ALBERT

Description: Ongoing and future space missions aim to identify potentially habitable planets in our Solar System and beyond. Planetary habitability is determined not only by a planet's current stellar insolation and atmospheric properties, but also by the evolutionary history of its climate. It has been suggested that icy planets and moons become habitable after their initial ice shield melts as their host stars brighten. Here we show from global climate model simulations that a habitable state is not achieved in the climatic evolution of those icy planets and moons that possess an inactive carbonate-silicate cycle and low concentrations of greenhouse gases. Examples for such planetary bodies are the icy moons Europa and Enceladus, and certain icy exoplanets orbiting G and F stars. We find that the stellar fluxes that are required to overcome a planet's initial snowball state are so large that they lead to significant water loss and preclude a habitable planet. Specifically, they exceed the moist greenhouse limit, at which water vapour accumulates at high altitudes where it can readily escape, or the runaway greenhouse limit, at which the strength of the greenhouse increases until the oceans boil away. We suggest that some icy planetary bodies may transit directly to a moist or runaway greenhouse without passing through a habitable Earth-like state.

Description: Models of the glacial isostatic adjustment process, which is dominated by the influence of the Late Pleistocene cycle of glaciation and deglaciation, depend on two fundamental inputs: a history of ice-sheet loading and a model of the radial variation of mantle viscosity. These models may be tested and refined by comparing their local predictions of relative sea level history to geological inferences based upon appropriate sea level indicators. The U.S. Atlantic coast is a region of particular interest in this regard, due to the fact that data from the length of this coast provides a transect of the forebulge associated with the former Laurentide ice sheet. High-quality relative sea level histories from this region are employed herein to explore the ability of current models of mantle viscosity to explain the inferred evolution of relative sea level that have accompanied forebulge collapse following deglaciation. Existing misfits are characterized, and alternatives are explored for their reconciliation. It is demonstrated that a new model of mantle viscosity, referred to herein as VM6, when coupled with the latest model of deglaciation history ICE-6G_C, is able to eliminate the majority of these misfits, while continuing to reconcile a wide range of other important geophysical observables, as well as additional relative sea level data from the North American. West coast which also record the collapse of the forebulge but which have not been employed in tuning the viscosity profile to enable ICE-6G_C (VM6) to fit the East coast data set.

Description: Models of the glacial isostatic adjustment process, which is dominated by the influence of the Late Pleistocene cycle of glaciation and deglaciation, depend on two fundamental inputs: a history of ice-sheet loading and a model of the radial variation of mantle viscosity. These models may be tested and refined by comparing their local predictions of relative sea level history to geological inferences based upon appropriate sea level indicators. The U.S. Atlantic coast is a region of particular interest in this regard, due to the fact that data from the length of this coast provides a transect of the forebulge associated with the former Laurentide ice sheet. High-quality relative sea level histories from this region are employed herein to explore the ability of current models of mantle viscosity to explain the inferred evolution of relative sea level that have accompanied forebulge collapse following deglaciation. Existing misfits are characterized, and alternatives are explored for their reconciliation. It is demonstrated that a new model of mantle viscosity, referred to herein as VM6, when coupled with the latest model of deglaciation history ICE-6G_C, is able to eliminate the majority of these misfits, while continuing to reconcile a wide range of other important geophysical observables, as well as additional relative sea level data from the North American. West coast which also record the collapse of the forebulge but which have not been employed in tuning the viscosity profile to enable ICE-6G_C (VM6) to fit the East coast data set.

Description: Reconstructions of historical climate changes indicate that surface air temperatures decreased over the preindustrial last millennium. Conflicting explanations have been proposed for the cause of the transition from the Medieval Climate Anomaly (MCA) in the early part of the last millennium to the Little Ice Age (LIA) near its end. The possible causes include volcanic emissions, total solar irradiance (TSI) variations, greenhouse gas concentration fluctuations, and orbital forcing variations. In the present paper, it is demonstrated that all of these climate forcings contribute significantly to simulated surface air temperature (SAT) and sea ice concentration changes over this period. On the other hand, simulated ocean heat content appears to respond significantly only to volcanic and TSI variations. In model simulations at T85 spectral resolution, TSI reductions and volcanic emissions together generate significant increases in sea ice extent in the Barents Sea, which is found to be responsible for most of the temperature reductions over northwestern Europe. TSI appears less important to Arctic sea ice and SAT changes in simulations at T42 spectral resolution, which are weaker than at T85 resolution. Such resolution dependence is attributed to differences in background conditions in the responses to these external climate forcings. Nonlinearities in the forcing responses and sensitivities to background conditions challenge the assumption that sensitivity tests for given forcings can be run independently. Additionally, it is demonstrated that an ensemble of model simulations is required to isolate forcing responses even over a period as long as the last millennium.

Description: In order that it be correctly characterized, irreversible turbulent mixing in stratified fluids must distinguish between adiabatic 'stirring' and diabatic 'mixing'. Such a distinction has been formalized through the definition of a diapycnal diffusivity, Kρ (Winters & D'Asaro, J. Fluid Mech., vol. 317, 1996, pp. 179-193) and an appropriate mixing efficiency, ε (Caulfield & Peltier, J. Fluid Mech., vol. 413, 2000, pp. 1-47). Equivalent attention has not been paid to the definitions of a corresponding momentum diffusivity Km and hence an appropriately defined turbulent Prandtl number Prt = Km/Kρ. In this paper, the diascalar framework of Winters & D'Asaro (1996) is first reformulated to obtain an 'Osborn-like' formula in which the correct definition of irreversible mixing efficiency ε is shown to replace the flux Richardson number which Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83-89) assumed to characterize this efficiency. We advocate the use of this revised representation for diapycnal diffusivity since the proposed reformulation effectively removes the simplifying assumptions on which the original Osborn formula was based. We similarly propose correspondingly reasonable definitions for Km and Prt by eliminating the reversible component of the momentum production term. To explore implications of the reformulations for both diapycnal and momentum diffusivity we employ an extensive series of direct numerical simulations (DNS) to investigate the properties of the shear-induced density-stratified turbulence that is engendered through the breaking of a freely evolving Kelvin-Helmholtz wave. The DNS results based on the proposed reformulation of Kρ are compared with available estimations due to the mixing length model, as well as both the Osborn-Cox and the Osborn models. Estimates based upon the Osborn-Cox formulation are shown to provide the closest approximation to the diapycnal diffusivity delivered by the exact representation. Through compilation of the complete set of DNS results we explore the characteristic dependence of Kρ on the buoyancy Reynolds number Reb as originally investigated by Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193-214) in their idealized study of homogeneous stratified and sheared turbulence, and show that the validity of their results is only further reinforced through analysis of the turbulence produced in the more geophysically relevant Kelvin-Helmholtz wave life-cycle ansatz. In contrast to the results described by Shih et al. (2005) however, we show that, besides Reb, a vertically averaged measure of the gradient Richardson number Rib may equivalently characterize the turbulent mixing at high Reb. Based on the dominant driving processes involved in irreversible mixing, we categorize the intermediate (i.e. Reb = O(101-102)) and high (i.e. Reb〉O(102)) range of Reb as 'buoyancy-dominated' and 'shear-dominated' mixing regimes, which together define a transition value of Rib ∼ 0.2. Mixing efficiency varies non-monotonically with both Reb and Rib, with its maximum (on the order of 0.2-0.3) occurring in the 'buoyancy-dominated' regime. Unlike Kρ which is very sensitive to the correct choice of ε (i.e. Kρ α ε/(1 - ε), we show that Km is almost insensitive to the choice of ε (i.e. Km α 1/(1 - ε)) so long as ε is not close to unity, which implies Km ≈RibReb for the entire range of Reb. The turbulent Prandtl number is consequently shown to decrease monotonically with Reb and may be (to first order) simply approximated by Reb itself. Assuming Prt = 1, or Prt = 10 (as is common in large-scale numerical models of the ocean general circulation), is also suggested to be a questionable assumption. © 2015 Cambridge University Press.

Description: We consider numerically the transition to turbulence and associated mixing in stratified shear flows with initial velocity distribution and initial density distribution away from a hydrostatic reference state. When the ratio of the characteristic length scales over which the velocity and density vary is equal to one, this flow is primarily susceptible to the classic well-known Kelvin-Helmholtz instability (KHI). This instability, which typically manifests at finite amplitude as an array of elliptical vortices, strongly 'overturns' the density interface of strong initial gradient, which nevertheless is the location of minimum initial gradient Richardson number, where and is a bulk Richardson number. As is well known, at sufficiently high Reynolds numbers, the primary KHI induces a vigorous but inherently transient burst of turbulence and associated irreversible mixing localised in the vicinity of the density interface, leading to a relatively well-mixed region bounded by stronger density gradients above and below. We explore the qualitatively different behaviour that arises when, and so the density interface is sharp, with now being maximum at the density interface. This flow is primarily susceptible to Holmboe wave instability (HWI) (Holmboe, Geophys. Publ., vol. 24, 1962, pp. 67-113), which manifests at finite amplitude in this symmetric flow as counter-propagating trains of elliptical vortices above and below the density interface, thus perturbing the interface so as to exhibit characteristically cusped interfacial waves which thereby 'scour' the density interface. Unlike previous lower-experimental and numerical studies, when is sufficiently high the primary HWI becomes increasingly more three-dimensional due to the emergence of shear-aligned secondary convective instabilities. As increases, (i) the growth rate of secondary instabilities appears to saturate and (ii) the perturbation kinetic energy exhibits a spectrum for sufficiently large length scales that are influenced by anisotropic buoyancy effects. Therefore, at sufficiently high, vigorous turbulence is triggered that also significantly 'scours' the primary density interface, leading to substantial irreversible mixing and vertical transport of mass above and below the (robust) primary density interface. Furthermore, HWI produces a markedly more long-lived turbulence event compared to KHI at a similarly high. Despite their vastly different mechanics (i.e. 'overturning' versus 'scouring') and localisation, the mixing induced by KHI and HWI is comparable in both absolute terms and relative efficiency. Our results establish that, provided the flow Reynolds number is sufficiently high, shear layers with sharp density interfaces and associated locally high values of the gradient Richardson number may still be sites of substantial and efficient irreversible mixing. © 2016 Cambridge University Press.

Description: Current global ocean models rely on ad hoc parameterizations of diapycnal mixing, in which the efficiency of mixing is globally assumed to be fixed at 20 %, despite increasing evidence that this assumption is questionable. As an ansatz for small-scale ocean turbulence, we may focus on stratified shear flows susceptible to either Kelvin-Helmholtz (KHI) or Holmboe wave (HWI) instability. Recently, an unprecedented volume of data has been generated through direct numerical simulation (DNS) of these flows. In this paper, we describe the application of deep learning methods to the discovery of a generic parameterization of diapycnal mixing using the available DNS dataset. We furthermore demonstrate that the proposed model is far more universal compared to recently published parameterizations. We show that a neural network appropriately trained on KHI- and HWI-induced turbulence is capable of predicting mixing efficiency associated with unseen regions of the parameter space well beyond the range of the training data. Strikingly, the high-level patterns learned based on the KHI and weakly stratified HWI are 'transferable' to predict HWI-induced mixing efficiency under much more strongly stratified conditions, suggesting that through the application of appropriate networks, significant universal abstractions of density-stratified turbulent mixing have been recognized. © 2019 Cambridge University Press.

Description: Turbulent mixing plays a major role in enabling the large-scale ocean circulation. The accuracy of mixing rates estimated from observations depends on our understanding of basic fluid mechanical processes underlying the nature of turbulence in a stratified fluid. Several of the key assumptions made in conventional mixing parameterizations have been increasingly scrutinized in recent years, primarily on the basis of adequately high resolution numerical simulations. We add to this evidence by compiling results from a suite of numerical simulations of the turbulence generated through stratified shear instability processes. We study the inherently intermittent and time-dependent nature of wave-induced turbulent life cycles and more specifically the tight coupling between inherently anisotropic scales upon which small-scale isotropic turbulence grows. The anisotropic scales stir and stretch fluid filaments enhancing irreversible diffusive mixing at smaller scales. We show that the characteristics of turbulent mixing depend on the relative time evolution of the Ozmidov length scale compared to the so-called Thorpe overturning scale which represents the scale containing available potential energy upon which turbulence feeds and grows. We find that when , the mixing is most active and efficient since stirring by the largest overturns becomes 'optimal' in the sense that it is not suppressed by ambient stratification. We argue that the high mixing efficiency associated with this phase, along with observations of in oceanic turbulent patches, together point to the potential for systematically underestimating mixing in the ocean if the role of overturns is neglected. This neglect, arising through the assumption of a clear separation of scales between the background mean flow and small-scale quasi-isotropic turbulence, leads to the exclusion of an highly efficient mixing phase from conventional parameterizations of the vertical transport of density. Such an exclusion may well be significant if the mechanism of shear-induced turbulence is assumed to be representative of at least some turbulent events in the ocean. While our results are based upon simulations of shear instability, we show that they are potentially more generic by making direct comparisons with data from ocean and lake observations which represent a much wider range of turbulence-inducing physical processes. © 2017 Cambridge University Press.

Description: Motivated by the importance of stratified shear flows in geophysical and environmental circumstances, we characterize their energetics, mixing and spectral behaviour through a series of direct numerical simulations of turbulence generated by Holmboe wave instability (HWI) under various initial conditions. We focus on circumstances where the stratification is sufficiently 'strong' so that HWI is the dominant primary instability of the flow. Our numerical findings demonstrate the emergence of self-organized criticality (SOC) that is manifest as an adjustment of an appropriately defined gradient Richardson number, , associated with the horizontally averaged mean flow, in such a way that it is continuously attracted towards a critical value of . This self-organization occurs through a continuously reinforced localization of the 'scouring' motions (i.e. 'avalanches') that are characteristic of the turbulence induced by the breakdown of Holmboe wave instabilities and are developed on the upper and lower flanks of the sharply localized density interface, embedded within a much more diffuse shear layer. These localized 'avalanches' are also found to exhibit the expected scale-invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a 'quasi-equilibrium' state for an extended period of time. Most importantly, the irreversible mixing that results from such self-organized behaviour appears to be characterized generically by a universal cumulative turbulent flux coefficient of only for turbulent flows engendered by Holmboe wave instability. The existence of this self-organized critical state corroborates the original physical arguments associated with self-regulation of stratified turbulent flows as involving a 'kind of equilibrium' as described by Turner (1973, Buoyancy Effects in Fluids, Cambridge University Press). © 2018 Cambridge University Press.