A general theory for the exchange timescale of lock-exchange flows where both the lock and the ambient are stratified has not been established yet. Here, two-dimensional large-eddy simulations of the lock exchange are performed, to quantify the dependence of the adjustment time on linear stratification in the lock and ambient. After validation of the model, simulations show that stratification in the ambient decreases the adjustment time, which is related to an increase of the hydrostatic pressure difference driving the front traveling into the lock. Stratification in the lock also decreases the adjustment time, because a larger stratification is associated with faster internal waves, thereby highlighting the role of internal wave speed in the stratified lock exchange. A reduced model for adjustment time is developed, that extends known relations for front speeds in unstratified conditions to situations with a vertically stratified lock and ambient. Stratification is incorporated by combining its effects on hydrostatic pressure and internal wave speed. This reduced model reproduces the dependence of the adjustment time on the initial density field with reasonable accuracy.

In recent years, increased salt intrusion in surface waters has threatened freshwater availability in coastal regions worldwide. Yet, current future projections of salt intrusion are limited to local regions or changes to single forcing agents. Here, we quantify compounding contributions from changes in river discharge and relative sea level to changing future salt intrusion under a high-emission scenario (Shared Socioeconomic Pathway, SSP3-7.0) for 18 estuaries around the world. We find that the annual 90th percentile future salt intrusion is projected to increase between 1.3% and 18.2% (median 9.1%) in 89% of the studied estuaries worldwide. Our analysis also indicates that, on average, sea-level rise contributes approximately two times more to increasing future salt intrusion than reduced river discharge. We further show that the return levels of present-day 100-year salt intrusion events are projected to increase between 3.2% and 25.2% (median 10.2%) in 83% of the studied estuaries.