| Bruce Fabijonas For better or for worse, I am no longer associated with SMU. Presently, I am a Reserach Scientist at Kingsbury, Inc in Philadelphia, PA |
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- Research Interests:
- Turbulence
- I examine the effects certain turbulence models, known as
alpha-models, have on
the classic solution of the Navier-Stokes equations known
as elliptic instability.
The simplest form of the instability
occurs when a Kelvin wave traveling in three dimensions interacts with
a two-dimensional, rotating flow with elliptic streamlines.
The picture on the left shows
the parameter plane for elliptic instability for the
Lagragrian-averaged Euler-Boussinesq-alpha model. The horizontal
axis denotes the eccentricity of the elliptic flow, and the vertical
axis is the cosine of the angle the wave vector of the Kelvin wave
makes with the z-axis, the axis of the base flow. Regions in white
correspond to parameter values which yield flows whose amplitudes
are bounded in time, and regions in color correspond to flows whose
amplitude grows exponentially in time. See:
Phys.Fluids 17 (2005) 054113.
- Computation of special functions
- And now for something completely different. I write computer
codes which compute special function values.
Special functions are "useful" functions which are solutions
to algebraic, differential, and/or integral equations that cannot
be expressed in simple forms.
Shown here are the graphs of the Airy functions Ai(x) and Bi(x)
computed by my code for real values x.
The Airy functions are solutions to the ordinary differential equation
y" - xy = 0. Notice from the equation that if x > 0, the solutions
should behave like exponentials, and if x < 0, the solutions should
behave like trigonometric functions. This behavior is seen in the
graph. See: ACM TOMS 30 (2004) 471-490 & 491-501.
Newsflash: The complex-variable version of this code
will be incorporated into the next release of the IMSL library.
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The contents of this home page are the sole responsibility of Bruce Fabijonas, and do not necessarily represent the opinions or policies of Southern Methodist University. The administrator of this page is Bruce Fabijonas who may be contacted at the address listed at the top of this page.
Last revision: 09/18/07