I am wondering how I can create a splash as in the attached image. I have tried an emitter along a path, an emitter with curve force and a combination of the two. I get results that are too wild and complex. Is there an easier way? Thanks.

I don't think there's an easy way. Look at the point - you have an artistic drawing in your picture. A Houdini simulation is an attempt to simulate real physical processes to achieve behavior close to that of physical reality. There's no such thing as "beautiful" or "artistic." So if you want to use a simulation to achieve that beautiful drawing, you need to ask yourself what physical forces could have caused the fluid to bend like that. Then, model these forces using Houdini. If you've guessed correctly and modeled correctly, perhaps these forces will direct the fluid in the right direction. This is highly unlikely. And you're unlikely to want to solve such a complex physics problem; you just want an image, not a true match to physics. So, choosing a simulation to create an image seems like a bad idea to me.
I think this is a modeling task, and you need to find tricks there. Simulation can be used to create some basic shapes, if that's easier than doing it manually, or to calculate some data for further procedural processing.
For example, someone created a velocity vector field and made particles move along predetermined paths.
Or you can easily create a wall of the desired rounded shape and then inject liquid into it to create both the shape and splashes along the edges. Or you can create a beautiful main shape separately, then separate splashes, and then attach the splashes. Well, that's for a static image. But if you need animation, things get more complicated.
I also thought—if you're so keen to play with the simulation, there's definitely an invisible collider involved. For example, a sphere containing a viscous fluid moves around a larger sphere. Liyu creates a flow, and when you push it with the larger sphere, the flow bends and flies apart at the edges. I hope you get the idea.