We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region.

Abstract. Marine sediment records from a series of core sites along the northwest African margin show a sudden increase in North Atlantic dust deposition at about 5 ka BP that has been associated with an abrupt end of the African Humid Period (AHP). To assess the causes of the abrupt shift in North Atlantic dust deposition, we explore changes in the Holocene dust cycle and in North African climate and landscape by performing several time slice simulations from 8 ka BP until the preindustrial era. To do this, we use the coupled aerosol–climate model ECHAM6–HAM2 including dynamic vegetation and interactive dust, wherein ocean conditions and lake surface area are prescribed for each time slice. We find a rapid increase in simulated dust deposition between 6 and 4 ka BP that is fairly consistent with the abrupt change in marine sediment records at around 20∘ N close to the northwest African margin. At more northern and more remote cores, a significant change in dust deposition is noticeable roughly between 6 and 2 ka BP in the simulations as well as in the records, but the change is less sharp compared to the near-margin core sites. The rapid change in simulated dust deposition is caused by a rapid increase in simulated dust emissions in the western Sahara, where the main dust sources for dust transport towards the North Atlantic are located. The sudden increase in dust emissions in the western Sahara is according to our simulations a consequence of a fast decline of vegetation cover from 22 to 18∘ N that might occur due to vegetation–climate feedbacks or due to the existence of a precipitation threshold on vegetation growth. Additionally, the prescribed gradual reduction of lake area enforces accelerated dust release as highly productive dust sources are uncovered. Concurrently with the continental drying, surface winds in the western Sahara are accelerated. Changes in the Saharan landscape and dust emissions south of 18∘ N and in the eastern Sahara play a minor role in driving the dynamics of North Atlantic dust deposition at the core sites. Our study identifies spatial and temporal heterogeneity in the transition of the North African landscape. As a consequence, implications from local data records on large-scale climate have to be treated with caution.

Abstract. Marine sediment records reveal an abrupt and strong increase in dust deposition in the North Atlantic at the end of the African Humid Period about 4.9 to 5.5 ka ago. The change in dust flux has been attributed to varying Saharan land surface cover. Alternatively, the enhanced dust accumulation is linked to enhanced surface winds and a consequent intensification of coastal upwelling. Here we demonstrate for the first time the direct link between dust accumulation in marine cores and changes in Saharan land surface. We simulate the mid-Holocene (6 ka BP) and preindustrial (1850 AD) dust cycle as a function of Saharan land surface cover and atmosphere-ocean conditions using the coupled atmosphere-aerosol model ECHAM6.1-HAM2.1. Mid-Holocene surface characteristics, including vegetation cover and lake surface area, are derived from proxy data and simulations. In agreement with data from marine sediment cores, our simulations show that mid-Holocene dust deposition fluxes in the North Atlantic were two to three times lower compared with pre-industrial fluxes. We identify Saharan land surface characteristics to be the main control on dust transport from North Africa to the North Atlantic. We conclude that the increase in dust accumulation in marine cores is directly linked to a transition of the Saharan landscape during the Holocene and not due to changes in atmospheric or ocean conditions alone.