The plume this website in run D (S = 35.00, Q = 0.01 Sv, Fig. 6) slows noticeably at the 200 m interface (between ESW-AW), while the other runs are less affected at this depth level. In all runs the plume is slowed upon encountering the 500 m depth level of the AW-NSDW interface, but the plume in run A which has the strongest inflow (S = 35.81, Q = 0.08 Sv) is least affected and reaches the bottom of the slope after only 20 days. Fig. 6 demonstrates that plumes with different initial parameters spend varying lengths of time flowing through and mixing with the different

layers of ambient water which affect the final fate of the plume (see Sections 3.3 and 3.4). At this point it is appropriate to include a note on the relationship between the downslope speed of the plume front and its alongslope speed. For each model run the downslope

Tofacitinib in vivo speed uFuF is calculated for the latter part of the experiment when the descent rate is roughly constant – from 20 days (or when the plume edge has passed 800 m depth, if earlier) until the end of the model run or when the plume edge has reached 1400 m (cf. Fig. 6). For the same time period we also derive the reduced gravity g′=gΔρρ0 based on the density gradient across the plume front. Experiments where the plume is arrested and g′g′ is close to 0 or even negative (due to the overshoot at the front) are excluded. Fig. 7 compares the downslope velocity component

uFuF to the alongslope component VNof=g′ftanθ (Nof, 1983), where f=1.415×10-4s-1 is the Coriolis parameter and θ=1.8°θ=1.8° is the slope angle. An overall average ratio of all downslope and alongslope velocities from Celecoxib all 45 runs is calculated using linear regression as uFVNof=0.19 (R2=0.977R2=0.977) which is surprisingly close to the ratio of uFVNof=0.2 given by Shapiro and Hill (1997) as a simplified formula for the quick estimation of cascading parameters from observations. The Killworth (2001) formula for the rate of descent of a gravity current can be written for our slope angle (θ=1.8°θ=1.8°) as uF=1400VNofsinθ=0.08VNof making our modelled downslope velocities approximately 2.4×2.4× greater than Killworth’s prediction. Shapiro and Hill (1997) developed their formula for a 112-layer model of cascading on a plane slope and assuming a sharp separation between ambient water and a plume with a normalised thickness of hFHe≈1.78. Our ratio of uFVNof=0.19 was computed for those runs with a positive density gradient at the plume front, which naturally puts them in the ‘piercing’ category. The normalised plume height averaged over those runs is hFHe=4.7, which indicates a more diluted plume than assumed for the Shapiro and Hill (1997) model. Wobus et al.