rot[x_, y_]=Curl[{Cos[x + y^3],Sin[y + x^3]},{x,y}];

StreamDensityPlot[{{Cos[x+y^3],Sin[y+x^3]},Log[Abs[rot[x,y]]+1]},{x,-2,2},{y,-2,2},StreamPoints->Fine,ColorFunction->"RedBlueTones",MaxRecursion->4,LightingAngle->Automatic,StreamStyle->Black]