1: Create a comp of appropriate size and duration and call it FXSubject.

In this comp, create your title. It doesn't have to be a title; it can be any small visual element that you wish to draw attention to. Make the comp large enough to include the potential size of the flowing elements.

I usually add an adjustment layer and apply a ramp with just one color to discard color information of the artwork in the layer to just keep old alpha and new solid color.

2: Create a new comp the same size and duration as FXSubject and call it FXMatte. This will be an intermediate image, used to locate the effect action over the initial image.

Add a new solid the size of the comp. Create an oval mask of a size that will cover your artwork. Choose the add setting for the mask. Feather the mask. (Mine is 150 pixels horizontal and 50 pixels vertical --experiment to see what works best for you.)

Add Effect>Cult Effects>CE Noise Turbulent. Animate the Evolution. Start with -1x and end with +2x. Experiment with the timing here, You can also duplicate this layer and offset the second layer to increase the "flowiness."

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3: Create a new comp, 500 X 200. Add a new solid, size of the comp,
50% gray.

This gray layer is needed for the Displacement Map, because gray value means zero displacement.

Add the comp FXMatte to the timeline. It should be above the gray layer.

FXDisplacement includes FXMatte as a layer. It is different from FXMatte only in that it is includes a 50%-gray layer as a background.

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3: Create a full size comp. (Mine is 768 X 576, 25 fps and 10 seconds long.)

Add the FXMatte comp. Create a new adjustment layer.

Call this layer Luminosity Bounce.

Apply Effect>Adjust> Curves to this layer with these settings: black color turns to white, gray color turns to black, white color to white. The RBG curve should look like upturned triangle. (see below) This is done to avoid blurring undistorted areas.

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4: Create the final comp, the same size and duration as FXBlur.Add, in this order, FXBlur, FXDisplacement and FXSubject. Turn off the visibility for both the FXDisplacement and FXBlur layers.

To the FXSubject layer:

Apply >Effect >Blur&Sharpen >Compound Blur. Set the Blur layer to FXBlur. Maximum blur = 200. Check the box "stretch map to fit."

Apply> Effect> Distort> Displacement Map Effects. To the Displacement Map, specify the FXDisplacement layer as the map layer. Tune the controls of the displacement map to achieve the effect you need.

Animate the opacity value for the FXSubject layer if necessary.

Also, you may wish to animate the opacity value of the spots in FXMatte layer.
Use the Levels and Glow or whatever you want to control final image of the flow. With these two, you can colour your flow look like fire, smoke or something unreal. You can also add additional graphic elements to create further interesting effects.

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