| 1 |
sumM=zeros(Nx,Ny); |
| 2 |
sumN=zeros(Nx,Ny); |
| 3 |
sumD=zeros(Nx,Ny); |
| 4 |
sumW=zeros(Nx,Ny); |
| 5 |
|
| 6 |
|
| 7 |
dz=0.005; |
| 8 |
|
| 9 |
% DEFINE BOX OF INTEGRATION |
| 10 |
Nx1=4; |
| 11 |
Nx2=Nx-3; |
| 12 |
Ny1=4; |
| 13 |
Ny2=Ny-3; |
| 14 |
Nz1=5; |
| 15 |
Nz2=Nz-4; |
| 16 |
|
| 17 |
|
| 18 |
for k=Nz1:Nz2 |
| 19 |
sumM(3:Nx-2,3:Ny-2)=sumM(3:Nx-2,3:Ny-2)+Mp(3:Nx-2,3:Ny-2,k).*pv(3:Nx-2,3:Ny-2,k)*dz; |
| 20 |
sumN(3:Nx-2,3:Ny-2)=sumN(3:Nx-2,3:Ny-2)+Np(3:Nx-2,3:Ny-2,k).*pv(3:Nx-2,3:Ny-2,k)*dz; |
| 21 |
sumD(3:Nx-2,3:Ny-2)=sumD(3:Nx-2,3:Ny-2)+Dp(3:Nx-2,3:Ny-2,k).*pv(3:Nx-2,3:Ny-2,k)*dz; |
| 22 |
end |
| 23 |
sumW(3:Nx-2,3:Ny-2)=0.5*meanw(3:Nx-2,3:Ny-2,Nz1).*pv(3:Nx-2,3:Ny-2,Nz1).*pv(3:Nx-2,3:Ny-2,Nz1); |
| 24 |
|
| 25 |
|
| 26 |
for k=1:3 |
| 27 |
sumM1(:,:,k)=sumM(:,:); |
| 28 |
sumN1(:,:,k)=sumN(:,:); |
| 29 |
sumD1(:,:,k)=sumD(:,:); |
| 30 |
sumW1(:,:,k)=sumW(:,:); |
| 31 |
end |
| 32 |
|
| 33 |
for k=1:20 |
| 34 |
|
| 35 |
sumM1=smooth3(sumM1); |
| 36 |
sumN1=smooth3(sumN1); |
| 37 |
sumD1=smooth3(sumD1); |
| 38 |
sumW1=smooth3(sumW1); |
| 39 |
end |
| 40 |
|
| 41 |
v=zeros(15,1); |
| 42 |
v1=zeros(15,1); |
| 43 |
for i=1:15 |
| 44 |
% v(i)=-0.1*(i-0.5)*7; |
| 45 |
% v1(i)=0.1*(i-0.5)*7; |
| 46 |
v(i)=-0.1*(i)*15; |
| 47 |
v1(i)=0.1*(i)*15; |
| 48 |
end |
| 49 |
|
| 50 |
|
| 51 |
%V=[-10 10]; |
| 52 |
% title='Vorticity input'; |
| 53 |
% imagesc(lat,long,sumW1(Nx1:Nx2,Ny1:Ny2)');shading flat;axis image;colorbar('vertical'); |
| 54 |
% set(gca,'ydir','norm') |
| 55 |
% text(0,110,title); |
| 56 |
%figure |
| 57 |
% title='Buoyancy diffusion integral'; |
| 58 |
% imagesc(lat,long,sumD1(Nx1:Nx2,Ny1:Ny2)');shading flat;axis image;colorbar('vertical'); |
| 59 |
% set(gca,'ydir','norm') |
| 60 |
% text(0,110,title); |
| 61 |
%figure |
| 62 |
% title='Non-linear terms integral'; |
| 63 |
% imagesc(lat,long,sumN1(Nx1:Nx2,Ny1:Ny2)');shading flat;axis image;colorbar('vertical'); |
| 64 |
% set(gca,'ydir','norm') |
| 65 |
% text(0,110,title); |
| 66 |
%figure |
| 67 |
% title='Momentum diffusion integral'; |
| 68 |
% imagesc(lat,long,sumM1(Nx1:Nx2,Ny1:Ny2)');shading flat;axis image;colorbar('vertical'); |
| 69 |
% set(gca,'ydir','norm') |
| 70 |
% text(0,110,title); |
| 71 |
subplot(3,1,1) |
| 72 |
contour(squeeze(sumD1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 73 |
hold on |
| 74 |
contour(squeeze(sumD1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 75 |
text(10,98,'Buoyancy diffusion integral','Fontsize',14); |
| 76 |
hold off |
| 77 |
% xlabel('X (gridpoints)') |
| 78 |
% ylabel('Y (gridpoints)') |
| 79 |
set(gca,'DataAspectRatio',[1,1.6,2]) |
| 80 |
|
| 81 |
subplot(3,1,2) |
| 82 |
contour(squeeze(sumM1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 83 |
|
| 84 |
set(gca,'DataAspectRatio',[1,1.6,1]) |
| 85 |
text(10,98,'Momentum diffusion integral','Fontsize',14); |
| 86 |
hold on |
| 87 |
contour(squeeze(sumM1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 88 |
hold off |
| 89 |
% xlabel('X (gridpoints)') |
| 90 |
% ylabel('Y (gridpoints)') |
| 91 |
|
| 92 |
|
| 93 |
subplot(3,1,3) |
| 94 |
contour(squeeze(sumN1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 95 |
|
| 96 |
set(gca,'DataAspectRatio',[1,1.6,1]) |
| 97 |
text(10,98,'Nonlinear terms','Fontsize',14); |
| 98 |
hold on |
| 99 |
contour(squeeze(sumN1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 100 |
hold off |
| 101 |
% xlabel('X (gridpoints)') |
| 102 |
% ylabel('Y (gridpoints)') |
| 103 |
|
| 104 |
text(40,-25,'countour interval - 1.5 (non-dimensional units)','FontSize',7); |
| 105 |
text(40,-30,'negative values - solid line','FontSize',7); |
| 106 |
text(40,-35,'positive values - dashed line','FontSize',7); |
| 107 |
figure |
| 108 |
contour(squeeze(sumN1(Nx1:Nx2,Ny1:Ny2,1))',2*v) |
| 109 |
hold on |
| 110 |
contour(squeeze(sumN1(Nx1:Nx2,Ny1:Ny2,1))',2*v1,'--') |
| 111 |
hold off |
| 112 |
|
| 113 |
|
| 114 |
|
| 115 |
|
| 116 |
%-----TEST------------------------------------------------- |
| 117 |
|
| 118 |
sum=0; |
| 119 |
sumT=0; |
| 120 |
for i=Nx1:Nx2 |
| 121 |
for j=Ny1:Ny2 |
| 122 |
sum=sum+0.5*meanw(i,j,Nz1)*pv(i,j,Nz1)*pv(i,j,Nz1)*dx*dy; |
| 123 |
sumT=sum-0.5*meanw(i,j,Nz2)*pv(i,j,Nz2)*pv(i,j,Nz2)*dx*dy; |
| 124 |
end |
| 125 |
end |
| 126 |
|
| 127 |
for j=Ny1:Ny2 |
| 128 |
for k=Nz1:Nz2 |
| 129 |
sumT=sumT+0.5*meanu(Nx2,j,k)*pv(Nx2,j,k)*pv(Nx2,j,k)*dz*dy; |
| 130 |
sumT=sumT-0.5*meanu(Nx1,j,k)*pv(Nx1,j,k)*pv(Nx1,j,k)*dz*dy; |
| 131 |
end |
| 132 |
end |
| 133 |
|
| 134 |
for i=Nx1:Nx2 |
| 135 |
for k=Nz1:Nz2 |
| 136 |
sumT=sumT+0.5*meanv(i,Ny2,k)*pv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; |
| 137 |
sumT=sumT-0.5*meanv(i,Ny1,k)*pv(i,Ny1,k)*pv(i,Ny1,k)*dz*dx; |
| 138 |
end |
| 139 |
end |
| 140 |
'VORTICITY GENERATION' |
| 141 |
sum |
| 142 |
sumT |
| 143 |
|
| 144 |
|
| 145 |
sum=0; |
| 146 |
for i=Nx1:Nx2 |
| 147 |
for j=Ny1:Ny2 |
| 148 |
sum=sum+sumD(i,j)*dx*dy; |
| 149 |
end |
| 150 |
end |
| 151 |
'DISSIPATION BY EDDY-DIFFUSIVITY' |
| 152 |
sum |
| 153 |
|
| 154 |
sum=0; |
| 155 |
for i=Nx1:Nx2 |
| 156 |
for j=Ny1:Ny2 |
| 157 |
sum=sum+sumM(i,j)*dx*dy; |
| 158 |
end |
| 159 |
end |
| 160 |
'DISSIPATION BY EDDY-VISCOSITY' |
| 161 |
sum |
| 162 |
|
| 163 |
sum=0; |
| 164 |
for i=Nx1:Nx2 |
| 165 |
for j=Ny1:Ny2 |
| 166 |
sum=sum+sumN(i,j)*dx*dy; |
| 167 |
end |
| 168 |
end |
| 169 |
'NONLINEARITY' |
| 170 |
sum |
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