GraphicsGrid[{{StreamDensityPlot[{y, -x}, {x, -2, 2}, {y, -2, 2}, 

    RegionFunction -> Function[{x, y}, 0.55 < x^2 + y^2 < 4.2], 

    ColorFunction -> "RedBlueTones", Frame -> False, 

    StreamScale -> Medium, ImageSize -> Medium, 

    LightingAngle -> Automatic, BoundaryStyle -> {Black, Thick}], 

   StreamDensityPlot[{Cos[x^2 + y], 1 + x - y^2}, {x, -3, 3}, {y, -3, 

     3}, ColorFunction -> "BeachColors", 

    StreamColorFunction -> "DeepSeaColors", StreamStyle -> Black, 

    StreamScale -> {Automatic, Automatic, Scaled[0.8]}, 

    Frame -> False, LightingAngle -> Automatic, 

    RegionFunction -> Function[(#1 + 3) >= 0.45 #2^2], 

    BoundaryStyle -> {Blue, Thick}]}, {VectorDensityPlot[{Cos[y] - 

      Sin[x]^3, -.1 y - Sin[x]}, {x, -4, 4}, {y, -4, 4}, 

    Frame -> False, VectorScale -> {0.05, Automatic, None}, 

    VectorPoints -> 25, AspectRatio -> Automatic, 

    ColorFunction -> "IslandColors", 

    VectorColorFunction -> "RedBlueTones", 

    BoundaryStyle -> {Red, Thick}, 

    RegionFunction -> Function[#2 + #1 + 0.3 >= Sin[#1]]],

   VectorDensityPlot[{Cos[x + y^3], Sin[y + x^3]}, {x, -3, 3}, {y, -3,

      3}, Frame -> False, ColorFunction -> "TemperatureMap", 

    VectorScale -> {Automatic, Automatic, Automatic}, 

    RegionFunction -> Function[#1^2 + #2^2 <= 9], 

    BoundaryStyle -> Thick, MaxRecursion -> 2, 

    VectorColorFunction -> "RoseColors", VectorPoints -> Fine]}}]