Balance in non-hydrostatic rotating shallow-water flows

DATA AVAILABILITY: The data that support the findings of this study are available from the corresponding author upon reasonable request.Unsteady nonlinear shallow-water flows typically emit inertia-gravity waves through a process called “spontaneous adjustment-emission.” This process has been studied extensively within the rotating shallow-water model, the simplest geophysical model having the required capability. Here, we consider what happens when the hydrostatic assumption underpinning the shallow-water model is dropped. This assumption is in fact not necessary for the derivation of a two-dimensional or single-layer flow model. All one needs is that the horizontal flow field be independent of height in the fluid layer. Then, vertical averaging yields a single-layer flow model with the full range of expected conservation laws, similar to the shallow-water model yet allowing for non-hydrostatic effects. These effects become important for horizontal scales comparable to or less than the depth of the fluid layer. In a rotating flow, such scales may be activated if the Rossby deformation length (the ratio of the characteristic gravity-wave speed to the Coriolis frequency) is comparable to the depth of the fluid layer. Then, the range of frequencies supporting inertia-gravity waves is compressed, and the group velocity of these waves is reduced. We find that this change in wave properties has the effect of strongly suppressing spontaneous adjustment-emission and trapping inertia-gravity waves near regions of relatively strong circulation

Comparison of the Moist Parcel‐in‐Cell (MPIC) model with Large‐Eddy Simulation for an idealised cloud

The ascent of a moist thermal is used to test a recently developed essentially Lagrangian model for simulating moist convection. In this Moist‐Parcel‐In‐Cell (MPIC) model, a number of parcels are used to represent the flow in each grid cell. This has the advantage that the parcels provide an efficient and explicit representation of subgrid scale flow. The model is compared against Eulerian Large‐Eddy Simulations with a version of the Met Office NERC Cloud model (MONC) that solves the same equations in a more traditional Eulerian scheme. Both models perform the same idealised simulation of the effects of latent heat release and evaporation, rather than a specific atmospheric regime. Dynamical features evolve similarly throughout the development of the thermal using both approaches. Subgrid scale properties of small‐scale eddies captured by the MPIC model can be explicitly reconstructed on a finer grid. MPIC simulations thus resolve smaller features when using the same grid spacing as MONC, which is useful for detailed studies of turbulence in clouds. The convergence of bulk properties is also used to compare the two models. Most of these properties converge rapidly, though the probability distribution function of liquid water converges only slowly with grid resolution in MPIC. This may imply that the current implementation of the parcel mixing mechanism underestimates small‐scale mixing. Finally, it is shown how Lagrangian parcels can be used to study the origin of cloud air in a consistent manner in MPIC

Self-sharpening induces jet-like structure in seafloor gravity currents

Gravity currents are the primary means by which sediments, solutes and heat are transported across the ocean-floor. Existing theory of gravity current flow employs a statistically-stable model of turbulent diffusion that has been extant since the 1960s. Here we present the first set of detailed spatial data from a gravity current over a rough seafloor that demonstrate that this existing paradigm is not universal. Specifically, in contrast to predictions from turbulent diffusion theory, self-sharpened velocity and concentration profiles and a stable barrier to mixing are observed. Our new observations are explained by statistically-unstable mixing and self-sharpening, by boundary-induced internal gravity waves; as predicted by recent advances in fluid dynamics. Self-sharpening helps explain phenomena such as ultra-long runout of gravity currents and restricted growth of bedforms, and highlights increased geohazard risk to marine infrastructure. These processes likely have broader application, for example to wave-turbulence interaction, and mixing processes in environmental flows

Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number

In this paper we examine the role of weak magnetic fields in breaking Kelvin’s circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a fluid with low magnetic Prandtl number (low  $Pm$ ). We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation \unicode[STIX]{x1D6E4} and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex, the loss of circulation depends on the total area swept out by the rotating vortex, and so this leads to more efficient circulation loss than for a circular vortex