Details on the initial conditions

• Theta: for the 'official' problem, use usual bubble formula but set the Y radius to some very large number.  So: your thermal perturbations on each side are north-south lines centered along & parallel to the X boundaries.  Because of periodic Y boundary conditions, this thermal line effectively continues indefinitely in +/-Y.
  
  
• V-wind: you set a perturbation value in the same bubble code as theta.  Your sinking cold sources on the left and/or right X boundaries carry the imposed V perturbations into the lower levels of the model.  And yes, the grid location for v is different from theta, but don't worry about that here -- use the same code you do for theta perturbations to also set V perturbations.  My (Fortran) code looks like the following:
  
        t1 = 300.0   (everywhere)
        v1 = 0.0      (everywhere)
        Triply-nested do-loop: do k, do j, do i; also loop over up to two thermal perturbations m=1,2 -- as in program 6 ...
        Compute staggered grid coordinates the usual way for x,y,z
              xdiff = (x-x0)
              ydiff = (y-y0)
              zdiff = (z-z0)
              radius = sqrt( (xdiff/xradius(m))**2 + (ydiff/yradius(m))**2 + (zdiff/zradius)**2 )
              if (radius.lt.1.0) then
                 t1(i,j,k)  = t1(i,j,k) + tpertur(m)*0.5*(cos(pi*radius)+1.0)            (tpertur is theta perturbation)
                 v1(i,j,k) = v1(i,j,k)  vpertur(m)*0.5*(cos(pi*radius)+1.0)            (vpertur is V perturbation)(ignore staggering!)
              endif
           End of loops for i,j,k, and m
        v2=v1
  
  
• U-wind:    u1 = u2 = a random number.  Please use the default Intel fortran/C random number generator;
  
• In fortran my code looks like the following.
  
        real ranval,upertur,rand
        call srand(0.0)                                       (srand initializes the random number generator)
        Triply-nestd do-loop: do k, do j, do i=1,nx+1
              ranval = rand(0)                              (rand() is the Intel Fortran/C random number generator, returning number from 0-1)
              u1(i,j,k) = (ranval-0.5)*upertur       (upertur=25.0 here, so perturbations are up to +/- 12.5 m/s)
        Enddo for i, enddo for j, enddo for k
        u2 = u1
  
  
• The C language standard library supports srand() and rand(), though rand() behavior is different in C than Fortran.  You can probably get away with using the following for numbers between (-upertur/2.) and (+upertur/2.0); note RAND_MAX is defined in stdlib.h:
  
  
  #include <stdlib.h>
  main()
  ...
  float upertur;
  ...
  srand(0.0);  /* only do this once; suggest using same "seed" (e.g. 0.0) each time, for reproducibility */
  Triply-nested for-loop: for k, for j, for i; also loop over up to two thermal perturbations m=1,2 -- as in program 6 ...
        Compute staggered grid coordinates the usual way for x,y,z
        u1[i][j][k] = upertur * ( rand() / (RAND_MAX + 1.0) ) - upertur/2.0;
  End of loops for i,j,k, and m
  [Set u2=u1]
  
  
• ... and, some added references and warnings regarding use of rand() in C include: here