A synthetic Schlieren method for laboratory measuring density profiles of a stratified fluid

A synthetic Schlieren method is developed to measure the density field of a stratified fluid. A transparent sheet of background markers is attached on one side of a tank which is made of acrylic plates, and a camera is positioned on the opposite side of the tank. The markers are virtually displaced due to light refraction in the stratified fluid in the tank, in reference to those from the water tank. The governing equation is derived based on the observation that the marker displacements depend on the light refraction at the interface of media, the refractive indices of the transparent liquids and their spatial gradient. The density of the fluid is associated with the refractive index via the relationship obtained in a calibration process. We solve this governing equation, an over-determined system with only the target variable unknown, using the optimization method. We examine the present method by performing laboratory experiments for two cases of the density stratification, i.e., a linear stratification and a pycnocline. We also carry out ray tracing simulations of three characteristic density profiles (i.e., a linear stratification, a nonlinear stratification and a pycnocline). The present method is compared with the method of solving the Poisson equation in detail, emphasizing the difference between the two methods. Measurement uncertainty is discussed at last.