floe_breaking.f90 3.71 KB
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!_______________________________________________________________________________

                        !DESCRIPTION: Here is the parametrization proposed by
                        !Williams et al. (2013)  for wave induced
                        !floe breaking. In this routine, the maximum floe size
                        !is computed using the significant strain imposed by
                        !passing waves in ice.


!_______________________________________________________________________________



                        !INTERFACE:
                        subroutine floe_breaking

                        !USES:
                        use parameters

                        !LOCAL PARAMETERS:
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                        implicit none
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                        double precision, allocatable :: WN_ice(:)
                        double precision, allocatable :: fnt(:)
                        double precision, allocatable :: k(:)
                        double precision              :: rho=1025
                        double precision              :: d
                        double precision              :: F
                        double precision              :: Y=5.5
                        double precision              :: v=0.3
                        integer                       :: acc=10000
                        double precision, allocatable :: W(:)
                        double precision, allocatable :: fnt_d(:)

                        double precision, allocatable :: S(:)
                        double precision              :: SS
                        double precision              :: WN_ice_d
                        double precision              :: RS=7.05e-05
                        double precision              :: m0_s
                        double precision              :: m0_a
                        double precision              :: m2_a
                        double precision              :: Tw
                        double precision              :: om_d
                        double precision              :: wl_w

                        allocate(fnt(acc+1))
                        allocate(k(acc+1))
                        allocate(WN_ice(nfreq))
                        allocate(W(nfreq))
                        allocate(fnt_d(acc+1))
                        allocate(S(nfreq))

!_______________________________________________________________________________

                F=Y*h(i)**3/12d0*(1-v**2)
                d=0.9*h(i)

                jj=1            !create a wavelength vector (this is used to
                                !find the root of the polynom fnt
                do ii=0,acc
                k(jj)=real(ii)*10d0/real(acc)
                jj=jj+1
                end do


                do j=1,nfreq
                fnt=F*k**5+rho*(g-d*omega(j)**2)*k-rho*omega(j)**2
                WN_ice(j)=k(minloc(abs(fnt),DIM=1))!calculate wavelength in ice
                
                end do

 
                W=g*WN_ice/omega**2
                S=(0.5*h(i))*WN_ice**2*W
                m0_s=sum(E(n,i,1:nfreq)*S**2)*domega !0th moment of the strain spectrum
                SS=2*sqrt(m0_s)                      !significant strain
                if (SS.gt.RS) then
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                m0_a=sum(E(n,i,1:nfreq)*W**2)*domega 
                m2_a=sum(omega**2*E(n,i,1:nfreq)*W**2)*domega
                Tw=2*pi*sqrt(m0_a/m2_a)
                om_d=2*pi/Tw
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                fnt_d=F*k**5+rho*(g-d*om_d**2)*k-rho*om_d**2
                WN_ice_d=k(minloc(abs(fnt_d),DIM=1))
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                wl_w=2*pi/WN_ice_d
                Dmax(i)=max(Dmin,min(0.5*wl_w,Dmax(i)))
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                end if
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!_________________________________________________________________________________
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end subroutine floe_breaking