Books


  1. 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.

(amazon, AMS)






       




       



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


  1. 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.