Hello, I am working on a solo project outside my domain of expertise (Physics PhD student). I am trying to analyze/replicate the wave phenomena shown in the following video: To summarize what I am doing: I need to analyze a simple (cylindrical) pool, say 17.5" wide, 4" deep Figure out how to periodically force over a finite region Find the expression for surface height η Find the expression for wavelength λ Determine the decay time of the wave (not sure the expression for half-life τ=ln(2)/λ works here) Scale up to larger dimensions and repeat Fluid flow problems have so many approximations and domains of validity that I am not quite sure where to start. After exhaustive searches, I have concluded that Airy Wave Theory is likely my best starting point. I looked through slosh dynamics books and found some expressions for η in cylindrical and conical (what I need to analyze once I have figured out the cylindrical case) containers. I will need to use the appropriate initial and boundary conditions to get the constants correct, but that is another story. The most important parts of my analysis include what happens when I scale up the dimensions, how does that affect the decay time, and what is the best way to produce this phenomenon. Since my primary interest is for shallow and wide pools, I am assuming that scaling up the calculations should be rather trivial as long as λ >> h. However, I do not have an expression for λ. I have only observed the "nodal circles" to be near (but not at) the boundaries. I can't be sure until I have an expression. I believe that I found the appropriate dispersion relation. If these waves are resonant capillary-gravity waves then I should have something like: ω2 = |k|(ρwater + ρair)-1[(ρwater-ρair)g + σk2], where ω is the frequency, k is the wavenumber, ρ are the densities, g is gravitational acceleration, and σ is the surface tension. This comes from Airy wave theory. For a cylindrical geometry, I have something like η(r,θ,t) = (1/g) Σm∑n αmncos(mθ)Jm(λmnr)cosh(λmnh)[ωmncos(ωmnt)], where αmn is TBD, Jm is a Bessel function of 1st kind (order m), h is the water depth, m=(0,...,inf), and n=(1,...,inf). Furthermore, since we appear to be generating a fundamental mode, I think I can take m = 0. Hopefully, this much is correct. The next and most formidable part is how to add the forcing over a finite region of the surface (like over a circle of radius R). The problem seems simple at first, but turns out to be quite difficult. I spoke with a mathematician who specializes in fluid flow and he said "that's hard". He recommended incorporating it into the pressure, but I am having a hard time figuring out how to make that happen. The only idea I have is to partition the pool into regions (one with gravity, and one with gravity plus the forcing) and use derivatives to stitch them together, as I have done in certain problems in Quantum Mechanics. The slosh dynamics books and papers focused on moving the container itself, not moving the fluid with the container fixed. I assume that moving to the coordinate system of the container would be similar, but I'm not sure you can simply discard the inertial terms. I guess I am asking if I am on the right track and if there are any simple ways to incorporate the forcing. I tried doing stuff computationally and quickly realized it was over my head. Then, I tried to use ELMER to do some work for me, but it quickly got too technical. Any help is welcome.