Flow Decomposition by Optimal Balance With Time‐Averaging

Abstract Decomposing oceanic and atmospheric flow fields into their slowly evolving balanced components and fast evolving wave components is essential to study processes like spontaneous or stimulated wave emission. However, a decomposition into the linear geostrophic (slow) and non‐geostrophic (fast) components is often not precise enough to address the nonlinearity in the flow. Optimal balance (OB) and nonlinear normal mode decomposition account for nonlinear effects and thus are more precise, but their application has so far been limited to idealized model configurations that exclude lateral boundaries, varying stratification, a varying Coriolis parameter, or other changing flow parameters. Here we present a modified OB method that overcomes these limitations and is applicable to more complex model setups. The modification employs a time‐averaging procedure to project onto the linear geostrophic component, eliminating the need for a Fourier transformation as required in the original OB method. We demonstrate analytically and experimentally that the new method converges to the original method, when either the time‐averaging period or the number of OB iterations increases. We test the new method using a two‐dimensional single‐layer model and a three‐dimensional non‐hydrostatic model with varying initial conditions and Rossby numbers ranging from 0.05 to 0.5. In all tested configurations, the differences between balanced states obtained from the new method and those from the original method become exponentially small, indicating similar accuracy. We further show that the new method can indeed now be applied to complex models with lateral boundaries and varying background stratification to diagnose wave emission.