To study a limit of validity of balanced models, stability of a zonal jet is investigated both linearly and nonlinearly in an f-plane shallow water system for a wide range of parameter. It is shown that quasi-geostrophic approximation gives not only a good estimation of maximum growth rate for high Rossby number, Ro, but also is valid even in the nonlinear phase of instability for high Ro as long as Froude number, Fr, is low. While the maximum growth rate of unstable modes is well estimated by the quasi-geostrophic approximation, dominant balance is different between high and low Ro. In the low Ro regime (Ro < 5), geostrophic balance is dominant in the perturbation field, the ratio ||ϕ||/||ψ|| of the amplitudes of divergent flow to that of rotational flow is proportional to Fr2/Ro, where ϕ and ψ are velocity potential and streamfunction, respectively. On the other hand, in the high Ro regime (Ro > 5), cyclostrophic balance with basic shear is dominant, ||ϕ||/||ψ||∝Fr2. Considering that the barotropic instability is caused by the resonance of neutral Rossby wave modes, we can explain the difference of the ratio in each regime. Using the ratio ||ϕ||/||ψ|| being small, different approximation of the linear shallow water equations for each regime is deduced. Properties of the linear unstable modes are explained with these approximations.
We propose the use of a high-speed spherical self-organizing map (HSS-SOM) to visualize climate variability as a complementary alternative to empirical orthogonal function (EOF) analysis. EOF analysis, which is the same as principal component analysis, is often used in the fields of meteorology and climatology to extract leading climate variability patterns, its production of linear mapping with only a low contribution rate may preclude producing any meaningful results. Due to computational limitations, however, conventional self-organizing maps are difficult to apply to huge climate datasets. The development of HSS-SOMs with dynamically growing neurons has helped reduce computational time. After demonstrating validity of our HSS-SOM using observational climate data and HSS-SOM effectiveness as a complementary alternative to the EOF, we extract dominant atmospheric circulation patterns from huge amounts of climate data in the general circulation model, in which both present climatology and future climate are simulated. These patterns correspond to those obtained in previous studies, indicating the HSS-SOM's usefulness in climate research.
Abstract Spontaneous generation of inertia‐gravity waves from balanced flows is investigated in idealized simulations of dipoles. Long integrations are performed for dipoles with different Rossby numbers ( Ro ) to identify the backreaction of the waves. Emission of waves is detected only for large enough Ro (>0.15), and it then leads to a slow decay of the dipole's kinetic energy. A major finding is that this decay is well captured by the simulations, although positions of the waves appear still sensitive to the resolution, and their maximum vertical velocity increases linearly with resolution. The interpretation is that the emission process is well resolved and fairly insensitive to resolution, while the propagation and dissipation at small scales remains sensitive to resolution. The implication is that the simulations yield an estimate of the leakage of energy from balanced motions to gravity waves, providing a useful estimate of a poorly constrained flux in the ocean's energy budget.
