wave capture’ of the title refers to the eventual & inevitable limit of vanishing group velocity.
12. Bühler, O., 2005
Wave-mean interaction theory
Nonlinear Waves in Fluids, ed. R. Grimshaw, Springer CISM 483, 95-133
Lecture notes from a summer school, which later evolved into the “Waves and Mean Flows” book.
11. Bühler, O., McIntyre, M. E., 2003
Remote recoil: a new wave–mean interaction effect.
Journal of Fluid Mechanics, 492, 207-230.
The subject of this paper is the resolution of a confounding puzzle that had been stewing in our minds for a number of years. It is clear from first principles that creating a wavepacket requires a momentum input into the fluid equal to the pseudomomentum content of the wave packet. It is also clear that the pseudomomentum content can change subsequently due to refraction by the mean flow. Finally, when the wave packet eventually dissipates, it creates a vortex dipole whose impulse/momentum is equal to the wave packet pseudomomentum at that time. Given this chain of events, and the fact that the initial and final pseudomomentum can be different, how is momentum overall conserved? There must be some transfer of momentum between wave packet and mean flow that occurs during the refraction, but how? The classical wave-mean interaction theory for zonal-mean flows does not answer this question because in that theory only the zonal component of the pseudomomentum is relevant, and that component is conserved under refraction by a zonally symmetric mean flow. (This is what underpins the classical wave drag picture of equal-and-opposite drag exerted on the wave maker (eg a mountain range in the case of lee waves) and on the mean flow in the location of wave dissipation/breaking.) Resolving this puzzle becomes possible once we consider the mean flow vortices that produce the straining flow. Once that is realized it then follows fairly easily that the wave packet refraction goes hand-in-hand with a shift in the mean flow vortices that changes their impulse/momentum and thereby precisely balances the pseudomomentum budget. We termed this new effect `remote recoil’, because the wave packet and the mean-flow vortices do not need to overlap in physical space.
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 some conceptual issues when interpreting variable 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. pretty 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 picked 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. Ours was one of the first 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 paper 3. below, giving a better and simpler bound 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 from1 969 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.
