Curl on surface of unit sphere

1 次查看（过去 30 天）

Jon 2018-6-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/408148-curl-on-surface-of-unit-sphere

I have vectors of longitude and latitude on an approximately uniform grid (actually uniform is impossible) on the surface of a unit circle. This grid does not cover the whole sphere. At each point of this grid I have a local azimuth angle for a vector tangent to the sphere (as defined by the mapping toolbox function "distance") and a magnitude of a value measured in this direction. How would I got about calculating the curl at each grid point?

So that's a somewhat irregular vector of two spherical coordinate angles, a vector of azimuth tangent to the sphere at each coordinate, and the magnitude, and I want to calculate the curl at each coordinate.

When I try to do this approximately by just doing it locally and treating the problem in a flat plane the curl function says U,V must all be size 2x2 or greater. That's trying

if true
  [angle,az] = distance(lat1,long1,all_lat,all_long); 
  x = angle.*cos(az); 
  y = angle.*sin(az); 
  u = mag.*cos(az2); %thats the local azimuth of the sphere tangent 
  v = mag.*sin(az2);
  [curlz,cav]= curl(x,y,u,v);
end