| 1 | edhill | 1.1 | % PV diagnostics 'DIAG5' | 
| 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=4; | 
| 10 |  |  | Nx2=Nx-3; | 
| 11 |  |  | Ny1=4; | 
| 12 |  |  | Ny2=42; | 
| 13 |  |  | Nz1=5; | 
| 14 |  |  | Nz2=Nz-4; | 
| 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)*dz; | 
| 32 |  |  | sumD(3:Nx-2,3:Ny-2)=sumD(3:Nx-2,3:Ny-2)+Dp1(3:Nx-2,3:Ny-2,k)*dz; | 
| 33 |  |  | end | 
| 34 |  |  | sumW(3:Nx-2,3:Ny-2)=meanw(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)=-0.001*(i)*7; | 
| 62 |  |  | v1(i)=0.001*(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+meanw(i,j,Nz1)*pv(i,j,Nz1)*dx*dy; | 
| 119 |  |  | sumT=sum-meanw(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+meanu(Nx2,j,k)*pv(Nx2,j,k)*dz*dy; | 
| 126 |  |  | sumT=sumT-meanu(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+meanv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; | 
| 133 |  |  | sumY=sumY+meanv(i,Ny2,k)*pv(i,Ny2,k)*dz*dx; | 
| 134 |  |  | sumT=sumT-meanv(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 |