Drift of elastic floating ice sheets by waves and current, part I: single sheet

The drift motion of a freely floating deformable ice sheet in shallow water subjected to incident nonlinear waves and uniform current is studied by use of the Green–Naghdi theory for the fluid motion and the thin plate theory for an elastic sheet. The nonlinear wave- and current-induced forces are obtained by integrating the hydrodynamic pressure around the body. The oscillations and translational motion of the sheet are then determined by substituting the flow-induced forces into the equation of motion of the body. The resulting governing equations, boundary and matching conditions are solved in two dimensions with a finite difference technique. The surge and drift motions of the sheet are analysed in a broad range of body parameters and various wave-current conditions. It is demonstrated that wavelength to sheet length ratio plays an important role in the drift response of the floating sheet, while the sheet mass and rigidity have comparatively less impact. It is also observed that while the presence of the ambient current changes the drift speed significantly (almost linearly), it has little to no effect on its oscillations. However, under the same ambient current, the drift speed changes remarkably by the wave period (or wavelength).

The functional relation between three-body mean motion resonances and Yarkovsky drift speeds

ABSTRACT We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.

A new sea ice state dependent parameterization for the free drift of sea ice

Free drift estimates of sea ice motion are necessary to produce a seamless observational record combining buoy and satellite-derived sea ice motion vectors. We develop a new parameterization for the free drift of sea ice based on wind forcing, wind turning angle, sea ice state variables (concentration and thickness) and ocean current (as a residual). Building on the fact that the spatially varying standard wind-ice transfer coefficient (considering only surface wind stress) has a structure as the spatial distribution of sea ice thickness, we introduce a wind-ice transfer coefficient that scales linearly with thickness. Results show a mean error of −0.5 cm/s (low-speed bias) and a root-mean-square error of 5.1 cm/s, considering daily buoy drift data as truth. This represents a 31 % reduction of the error on drift speed compared to the free drift estimates used in the Polar Pathfinder dataset. The thickness-dependent wind transfer coefficient provides an improved seasonality and long-term trend of the sea ice drift speed, with a minimum (maximum) drift speed in May (October), compared to July (January) for the constant wind transfer coefficient parameterizations which simply follow the peak in mean surface wind stresses. The trend in sea ice drift in this new model is +0.45 cm/s decade−1 compared with +0.39 cm/s decade−1 from the buoy observations, whereas there is essentially no trend in the standard free drift parameterization (−0.01 cm/s decade−1) or the Polar Pathfinder free drifts (−0.03 cm/s decade−1). The wind turning angle that minimize the cost function is equal of 25°, with a mean and root-mean square error of +2.6° and 51° on the direction of the drift, respectively. The residual from the minimization procedure (i.e. the ocean currents) resolves key large scale features such as the Beaufort Gyre and Transpolar Drift Stream, and is in good agreement with ocean state estimates from the ECCO, GLORYS and PIOMAS ice-ocean reanalyses, and geostrophic currents from dynamical ocean topography, with a root-mean-square difference of 2.4, 2.9, 2.6 and 3.8 cm/s, respectively. Finally, a repeat of the analysis on a two sub-section of the time series (pre- and post-2000) clearly shows the acceleration of the Beaufort Gyre (particularly along the Alaskan coastline) and an expansion of the gyre in the post-2000 concurrent with a thinning of the sea ice cover and observations acceleration of the ice drift speed and ocean current. This new dataset is publicly available for complementing merged observations-based sea ice drift datasets that includes satellite and buoy drift records.

Unprecedented decline of sea ice thickness in Fram Strait in 2017-2018

<p><span><span>Fram Strait is the major gateway connecting the Arctic Ocean and the northern North Atlantic Ocean where about 80 to 90% of sea ice outflow from the Arctic Ocean takes place. Long-term observations from the Fram Strait Arctic Outflow Observatory maintained by the Norwegian Polar Institute captured an unprecedented decline<!-- should we somehow add information that this statement is limited to the time since the early 1990s? --><!-- Reply to Sebastian Gerland (2021/01/12, 15:45): "..." I slightly modified the sentence to mention this. --> of sea ice thickness in 2017 – 2018 since comprehensive observations started in the early 1990s. Four Ice Profiling Sonars moored in the East Greenland Current in Fram Strait simultaneously recorded 50 – 70 cm decline of annual mean ice thickness in comparison with preceding years. A backward trajectory analysis revealed that the decline was attributed to an anomalous sea level pressure pattern from 2017 autumn to 2018 summer. Southerly wind associated with a dipole pressure anomaly between Greenland and the Barents Sea prevented southward motion of ice floes north of Fram Strait. Hence ice pack was exposed to warm Atlantic Water in the north of Fram Strait 2 – 3 times longer than the average year, allowing more melt <!-- should also slower freezing or reduced freezing rates mentioned here during winter and spring (in addition to melt in summer and autumn)? --><!-- Reply to Sebastian Gerland (2021/01/12, 15:46): "..." I would like to keep this sentence as it is, since the analysis implies sea ice melt occurred in the vicinity of Fram Strait in winter (probably due to ocean heat flux), though we don’t have direct measurements of 2018 event. This could be an interesting implications of this study, and seeds for further investigation. -->to happen. At the same time, the dipole anomaly was responsible for the slowest observed annual mean ice drift speed in Fram Strait in the last two decades. As a consequence of the record minimum of ice thickness and the slowest drift speed, the sea ice volume transport through the Fram Strait dropped by more than 50% in comparison with the 2010 – 2017 average.</span></span></p>

The functional relation between mean motion resonances and Yarkovsky force on small eccentricities

ABSTRACT This work examines asteroid’s motion with orbital eccentricity in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our final results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag 〈dtr〉, the strength of the resonance SR, and the semimajor axis drift speed da/dt with asteroids’ orbital eccentricities in the range (0.1, 0.2). We analysed average values of 〈dtr〉 using this functional relation comparing with obtained values of 〈dtr〉 from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1), on the present results for eccentricities in the range (0.1, 0.2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids’ orbital eccentricities (0, 0.2) and discussed it.

Non-Linear Wave Run-Up Along the Side of Sailing Ships Causing Green Water on Deck: Experiments and Deterministic Calculations

Experiments with a flat plate in oblique waves at different speeds, wave conditions, headings and drift speed were done to evaluate non-linear wave run-up along a sailing ship. Both the incoming and diffracted part of the run-up were highly nonlinear in all test conditions. The run-up was larger at 135 than at 150 deg heading, the influence of speed was small, wave steepness increased run-up up to the point of breaking and a drift speed decreased the run-up. Most of the observed differences were larger than the seed and basin variability. (Semi-) linear diffraction methods are not sufficient to predict the highest runup crests, but applying them to screen for critical events could be further studied. CFD is able to accurately predict the nonlinear run-up in such selected events. Combining different levels of tools seems the most efficient way to predict extreme wave events such as green water due to run-up.

Evaluation of Arctic sea ice drift and its dependency on near-surface wind and sea ice conditions in the coupled regional climate model HIRHAM–NAOSIM

We examine the simulated Arctic sea ice drift speed for the period 2003–2014 in the coupled Arctic regional climate model HIRHAM–NAOSIM 2.0. In particular, we evaluate the dependency of the drift speed on the near-surface wind speed and sea ice conditions. Considering the seasonal cycle of the Arctic basin averaged drift speed, the model reproduces the summer–autumn drift speed well but significantly overestimates the winter–spring drift speed, compared to satellite-derived observations. Also, the model does not capture the observed seasonal phase lag between drift and wind speed, but the simulated drift speed is more in phase with the near-surface wind. The model calculates a realistic negative correlation between drift speed and ice thickness and between drift speed and ice concentration during summer–autumn when the ice concentration is relatively low, but the correlation is weaker than observed. A daily grid-scale diagnostic indicates that the model reproduces the observed positive correlation between drift and wind speed. The strongest impact of wind changes on drift speed occurs for high and moderate wind speeds, with a low impact for rather calm conditions. The correlation under low-wind conditions is overestimated in the simulations compared to observation/reanalysis data. A sensitivity experiment demonstrates the significant effects of sea ice form drag from floe edges included by an improved parameterization of the transfer coefficients for momentum and heat over sea ice. However, this does not improve the agreement of the modeled drift speed / wind speed ratio with observations based on reanalysis data for wind and remote sensing data for sea ice drift. An improvement might be achieved by tuning parameters that are not well established by observations.

Patterns of sea ice drift and polar bear (Ursus maritimus) movement in Hudson Bay

Sea ice habitats are highly dynamic, and ice drift may affect the energy expenditure of travelling animals. Several studies in the high Arctic have reported increased ice drift speeds, and consequently, polar bears Ursus maritimus in these areas expended more energy on counter-ice movement for station-keeping. However, little is known about the spatiotemporal dynamics of ice drift in Hudson Bay (HB) and its implications for the declining Western Hudson Bay (WH) polar bear subpopulation. Using sea ice drift data from 1987-2015 and polar bear satellite telemetry location data from 2004-2015, we examined trends in drift speeds in HB, polar bear movement relative to drift, and assessed annual and individual variation. In contrast to other areas of the Arctic, we did not find an increase in ice drift speed over the period examined. However, variability in ice drift speed increased over time, which suggests reduced habitat predictability. Polar bear movement direction was not strongly counter to ice drift in any month, and ice drift speed and direction had little effect on bear movement rates and, thus, energy expenditure. On an annual scale, we found individuals varied in their exposure and response to ice drift, which may contribute to variability in body condition. However, the lack of a long-term increase in ice drift speed suggests this is unlikely to be the main factor affecting the body condition decline observed in the WH subpopulation. Our results contrast findings in other subpopulations and demonstrate the need for subpopulation-specific research and risk evaluation.

The relationship between the `limiting' Yarkovsky drift speed and asteroid families' Yarkovsky V-shape

The Yarkovsky effect is an important force to consider in order to understand the long-term dynamics of asteroids. This non-gravitational force affects the orbital elements of objects revolving around a source of heat, especially their semi-major axes. Following the recently defined `limiting' value of the Yarkovsky drift speed at 7x10-5 au/Myr in Milic Zitnik (2019) (below this value of speed asteroids typically jump quickly across the mean motion resonances), we decided to investigate the relation between the asteroid family Yarkovsky V-shape and the `limiting' Yarkovsky drift speed of asteroid's semi-major axes. We have used the known scaling formula to calculate the Yarkovsky drift speed (Spoto et al. 2015) in order to determine the inner and outer `limiting' diameters (for the inner and outer V-shape borders) from the `limiting' Yarkovsky drift speed. The method was applied to 11 asteroid families of different taxonomic classes, origin type and age, located throughout the Main Belt. Here, we present the results of our calculation on relationship between asteroid families' V-shapes (crossed by strong and/or weak mean motion resonances) and the `limiting' diameters in the (a, 1=D) plane. Our main conclusion is that the `breakpoints' in changing V-shape of the very old asteroid families, crossed by relatively strong mean motion resonances on both sides very close to the parent body, are exactly the inverse of `limiting' diameters in the a versus 1=D plane. This result uncovers a novel interesting property of asteroid families' Yarkovsky V-shapes.