A numerical forecast of fluid motion in a rotating tank and a study of how finite-difference approximations affect non-linear interactions

Abstract

Using observational data of the fluid motion in a laboratory experiment with a rotating tank numerical forecasts with three different models were made. The Ekman friction was taken into account. The forecasts were verified statistically and the results for the different models were compared.

An investigation of the effect of observational errors was made and it was found that errors in the initial field do not affect the prediction severely.

The spectral distribution of kinetic energy in the forecast data and the verification data were compared. Systematic differences between observed and forecast distributions stimulated a study of the effect of finite differences on non-linear interactions. A theoretical discussion shows that when finite differences are applied to the nonlinear vorticity equation a leakage of energy from the long waves to the shortest ones occurs.

To test this conclusion a numerical forecast was made with three different grid intervals, as well as a forecast of the Fourier components of the field of motion.

Finally, it is discussed how the fictitious flow of energy may give rise to the special kind of computational instability that Phillips has investigated.