Salt-Wedge Response to Variable River Flow and Sea-Level Rise in the Microtidal Rječina River Estuary, Croatia

Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity

“…(16) is valid only when dealing with two layers of similar densities (r = ρ 1 /ρ 2 ≈ 1) and when velocities in both layers are comparable (u 1 ≈ u 2 ). These conditions are found in some stratified flows in nature, such as exchange flows through sea straits Chakir et al, 2009) or some cases of highly stratified estuaries Krvavica et al (2017b). For a general application, however, this condition may not be necessary to ensure hyperbolicity, as demonstrated by Sarno et al (2017).…”

Assessment of sea-level rise impacts on salt-wedge intrusion in idealized and Neretva River Estuary

“…Two-layer shallow water models have been previously applied and validated for the Neretva River Estuary (Ljubenkov and Vranješ, 2012) and several other microtidal estuaries (Ljubenkov, 2015;Krvavica et al, 2016b). The numerical results in the Neretva River Estuary showed a good agreement with salinity measurements throughout the year, under a wide range of hydrological conditions (Ljubenkov and Vranješ, 2012).…”

Re-evaluating efficiency of first-order numerical schemes for two-layer shallow water systems by considering different eigenvalue solutions

“…(10) and (11) are valid only when dealing with two layers of similar densities (r = ρ 1 /ρ 2 ≈ 1) and when velocities in both layers are comparable (u 1 ≈ u 2 ). Those conditions are found in some stratified flows in nature, such as exchange flows through sea straits [14,17] or some cases of highly stratified estuaries [24]. However, for geophysical flows characterized by a larger relative density difference, such as granular, debris or mud flows, the approximated values may significantly deviate from exact values and cannot accurately predict a possible hyperbolicity loss [1,37,25].…”