Optimal Ratio of Lamé Moduli with Application to Motion of Jupiter Storms
Fluid dynamics models the distribution of sources, sinks and vortices in imaged motion. A variety of different flow types can be obtained by specifying a key quantity known as the ratio of the Lamé moduli λ/μ. Special cases include the weakly elliptic flow λ/μ→ –2, often utilized in the Monge-Ampère transport, the Laplacian diffusion model λ/μ =–1, and the hyper-elliptic flow λ/μ → ∞ of the Stokesian dynamics. Bayesian Gaussian process generalization of the fluid displacement estimation indicates that in the absence of the specific knowledge about the ratio of the Lamé moduli, it is better to temporally balance between the rotational and divergent motion. At each time instant the Lamé moduli should minimize the difference between the fluid displacement increment and the negative gradient of the image mismatch measure while keeping the flow as incompressible as possible. An experiment presented in this paper with the interpolation of the photographed motion of Jupiter storms supports the result.