On the numerical dependence of balance state in geophysical flows

Balance flows dictate the evolution and dynamics of geophysical flows, such as the atmosphere and ocean, that are central to the Earth's climate. Here, balance geophysical flows are balanced using two different methods and compared in simulations of the single-layer shallow water model with two different numerical model codes and two different initial conditions over a range of different parameters. Both methods: nonlinear higher order balancing and optimal balance, add to the linear geostrophic mode, the linear wave mode contributions. The resulting approximately balanced states are characterized by very small residual wave emission during time evolution of the flow. Overall, the performance of both methods is comparable. Cross-balancing suggests that both methods find approximately the same balanced states. The results contradict previous studies claiming significant spontaneous wave emission from balanced flow. Further, the results clearly show that the notion of balance in numerical models of geophysical flows is ultimately related to the particular discretization.