On the Form Drag Coefficient Under Ridged Ice: Laboratory Experiments and Numerical Simulations From Ideal Scaling to Deep Water

Abstract

The bottom topography of ridged sea ice differs greatly from that of other sea‐ice types. The form drag of ridge keels has an important influence on sea‐ice drift and deformation. In this study, both laboratory experiment (LabE) and fluid dynamics numerical simulation (FDS) have been carried out for a physical ridge model in a tank to better understand the quantitative characteristics of the form drag. The LabEs covered both laminar and turbulent conditions. The local form drag coefficient of a keel, Cdw, varied with the keel depth hw and the slope angle αw in the turbulent regime. After validated by the LabE measurements, the FDSs were employed to extend the parameterization from the finite water depth to deep water. The results gave Cdw = 0.68∙ln (αw/7.8°), R2 = 0.998, 10° ≤ αw ≤ 90°, with Cdw ranging from 0.17 to 1.66, when the keel depth was much less than the water depth. For a large ridging intensity (keel depth/spacing ≥0.01), the variation of the local form drag coefficient and its contribution to total drag coefficient were sensitive to the keel slope angle. Assuming the log‐normal distribution for this angle, the average value of the local form drag coefficient was 0.75, recommended for sea‐ice dynamic models.

Sheltering of sea ice ridges in the ice-ocean drag force: implications from laboratory experiments

“…The former provides the physical truth of flow characteristics at ridges, and the latter extends the experimental results to real ocean conditions (Mortikov, 2016;Pite et al, 1995;Zu et al, 2021).…”

“…The inclination angle of obstacles has been validated in hydrodynamics and sea ice dynamics as a key parameter of the drag force of two square pillars (Du et al, 2019;Yen et al, 2008) and ridge keels (Zu et al, 2021). In particular, the geometry of ridged ice varies greatly for the depth and cross-sectional shape, e.g., a maximum depth of 27 m and a maximum slope angle of 87.5° were observed by Kharitonov & Borodkin (2020).…”

“…Similarity treatment was adopted for the major parameters based on dimensional analysis. The keel model was set up as a solid isosceles triangle, which has been used in many laboratory experiments (e.g., Pite et al, 1995;Zu et al, 2021) and geophysical applications (Roberts et al, 2019;Lemieux et al, 2015). The model material was plexiglass, as used by Waters and Bruno (1995), Pite et al (1995), andZu et al (2021).…”

“…The range of Re was 8×10 3 to 2.47×10 5 . The laboratory experiments were considered similar to the natural marine environment when the flow was turbulent or Re > 10 4 (Zu et al, 2021). The cases of Re < 10 4 were at the margin and may occur in nature at near stationary ice conditions.…”

“…5 shows this coefficient as a function of the squared flow velocity for α = 45° and H = 0.12 m. As u 2 increased, Г remained stable within 4.2%. According to the dimensional analysis in Table 1, the flow velocity u impacted the sheltering effect by changing only Re, which is crucial in the laminar flow regime but barely affects the turbulent regime (Zu et al, 2021). Since the ocean currents under sea ice are mostly turbulent (McPhee, 2008; Kharitonov & Borodkin, 2020), Г is independent of the u.…”