[Sea-mat] coastal-trapped waves

[Xu, Zhigang]

Hi, Alexander, 

    Have we met on the data assimilation workshop in 99 lecture by Professor
A. Bennett your school? I guess so. 

    I have just recently made a matlab program from scratch to calculate the
eigenvalues/egienfunctions for barotropic trapped waves on the continental
shelf/slope. It numerically solves the following eigen value problem:

           [ P(x) Y'  ]' + Q(x)Y = lambda F1(x) Y + lambda^2 F2(x) Y,   for
x=x(2:N-1)
           A(1) Y(1) + A(2) Y'(1) =lambda A(3) Y(1)
for x=x(1)
           B(1) Y(N) +B(2)Y'(N) = lambda B(3) Y(N)
for x=x(N)

where 
      x                     is the on-off shore direction co-ordinate, and
seaward positively; x(1)coast, x(N)=offshore end
 
      Y                    are the complex amplitude of the trapped waves
(to be solved as eigenfunctions)
 
     P(x)  and Q(x)  are arbitrary function of x;  for our coastal trapped
waves, they should be  water depth, say h(x),  and (sigma^2-f^2)/g
respectively (sigma is the frequency, and f and g are the Coriolis and
gravitational parameters) 

    lambda             are the eigvenvalues in interest (to be solved), it
can represent the alongshore wave numbers 

    F1(x) and F2(x)  are again two functions of x;  as far as the coastal
trapped wave concerns, 
                            they should be taken as F1(x)= f/(sigma h' ) and
F2(x)=h(x)

     A(1), A(2), A(3), B(1), B(2) and B(3)  are two groups of  arbitrary
(but should be meaningful) constants, to allow for  different types of
boundary conditions at the coast and at the deep sea end. For example,  if
you supply A(1:3) with [0 1 f/sigma] and B(1:3) with [1 0 0] then you will
have specified no-flux condition at the coast and clamp condition at the
deep sea side.  

     Upon you specify the coefficient functions and constants, the program
will give you all the possible alonshore wave numbers and amplitude
structures in the on-offshore direction per frequency. So if you run the
program for a range of frequencies, you can have dispersion curves. Possible
evanescent modes will also be among the outputs. 

     This program is not a translation of the WHOI Fortran code; it was made
from scratch, because for me it is easier to make it from scratch once you  
realise that the above ODE's can be discretized  to form  a general
eigenvalue problem things become quite easy with the matlab eigen functions.
I  have obtained interesting results with the program on double Kelvin waves
on the Newfoundland shelves.  But the program is not polished yet,
everything to me here is in a rush. I am planing  to make another program
for a baroclinic counterpart later on, and to polish them together before I
can contribute to our community. But if you are interested at this stage, I
can supply it to you first and facilitate you in using it. This way I can
also have your valuable feedback as well.

Regards!

Zhigang


Dr. Zhigang Xu
Research Scientist
Coastal Ocean Science, Ocean Sciences Division
Bedford Institute of Oceanography
P. O. Box 1006
Dartmouth, N.S. B2Y 4A2
Tel. 902-426-2307, Fax 902-426-6927
Office Email: xuz at mar.dfo-mpo.gc.ca   
 
 
 

> -----Original Message-----
> From:	Alexander Perlin [SMTP:aperlin at OCE.ORST.EDU]
> Sent:	Friday, July 20, 2001 7:11 PM
> To:	sea-mat at whoi.edu
> Subject:	[Sea-mat] coastal-trapped waves
> 
> Hello all,
> 
> I'm looking for a Matlab version of WHOI Fortran program for computing 
> properties of coastal-trapped waves over the continental shelf and slope. 
> Does such a version exist? If not, is it possible to get Fortran code?
> 
> Thank you,
> Alexander.
> 
> 
> 
> ****************************************************
> Alexander Perlin
> College of Oceanic & Atmos. Sci.
> 104 Ocean Admin. Bldg.
> Oregon State University
> Corvallis, OR 97331-5503
> ph: 541-737-2990 fx: 541-737-2064
> e-mail: aperlin at oce.orst.edu
> http://mixing.oce.orst.edu/people/perlin/
> ****************************************************
> 
> 
> 
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