Coastal Upwelling Limitation by Onshore Geostrophic Flow in the Gulf of Guinea Around the Niger River Plume

Wind-driven coastal upwelling can be compensated by onshore geostrophic flow, and river plumes are associated with such flow. We investigate possible limitation of the northeast Gulf of Guinea upwelling by the Niger River plume, using regional ocean model simulations with or without river and dynamical upwelling indices. Here, the upwelling is weakened by 50% due to an onshore geostrophic flow equally controlled by alongshore thermosteric and halosteric sea-level changes. The river contributes to only 20% of this flow, as its plume is shallow while upwelling affects coastal temperature and salinity over a larger depth. Moreover, the river-induced mixed-layer thinning compensates the current increase, with no net effect on upwelling. The geostrophic compensation is due to an abrupt change in coastline orientation that creates the upwelling cross-shore front. The river nonetheless warms the upwelling tongue by 1°C, probably due to induced changes in horizontal advection and/or stratification.

Interdependence of Internal Tide and Lee Wave Generation at Abyssal Hills: Global Calculations

The generation of internal waves at abyssal hills has been proposed as an important source of bottom-intensified mixing and a sink of geostrophic momentum. Using the theory of Bell, previous authors have calculated either the generation of lee waves by geostrophic flow or the generation of the internal tide by the barotropic tide, but never both together. However, the Bell theory shows that the two are interdependent: that is, the presence of a barotropic tide modifies the generation of lee waves, and the presence of a geostrophic (time mean) flow modifies the generation of the internal tide. Here we extend the theory of Bell to incorporate multiple tidal constituents. Using this extended theory, we recalculate global wave fluxes of energy and momentum using the abyssal-hill spectra, model-derived abyssal ocean stratification and geostrophic flow estimates, and the TPX08 tidal velocities for the eight major constituents. The energy flux into lee waves is suppressed by 13%–19% as a result of the inclusion of tides. The generated wave flux is dominated by the principal lunar semidiurnal tide (M2), and its harmonics and combinations, with the strongest fluxes occurring along midocean ridges. The internal tide generation is strongly asymmetric because of Doppler shifting by the geostrophic abyssal flow, with 55%–63% of the wave energy flux (and stress) directed upstream, against the geostrophic flow. As a consequence, there is a net wave stress associated with generation of the internal tide that reaches magnitudes of 0.01–0.1 N m−2 in the vicinity of midocean ridges.

The evolution of a front in turbulent thermal wind balance. Part 2. Numerical simulations

In Crowe & Taylor (J. Fluid Mech., vol. 850, 2018, pp. 179–211) we described a theory for the evolution of density fronts in a rotating reference frame subject to strong vertical mixing using an asymptotic expansion in small Rossby number, $Ro$. We found that the front reaches a balanced state where vertical diffusion is balanced by horizontal advection in the buoyancy equation. The depth-averaged buoyancy obeys a nonlinear diffusion equation which admits a similarity solution corresponding to horizontal spreading of the front. Here we use numerical simulations of the full momentum and buoyancy equations to investigate this problem for a wide range of Rossby and Ekman numbers. We examine the accuracy of our asymptotic solution and find that many aspects of the solution are valid for $Ro=O(1)$. However, the asymptotic solution departs from the numerical simulations for small Ekman numbers where the dominant balance in the momentum equation changes. We trace the source of this discrepancy to a depth-independent geostrophic flow that develops on both sides of the front and we develop a modification to the theory described in Crowe & Taylor (2018) to account for this geostrophic flow. The refined theory closely matches the numerical simulations, even for $Ro=O(1)$. Finally, we develop a new scaling for the intense vertical velocity that can develop in thin bands at the edges of the front.

Determination of the instantaneous geostrophic flow within the three-dimensional magnetostrophic regime

In his seminal work, Taylor (1963 Proc. R. Soc. Lond. A 274 , 274–283. ( doi:10.1098/rspa.1963.0130 ).) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second-order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalization of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any three-dimensional Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully three-dimensional case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.

Taylor state dynamos found by optimal control: axisymmetric examples

Earth’s magnetic field is generated in its fluid metallic core through motional induction in a process termed the geodynamo. Fluid flow is heavily influenced by a combination of rapid rotation (Coriolis forces), Lorentz forces (from the interaction of electrical currents and magnetic fields) and buoyancy; it is believed that the inertial force and the viscous force are negligible. Direct approaches to this regime are far beyond the reach of modern high-performance computing power, hence an alternative ‘reduced’ approach may be beneficial. Taylor (Proc. R. Soc. Lond. A, vol. 274 (1357), 1963, pp. 274–283) studied an inertia-free and viscosity-free model as an asymptotic limit of such a rapidly rotating system. In this theoretical limit, the velocity and the magnetic field organize themselves in a special manner, such that the Lorentz torque acting on every geostrophic cylinder is zero, a property referred to as Taylor’s constraint. Moreover, the flow is instantaneously and uniquely determined by the buoyancy and the magnetic field. In order to find solutions to this mathematical system of equations in a full sphere, we use methods of optimal control to ensure that the required conditions on the geostrophic cylinders are satisfied at all times, through a conventional time-stepping procedure that implements the constraints at the end of each time step. A derivative-based approach is used to discover the correct geostrophic flow required so that the constraints are always satisfied. We report a new quantity, termed the Taylicity, that measures the adherence to Taylor’s constraint by analysing squared Lorentz torques, normalized by the squared energy in the magnetic field, over the entire core. Neglecting buoyancy, we solve the equations in a full sphere and seek axisymmetric solutions to the equations; we invoke $\unicode[STIX]{x1D6FC}$- and $\unicode[STIX]{x1D714}$-effects in order to sidestep Cowling’s anti-dynamo theorem so that the dynamo system possesses non-trivial solutions. Our methodology draws heavily on the use of fully spectral expansions for all divergenceless vector fields. We employ five special Galerkin polynomial bases in radius such that the boundary conditions are honoured by each member of the basis set, whilst satisfying an orthogonality relation defined in terms of energies. We demonstrate via numerous examples that there are stable solutions to the equations that possess a rapidly decreasing spectrum and are thus well-converged. Classic distributions for the $\unicode[STIX]{x1D6FC}$- and $\unicode[STIX]{x1D714}$-effects are invoked, as well as new distributions. One such new $\unicode[STIX]{x1D6FC}$-effect model possesses oscillatory solutions for the magnetic field, rarely before seen. By comparing our Taylor state model with one that allows torsional oscillations to develop and decay, we show the equilibrium state of both configurations to be coincident. In all our models, the geostrophic flow dominates the ageostrophic flow. Our work corroborates some results previously reported by Wu & Roberts (Geophys. Astrophys. Fluid Dyn., vol. 109 (1), 2015, pp. 84–110), as well as presenting new results; it sets the stage for a three-dimensional implementation where the system is driven by, for example, thermal convection.