| 1 |
% PV diagnostics 'DIAGtest' |
| 2 |
|
| 3 |
sumM=zeros(Nx,Ny); |
| 4 |
sumD=zeros(Nx,Ny); |
| 5 |
sumW=zeros(Nx,Ny); |
| 6 |
|
| 7 |
dz=0.005; |
| 8 |
|
| 9 |
% DEFINE BOX OF INTEGRATION |
| 10 |
Nx1=4; |
| 11 |
Nx2=Nx-3; |
| 12 |
Ny1=4; |
| 13 |
% for single gyre |
| 14 |
% Ny2=Ny-3; |
| 15 |
% for double-gyre |
| 16 |
Ny2=45; |
| 17 |
|
| 18 |
Nz1=5; |
| 19 |
Nz2=Nz-4; |
| 20 |
|
| 21 |
%Nx1=30; |
| 22 |
%Nx2=32; |
| 23 |
%Ny1=30; |
| 24 |
%Ny2=32; |
| 25 |
%Nz1=10; |
| 26 |
%Nz2=12; |
| 27 |
|
| 28 |
pv1=pv; |
| 29 |
Mp1=Mp; |
| 30 |
Dp1=Dp; |
| 31 |
|
| 32 |
% for kk=1:4 |
| 33 |
% pv1=smooth3(pv1); |
| 34 |
% Mp1=smooth3(Mp1); |
| 35 |
% Dp1=smooth3(Dp1); |
| 36 |
% end |
| 37 |
|
| 38 |
|
| 39 |
for k=Nz1:Nz2 |
| 40 |
|
| 41 |
if k==Nz1 |
| 42 |
a=0.5; |
| 43 |
elseif k==Nz2 |
| 44 |
a=0.5; |
| 45 |
else |
| 46 |
a=1; |
| 47 |
end |
| 48 |
|
| 49 |
sumM(3:Nx-2,3:Ny-2)=sumM(3:Nx-2,3:Ny-2)+a*Mp1(3:Nx-2,3:Ny-2,k)*dz; |
| 50 |
sumD(3:Nx-2,3:Ny-2)=sumD(3:Nx-2,3:Ny-2)+a*Dp1(3:Nx-2,3:Ny-2,k)*dz; |
| 51 |
end |
| 52 |
sumW(3:Nx-2,3:Ny-2)=meanw(3:Nx-2,3:Ny-2,Nz1).*pv1(3:Nx-2,3:Ny-2,Nz1); |
| 53 |
|
| 54 |
for k=1:3 |
| 55 |
sumM1(:,:,k)=sumM(:,:); |
| 56 |
sumD1(:,:,k)=sumD(:,:); |
| 57 |
sumW1(:,:,k)=sumW(:,:); |
| 58 |
end |
| 59 |
|
| 60 |
for k=1:15 |
| 61 |
|
| 62 |
sumM1=smooth3(sumM1); |
| 63 |
sumD1=smooth3(sumD1); |
| 64 |
sumW1=smooth3(sumW1); |
| 65 |
end |
| 66 |
|
| 67 |
V=[0.25*min(min(sumW(Nx1+2:Nx2,Ny1:Ny2-4))) 0]; |
| 68 |
|
| 69 |
% title='Vorticity input'; |
| 70 |
% imagesc(lat,long,sumW(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 71 |
% set(gca,'ydir','norm') |
| 72 |
% text(0,110,title); |
| 73 |
%figure |
| 74 |
v=zeros(10,1); |
| 75 |
v1=zeros(10,1); |
| 76 |
for i=1:10 |
| 77 |
%v(i)=-0.1*(i-0.5)*7; |
| 78 |
%v1(i)=0.1*(i-0.5)*7; |
| 79 |
v(i)=-0.01*(i); |
| 80 |
v1(i)=0.01*(i); |
| 81 |
end |
| 82 |
|
| 83 |
% contour(squeeze(sumW1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 84 |
% hold on |
| 85 |
% contour(squeeze(sumW1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 86 |
% hold off |
| 87 |
% text(20,0,'countour interval is 0.7 in the non-dimensional units'); |
| 88 |
% text(20,95,'Vorticity input','Fontsize',16); |
| 89 |
|
| 90 |
%figure |
| 91 |
|
| 92 |
%V=[-0.5*max(max(abs(sumD(Nx1:Nx2,Ny1:Ny2-4)))) 0.5*max(max(abs(sumD(Nx1:Nx2,Ny1:Ny2-4))))]; |
| 93 |
% title='Buoyancy diffusion integral'; |
| 94 |
% imagesc(lat,long,sumD(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 95 |
% set(gca,'ydir','norm') |
| 96 |
% text(0,110,title); |
| 97 |
|
| 98 |
|
| 99 |
% figure |
| 100 |
x=Nx1:Nx2; |
| 101 |
y=Ny1:Ny-2; |
| 102 |
subplot(2,1,1) |
| 103 |
contourf(x,y,squeeze(sumD1(Nx1:Nx2,Ny1:Ny-2,1))',10);colorbar; |
| 104 |
% contour(x,y,squeeze(sumD1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 105 |
%hold on |
| 106 |
% contour(x,y,squeeze(sumD1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 107 |
text(10,Ny2+5,'Buoyancy eddy-transfer','Fontsize',13); |
| 108 |
%hold off |
| 109 |
xlabel('X (gridpoints)') |
| 110 |
ylabel('Y (gridpoints)') |
| 111 |
set(gca,'DataAspectRatio',[2,2,2]) |
| 112 |
|
| 113 |
%figure |
| 114 |
%V=[-0.5*max(max(abs(sumM(Nx1:Nx2,Ny1:Ny2-4)))) 0.5*max(max(abs(sumM(Nx1:Nx2,Ny1:Ny2-4))))]; |
| 115 |
% title='Momentum eddy-transfer'; |
| 116 |
% imagesc(lat,long,sumM(Nx1:Nx2,Ny1:Ny2)');shading flat;caxis(V);axis image;colorbar('vertical'); |
| 117 |
% set(gca,'ydir','norm') |
| 118 |
% text(0,110,title); |
| 119 |
|
| 120 |
subplot(2,1,2) |
| 121 |
contourf(x,y,squeeze(sumM1(Nx1:Nx2,Ny1:Ny-2,1))',10);colorbar; |
| 122 |
% contour(x,y,squeeze(sumM1(Nx1:Nx2,Ny1:Ny2,1))',v) |
| 123 |
|
| 124 |
set(gca,'DataAspectRatio',[1,1,1]) |
| 125 |
text(10,Ny2+5,'Momentum eddy-transfer integral','Fontsize',13); |
| 126 |
%hold on |
| 127 |
% contour(x,y,squeeze(sumM1(Nx1:Nx2,Ny1:Ny2,1))',v1,'--') |
| 128 |
%hold off |
| 129 |
xlabel('X (gridpoints)') |
| 130 |
ylabel('Y (gridpoints)') |
| 131 |
% text(40,-20,'countour interval - 0.01 (non-dimensional units)','FontSize',7); |
| 132 |
% text(40,-30,'negative values - solid line','FontSize',7); |
| 133 |
% text(40,-35,'positive values - dashed line','FontSize',7); |
| 134 |
|
| 135 |
|
| 136 |
|
| 137 |
%-----TEST------------------------------------------------- |
| 138 |
|
| 139 |
dz |
| 140 |
|
| 141 |
bx=zeros(Nx,Ny,Nz); |
| 142 |
by=zeros(Nx,Ny,Nz); |
| 143 |
bz=zeros(Nx,Ny,Nz); |
| 144 |
zetax=zeros(Nx,Ny,Nz); |
| 145 |
zetay=zeros(Nx,Ny,Nz); |
| 146 |
zetaz=zeros(Nx,Ny,Nz); |
| 147 |
|
| 148 |
bx(2:Nx-1,2:Ny-1,2:Nz-1)=(meantheta(3:Nx,2:Ny-1,2:Nz-1)-meantheta(1:Nx-2,2:Ny-1,2:Nz-1))/(2*dx); |
| 149 |
by(2:Nx-1,2:Ny-1,2:Nz-1)=(meantheta(2:Nx-1,3:Ny,2:Nz-1)-meantheta(2:Nx-1,1:Ny-2,2:Nz-1))/(2*dy); |
| 150 |
bz(2:Nx-1,2:Ny-1,2:Nz-1)=-(meantheta(2:Nx-1,2:Ny-1,3:Nz)-meantheta(2:Nx-1,2:Ny-1,1:Nz-2))/(2*abs(dz)); |
| 151 |
|
| 152 |
zetax(2:Nx-1,2:Ny-1,2:Nz-1)=(meanv(2:Nx-1,2:Ny-1,3:Nz)-meanv(2:Nx-1,2:Ny-1,1:Nz-2))/(2*abs(dz)); |
| 153 |
zetay(2:Nx-1,2:Ny-1,2:Nz-1)=-(meanu(2:Nx-1,2:Ny-1,3:Nz)-meanu(2:Nx-1,2:Ny-1,1:Nz-2))/(2*abs(dz)); |
| 154 |
zetaz(2:Nx-1,2:Ny-1,2:Nz-1)=(meanv(3:Nx,2:Ny-1,2:Nz-1)/(2*dx)-meanv(1:Nx-2,2:Ny-1,2:Nz-1)/(2*dx) ... |
| 155 |
-meanu(2:Nx-1,3:Ny,2:Nz-1)/(2*dy)+meanu(2:Nx-1,1:Ny-2,2:Nz-1)/(2*dy) ... |
| 156 |
+ff(2:Nx-1,2:Ny-1,2:Nz-1)); |
| 157 |
|
| 158 |
|
| 159 |
sum=0; |
| 160 |
sumT=0; |
| 161 |
sumV=0; |
| 162 |
sumY=0; |
| 163 |
summ=0; |
| 164 |
sumd=0; |
| 165 |
for i=Nx1:Nx2 |
| 166 |
for j=Ny1:Ny2 |
| 167 |
|
| 168 |
if i==Nx1 |
| 169 |
a=0.5; |
| 170 |
elseif i==Nx2 |
| 171 |
a=0.5; |
| 172 |
else |
| 173 |
a=1; |
| 174 |
end |
| 175 |
|
| 176 |
if j==Ny1 |
| 177 |
b=0.5; |
| 178 |
elseif j==Ny2 |
| 179 |
b=0.5; |
| 180 |
else |
| 181 |
b=1; |
| 182 |
end |
| 183 |
|
| 184 |
|
| 185 |
summ=summ+a*b*(Mu(i,j,Nz1)*by(i,j,Nz1)-Mv(i,j,Nz1)*bx(i,j,Nz1))*dx*dy; |
| 186 |
summ=summ-a*b*(Mu(i,j,Nz2)*by(i,j,Nz2)-Mv(i,j,Nz2)*bx(i,j,Nz2))*dx*dy; |
| 187 |
sumd=sumd+a*b*zetaz(i,j,Nz1)*D(i,j,Nz1)*dx*dy; |
| 188 |
sumd=sumd-a*b*zetaz(i,j,Nz2)*D(i,j,Nz2)*dx*dy; |
| 189 |
sum=sum+a*b*meanw(i,j,Nz1)*pv(i,j,Nz1)*dx*dy; |
| 190 |
sumT=sum-a*b*meanw(i,j,Nz2)*pv(i,j,Nz2)*dx*dy; |
| 191 |
sumV=sumV+a*b*meanw(i,j,Nz1)*dx*dy; |
| 192 |
sumV=sumV-a*b*meanw(i,j,Nz2)*dx*dy; |
| 193 |
end |
| 194 |
end |
| 195 |
|
| 196 |
'xy' |
| 197 |
summ |
| 198 |
sumV |
| 199 |
sumd |
| 200 |
|
| 201 |
for j=Ny1:Ny2 |
| 202 |
for k=Nz1:Nz2 |
| 203 |
|
| 204 |
if k==Nz1 |
| 205 |
a=0.5; |
| 206 |
elseif k==Nz2 |
| 207 |
a=0.5; |
| 208 |
else |
| 209 |
a=1; |
| 210 |
end |
| 211 |
|
| 212 |
if j==Ny1 |
| 213 |
b=0.5; |
| 214 |
elseif j==Ny2 |
| 215 |
b=0.5; |
| 216 |
else |
| 217 |
b=1; |
| 218 |
end |
| 219 |
|
| 220 |
|
| 221 |
|
| 222 |
summ=summ+a*b*Mv(Nx2,j,k)*bz(Nx2,j,k)*dz*dy; |
| 223 |
summ=summ-a*b*Mv(Nx1,j,k)*bz(Nx1,j,k)*dz*dy; |
| 224 |
sumd=sumd+a*b*zetax(Nx2,j,k)*D(Nx2,j,k)*dz*dy; |
| 225 |
sumd=sumd-a*b*zetax(Nx1,j,k)*D(Nx1,j,k)*dz*dy; |
| 226 |
sumT=sumT+a*b*meanu(Nx2,j,k)*pv(Nx2,j,k)*dz*dy; |
| 227 |
sumT=sumT-a*b*meanu(Nx1,j,k)*pv(Nx1,j,k)*dz*dy; |
| 228 |
sumV=sumV+a*b*meanu(Nx2,j,k)*dz*dy; |
| 229 |
sumV=sumV-a*b*meanu(Nx1,j,k)*dz*dy; |
| 230 |
end |
| 231 |
end |
| 232 |
|
| 233 |
'xy+yz' |
| 234 |
summ |
| 235 |
sumd |
| 236 |
|
| 237 |
for i=Nx1:Nx2 |
| 238 |
for k=Nz1:Nz2 |
| 239 |
|
| 240 |
if k==Nz1 |
| 241 |
a=0.5; |
| 242 |
elseif k==Nz2 |
| 243 |
a=0.5; |
| 244 |
else |
| 245 |
a=1; |
| 246 |
end |
| 247 |
|
| 248 |
if i==Nx1 |
| 249 |
b=0.5; |
| 250 |
elseif i==Nx2 |
| 251 |
b=0.5; |
| 252 |
else |
| 253 |
b=1; |
| 254 |
end |
| 255 |
|
| 256 |
|
| 257 |
summ=summ-a*b*Mu(i,Ny2,k)*bz(i,Ny2,k)*dz*dx; |
| 258 |
summ=summ+a*b*Mu(i,Ny1,k)*bz(i,Ny1,k)*dz*dx; |
| 259 |
sumd=sumd+a*b*zetay(i,Ny2,k)*D(i,Ny2,k)*dz*dx; |
| 260 |
sumd=sumd-a*b*zetay(i,Ny1,k)*D(i,Ny1,k)*dz*dx; |
| 261 |
sumT=sumT+a*b*meanv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; |
| 262 |
sumY=sumY+a*b*meanv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; |
| 263 |
sumT=sumT-a*b*meanv(i,Ny1,k)*pv(i,Ny1,k)*dz*dx; |
| 264 |
sumV=sumV+a*b*meanv(i,Ny2,k)*dz*dx; |
| 265 |
sumV=sumV-a*b*meanv(i,Ny1,k)*dz*dx; |
| 266 |
end |
| 267 |
end |
| 268 |
'TOTAL' |
| 269 |
sum |
| 270 |
sumY |
| 271 |
sumT |
| 272 |
sumV |
| 273 |
summ |
| 274 |
sumd |
| 275 |
|
| 276 |
|
| 277 |
sum=0; |
| 278 |
for i=Nx1:Nx2 |
| 279 |
for j=Ny1:Ny2 |
| 280 |
|
| 281 |
if i==Nx1 |
| 282 |
a=0.5; |
| 283 |
elseif i==Nx2 |
| 284 |
a=0.5; |
| 285 |
else |
| 286 |
a=1; |
| 287 |
end |
| 288 |
|
| 289 |
if j==Ny1 |
| 290 |
b=0.5; |
| 291 |
elseif j==Ny2 |
| 292 |
b=0.5; |
| 293 |
else |
| 294 |
b=1; |
| 295 |
end |
| 296 |
|
| 297 |
sum=sum+a*b*sumD(i,j)*dx*dy; |
| 298 |
end |
| 299 |
end |
| 300 |
'DISSIPATION BY EDDY-DIFFUSIVITY' |
| 301 |
sum |
| 302 |
|
| 303 |
sum=0; |
| 304 |
for i=Nx1:Nx2 |
| 305 |
for j=Ny1:Ny2 |
| 306 |
|
| 307 |
if i==Nx1 |
| 308 |
a=0.5; |
| 309 |
elseif i==Nx2 |
| 310 |
a=0.5; |
| 311 |
else |
| 312 |
a=1; |
| 313 |
end |
| 314 |
|
| 315 |
if j==Ny1 |
| 316 |
b=0.5; |
| 317 |
elseif j==Ny2 |
| 318 |
b=0.5; |
| 319 |
else |
| 320 |
b=1; |
| 321 |
end |
| 322 |
|
| 323 |
sum=sum+a*b*sumM(i,j)*dx*dy; |
| 324 |
end |
| 325 |
end |
| 326 |
'DISSIPATION BY EDDY-VISCOSITY' |
| 327 |
sum |
| 328 |
|
| 329 |
'IMBALANCE' |
| 330 |
(sumT-(summ+sumd))/sumd |
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