| 1 |
% Enstrophy 'DIAG3' |
| 2 |
sumM=zeros(Nx,Ny); |
| 3 |
sumD=zeros(Nx,Ny); |
| 4 |
sumW=zeros(Nx,Ny); |
| 5 |
|
| 6 |
dz=0.005; |
| 7 |
|
| 8 |
% DEFINE BOX OF INTEGRATION |
| 9 |
Nx1=140; |
| 10 |
Nx2=Nx-4; |
| 11 |
Ny1=5; |
| 12 |
Ny2=Ny-4; |
| 13 |
Nz1=3; |
| 14 |
Nz2=Nz/2-2; |
| 15 |
|
| 16 |
pv1=pv; |
| 17 |
Mp1=Mp; |
| 18 |
Dp1=Dp; |
| 19 |
|
| 20 |
% pv1=smooth3(pv); |
| 21 |
% Mp1=smooth3(Mp); |
| 22 |
% Dp1=smooth3(Dp); |
| 23 |
|
| 24 |
% for kk=1:4 |
| 25 |
% pv=smooth3(pv); |
| 26 |
% Mp=smooth3(Mp); |
| 27 |
% Dp=smooth3(Dp); |
| 28 |
% end |
| 29 |
|
| 30 |
for k=Nz1:Nz2 |
| 31 |
sumM(3:Nx-2,3:Ny-2)=sumM(3:Nx-2,3:Ny-2)+Mp1(3:Nx-2,3:Ny-2,k).*pv1(3:Nx-2,3:Ny-2,k)*dz; |
| 32 |
sumD(3:Nx-2,3:Ny-2)=sumD(3:Nx-2,3:Ny-2)+Dp1(3:Nx-2,3:Ny-2,k).*pv1(3:Nx-2,3:Ny-2,k)*dz; |
| 33 |
end |
| 34 |
sumW(3:Nx-2,3:Ny-2)=0.5*meanw(3:Nx-2,3:Ny-2,Nz1).*pv1(3:Nx-2,3:Ny-2,Nz1).*pv1(3:Nx-2,3:Ny-2,Nz1); |
| 35 |
|
| 36 |
for k=1:3 |
| 37 |
sumM1(:,:,k)=sumM(:,:); |
| 38 |
sumD1(:,:,k)=sumD(:,:); |
| 39 |
sumW1(:,:,k)=sumW(:,:); |
| 40 |
end |
| 41 |
|
| 42 |
for k=1:25 |
| 43 |
|
| 44 |
sumM1=smooth3(sumM1); |
| 45 |
sumD1=smooth3(sumD1); |
| 46 |
sumW1=smooth3(sumW1); |
| 47 |
end |
| 48 |
|
| 49 |
V=[0.25*min(min(sumW(Nx1+2:Nx2,Ny1:Ny2-4))) 0]; |
| 50 |
|
| 51 |
% title='Vorticity input'; |
| 52 |
% imagesc(lat,long,sumW(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 53 |
% set(gca,'ydir','norm') |
| 54 |
% text(0,110,title); |
| 55 |
%figure |
| 56 |
v=zeros(10,1); |
| 57 |
v1=zeros(10,1); |
| 58 |
for i=1:10 |
| 59 |
%v(i)=-0.1*(i-0.5)*7; |
| 60 |
%v1(i)=0.1*(i-0.5)*7; |
| 61 |
v(i)=-0.1*(i)*7; |
| 62 |
v1(i)=0.1*(i)*7; |
| 63 |
end |
| 64 |
|
| 65 |
% contour(squeeze(sumW1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 66 |
% hold on |
| 67 |
% contour(squeeze(sumW1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 68 |
% hold off |
| 69 |
% text(20,0,'countour interval is 0.7 in the non-dimensional units'); |
| 70 |
% text(20,95,'Vorticity input','Fontsize',16); |
| 71 |
|
| 72 |
%figure |
| 73 |
|
| 74 |
%V=[-0.5*max(max(abs(sumD(Nx1:Nx2,Ny1:Ny2-4)))) 0.5*max(max(abs(sumD(Nx1:Nx2,Ny1:Ny2-4))))]; |
| 75 |
% title='Buoyancy diffusion integral'; |
| 76 |
% imagesc(lat,long,sumD(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 77 |
% set(gca,'ydir','norm') |
| 78 |
% text(0,110,title); |
| 79 |
|
| 80 |
|
| 81 |
% figure |
| 82 |
|
| 83 |
subplot(2,1,1) |
| 84 |
contour(squeeze(sumD1(Nx1:Nx2,Ny1:Ny2,1))',50) |
| 85 |
text(10,Ny2,'Buoyancy diffusion integral','Fontsize',15); |
| 86 |
hold off |
| 87 |
xlabel('X (gridpoints)') |
| 88 |
ylabel('Y (gridpoints)') |
| 89 |
set(gca,'DataAspectRatio',[2,2,2]) |
| 90 |
|
| 91 |
%figure |
| 92 |
%V=[-0.5*max(max(abs(sumM(Nx1:Nx2,Ny1:Ny2-4)))) 0.5*max(max(abs(sumM(Nx1:Nx2,Ny1:Ny2-4))))]; |
| 93 |
% title='Momentum diffusion integral'; |
| 94 |
% imagesc(lat,long,sumM(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 95 |
% set(gca,'ydir','norm') |
| 96 |
% text(0,110,title); |
| 97 |
|
| 98 |
subplot(2,1,2) |
| 99 |
contour(squeeze(sumM1(Nx1:Nx2,Ny1:Ny2,1))',50) |
| 100 |
|
| 101 |
set(gca,'DataAspectRatio',[1,1,1]) |
| 102 |
text(10,Ny2,'Momentum diffusion integral','Fontsize',15); |
| 103 |
xlabel('X (gridpoints)') |
| 104 |
ylabel('Y (gridpoints)') |
| 105 |
text(40,-25,'countour interval - 0.7 (non-dimensional units)','FontSize',7); |
| 106 |
text(40,-30,'negative values - solid line','FontSize',7); |
| 107 |
text(40,-35,'positive values - dashed line','FontSize',7); |
| 108 |
|
| 109 |
|
| 110 |
|
| 111 |
%-----TEST------------------------------------------------- |
| 112 |
|
| 113 |
sum=0; |
| 114 |
sumT=0; |
| 115 |
sumY=0; |
| 116 |
for i=Nx1:Nx2 |
| 117 |
for j=Ny1:Ny2 |
| 118 |
sum=sum+0.5*meanw(i,j,Nz1)*pv(i,j,Nz1)*pv(i,j,Nz1)*dx*dy; |
| 119 |
sumT=sum-0.5*meanw(i,j,Nz2)*pv(i,j,Nz2)*pv(i,j,Nz2)*dx*dy; |
| 120 |
end |
| 121 |
end |
| 122 |
|
| 123 |
for j=Ny1:Ny2 |
| 124 |
for k=Nz1:Nz2 |
| 125 |
sumT=sumT+0.5*meanu(Nx2,j,k)*pv(Nx2,j,k)*pv(Nx2,j,k)*dz*dy; |
| 126 |
sumT=sumT-0.5*meanu(Nx1,j,k)*pv(Nx1,j,k)*pv(Nx1,j,k)*dz*dy; |
| 127 |
end |
| 128 |
end |
| 129 |
|
| 130 |
for i=Nx1:Nx2 |
| 131 |
for k=Nz1:Nz2 |
| 132 |
sumT=sumT+0.5*meanv(i,Ny2,k)*pv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; |
| 133 |
sumY=sumY+0.5*meanv(i,Ny2,k)*pv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; |
| 134 |
sumT=sumT-0.5*meanv(i,Ny1,k)*pv(i,Ny1,k)*pv(i,Ny1,k)*dz*dx; |
| 135 |
end |
| 136 |
end |
| 137 |
'VORTICITY GENERATION' |
| 138 |
sum |
| 139 |
sumY |
| 140 |
sumT |
| 141 |
|
| 142 |
|
| 143 |
sum=0; |
| 144 |
for i=Nx1:Nx2 |
| 145 |
for j=Ny1:Ny2 |
| 146 |
sum=sum+sumD(i,j)*dx*dy; |
| 147 |
end |
| 148 |
end |
| 149 |
'DISSIPATION BY EDDY-DIFFUSIVITY' |
| 150 |
sum |
| 151 |
|
| 152 |
sum=0; |
| 153 |
for i=Nx1:Nx2 |
| 154 |
for j=Ny1:Ny2 |
| 155 |
sum=sum+sumM(i,j)*dx*dy; |
| 156 |
end |
| 157 |
end |
| 158 |
'DISSIPATION BY EDDY-VISCOSITY' |
| 159 |
sum |
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