To make splashing water, you should use particle based fluid. Particle based fluid uses a field of particles to produce splash-like liquid that can move anywhere in a scene. On the other hand, volume based fluid uses a sign distance volume which creates a glue-like liquid that is confined to a container.
Make a drop of water splash
Make splashing water in a river
Model a river bed for the water to flow, and turn it into a Terrain Object.
Make sure your terrain is slightly sloped to allow the particles to flow in one direction.
Create a grid that intersects the riverbed and is slightly below the riverbank. The area between this and the riverbank will be converted into particle fluid.
Model objects (such as rocks) that protrude from the river bed, and turn them into static objects.
Modeling the grid with high and low points will not create waves, as the particle fluid is affected by gravity and will sink down when the simulation is run. To create waves use the Waveform tool on the Deform shelf tab to create waves.
Use the Sculpted Particle Fluid tool on the Particle Fluids shelf tab to convert the area between your grid and riverbank to particle fluid.
This step is complex, since you will have to first select the fluid surface object, then the terrain object, and finally any obstacles embedded in the river. If there is more than one obstacle you can hold ⇧ Shift to select multiple objects. For more information, see the Sculpted Particle Fluid help.
Use the Whitecaps tool on the Particle Fluids shelf tab to make even more splashes, as particles are emitted when the sharpness of the wave crest reaches a certain threshold.
The Sculpted Particle Fluid tool calculates the volume of the space between the grid and river bed to create particle fluid; however, it does not continuously emit particle fluid. To create a constant flow of particles, use the Emit Particle Fluid tool and place it at the top of the river. You can also place a Sink Particle Fluid at the foot of the river to drain the water.