Show the divergence as a background density

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

StreamDensityPlot[{{Cos[x + y ^ 3], Sin[y + x ^ 3]}, div[x, y]}, {x, -2, 2}, {y, 0, 2}, StreamPoints -> Fine, ColorFunction -> "MintColors", MaxRecursion -> 2, StreamStyle -> Black, StreamColorFunction -> None]

-Graphics-