Simple analytic models developed in this study are applied to long-term averages of reanalysis surface salinity data to quantify two fundamental properties of ocean currents. The first model is based on the new Freshening Length schema and its application to the Irminger Current yields a ratio of about 5 between the turbulent entrainment rates of surrounding fresher surface waters west and east of Greenland. The second model is based on the steady solution of the advection-diffusion equation subject to suitable boundary conditions. The application of this model to the spreading of fresh, snow-melt, water from the delta of the Po river in the northwest Adriatic Sea into the rest of the Sea yields a ratio of $8 \times 10^4$ m between the eddy exchange coefficient and the speed of advection in the Sea

An intermediate complexity moist General Circulation Model is used to investigate the sensitivity of the Quasi-Biennial Oscillation (QBO) to resolution, diffusion, tropical tropospheric waves, and parameterized gravity waves. Finer horizontal resolution is shown to lead to a shorter period, while finer vertical resolution is shown to lead to a slower period and to an accelerated amplitude in the lowermost stratosphere. More scale-selective diffusion leads to a faster and stronger QBO, while enhancing the sources of tropospheric stationary wave activity leads to a weaker QBO. In terms of parameterized gravity waves, broadening the spectral width of the source function leads to a longer period and a stronger amplitude although the amplitude effect saturates when the half-width exceeds $\sim25$m/s. A stronger gravity wave source stress leads to a faster and stronger QBO, and a higher gravity wave launch level leads to a stronger QBO. All of these sensitivities are shown to result from their impact on the resultant wave-driven momentum torque in the tropical stratosphere. Atmospheric models have struggled to accurately represent the QBO, particularly at moderate resolutions ideal for long climate integrations. In particular, capturing the amplitude and penetration of QBO anomalies into the lower stratosphere (which has been shown to be critical for the tropospheric impacts) has proven a challenge. The results provide a recipe to generate and/or improve the simulation of the QBO in an atmospheric model.

The two seminal studies on westward intensification, carried out by Stommel and Munk over 70 years ago, are revisited to elucidate the role of the domain aspect ratio (i.e.~meridional to zonal extents of the basin) in determining the width and speed of a western boundary current (WBC). We examine the general mathematical properties of the two models by transforming them to differential problems that contain only two parameters — the domain aspect ratio and the non-dimensional damping (viscous) coefficient. Simple proxies of width and speed (and hence the transport that equals their product) of the WBC are derived from analytical solutions of the non-dimensional vorticity equations in the relevant region of the (damping, aspect ratio) parameter space. These analytically determined proxies are then benchmarked against numerical simulations of the corresponding time-dependent equations. In both models, the three proxies vary as a power law in the domain aspect ratio and in particular, the non-dimensional transport varies linearly with the domain aspect ratio.

The angle between the wind stress that overlies the ocean and the resulting current at the ocean surface is calculated for a two-layer ocean with uniform eddy viscosity in the lower layer and for several assumed eddy viscosity profiles in the upper layer. The calculation of the deflection angle is greatly simplified by transforming the linear, second order, vertical structure equation to its associated nonlinear, first order, Riccati equation. Though the transformation to a Riccati equation can be used as an alternate numerical scheme, its main advantage is that it yields analytic expressions for particular eddy viscosity profiles.