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Linear Mountain (Lee) Wave Theory

Linear Mountain (Lee) Wave Theory

Linear Mountain (Lee) Wave Theory


I've been looking into linear mountain wave theory to find the downward, ie toward ground, velocity of a horizontal wind flow perturbed by a mountain.

However, linear theories tend to be fairly inaccurate due to sensitivity to variations in Scorer parameter amoung other things.

I am looking to model the wind behaviour for clear-air turbulence but am unsure whether to proceed using a linear theory, or since there are significant inaccuracies should I proceed with something more indepth, ie non-linearized.

Does anyone have experience modeling Lee waves, in particular the vertical perturbations?  I would like to hear which path you chose and why.

For anyone interested below and attached you will find papers related to the subject.

 - Kirk

Journal of Wind Engineering
and Industrial Aerodynamics 74-76 (1998) 273-282
Validation of a non-hydrostatic numerical model
to simulate stratiÞed wind Þelds over complex topography
Christiane Montavon

Quarterly Journal of the Royal Meteorological Society
Volume 136, Issue 647, pages 429–441, January 2010 Part B
The accuracy of linear theory for predicting mountain-wave drag: Implications for parametrization schemes
H. Wells, S. B. Vosper

Quarterly Journal of the Royal Meteorological Society
Volume 96, Issue 407, pages 50–66, January 1970
Some aspects of linear lee wave theory for the stratosphere
F. H. Berkshire1, F. W. G. Warren

RE: Linear Mountain (Lee) Wave Theory

Probably no help, but I can offer empirical information. I have encountered lift that exceeds 1000 fpm (max variometer reading) several times in mountain wave, while normal sink rate in my glider would be 150-200 fpm in still air. I would imagine that corresponding sinking air would be approximately equal. I tend to avoid the air going down, so have less data on it smile

RE: Linear Mountain (Lee) Wave Theory

Hey pgs2,

Thanks for the help, At least that'll give me some reasonable values to compare to, actually this side project got a little neglected while I worked on another project, but when I get it back and running, I'll let you know how it goes.  As I left it, the basic formula followed closely to Montavon's work, plus some matlab to try and model something other than a bell-shaped mountain, but it became much more complex then I thought - assumptions are such a nice thing ;) and so before I spent a day or two just re-deriving the equations I wanted to make sure it wasn't all for not.  

I guess I'll just have to find out myself when I get some spare time.

Thanks again, it shows a lot of respect that you'd post on a month old topic, and I appreciate it.

BTW I'd also avoid the sinks as well, unfortunately when programming UAS they don't always have the luxury of common "sense" ;)

 - Kirk

RE: Linear Mountain (Lee) Wave Theory

Hey Michael,

Thanks, I just briefly looked over the site and it looks very interesting, I'll let you know what I find out.

 - Kirk

RE: Linear Mountain (Lee) Wave Theory

curtain call
Have you thought about talking to folks who use this information every day for a living.
 The folks at Sugarbush soaring in Vermont pride themselves on being a mountain wave gliderport. They have empirical information on the strength of the wave, position to the mountain, position and strength of the rotor etc., I am adding a link to their site, however this time of year they may be closed.


RE: Linear Mountain (Lee) Wave Theory

To follow-up berkshire's post (and mohr's), and in line with your reference papers, have you tried contacting local (or regional) weather forecasters (e.g., US National Weather Service, NOAA), or university researchers?

College research types in particular, if you can track them down, tend to be very eager to talk about their research or areas of interest.

RE: Linear Mountain (Lee) Wave Theory


Some aditional information for your request:

Laprise, R., and W. R. Peltier, 1989: The linear stability of nonlinear mountain waves: Implications for the understanding of severe downslope windstorms. J. Atmos. Sci. 46(4), 545-564.

Pinty, J.-P., R. Benoit, É. Richard and R. Laprise, 1995: Simple tests of a semi-implicit semi-Lagrangian model on 2D mountain wave problems. Mon. Wea. Rev. 123(10), 3042-3058.


RE: Linear Mountain (Lee) Wave Theory

Thanks berkshire, IceMan30, and mohr,

berkshire - Checked out the site, looks like they open in a few days so I'll give them a call sometime next weekend.

IceMan30 - I think I may just have to do that, unfortunately any university researches I have a rapport with are all from the prairies, needless to say that kind of research in in it's infancy here, on the other hand I could always use some new contacts out west, thanks for the tip.

mohr - I'll check those papers out tomorrow evening, I appreciate the search, Laprise seems to pop up more and more, Thank you for pointing it out to me.

Thanks again for all the love today,

 - Kirk

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