The effect of hydrodynamics on the interaction between floating structures and flexible ice floes: A study based on potential theory

The Arctic presents a great opportunity for two major industries. First, since the region is expected to contain a significant amount of hydrocarbon reserves, it is very attractive for the oil and gas industry. Second, the receding extent of sea ice is making the region more accessible for shipping and, therefore, an opportunity is emerging for the shipping industry. In order to exploit both economic opportunities in a safe and sustainable manner, a thorough understanding of the interaction between ice and floating structures is needed. The most common method for studying ice-floater interaction (IFI) is via numerical modeling, which the fluid is a major component of. As fluid-ice interaction is challenging to model, a wide range of simplified and sophisticated models are employed to meet the challenge. A literature study was performed on the usage of fluid models employed in IFI and it was found that they can be divided into four categories: hydrostatic models, models based on potential flow, models based on Reynolds-averaged Navier–Stokes or a similarly advanced method, and effective fluid models. The hydrostatic models are by far the most prevalent despite only accounting for buoyancy. Most IFI models that account for hydrodynamics make use of potential theory. These models account for fluid flow and surface waves, which together alter the dynamic behavior of floating ice, resulting in hydroelastic effects. The surface-wave-based coupling between ice and floater has not been studied before and there are still open questions regarding the effects of hydroelasticity on the bending failure of ice. The advanced fluid models are a recent trend in IFI and, consequently, most of those are still under development. These models are very promising and may be the future of IFI modeling. Finally, the effective models avoid the practical issues associated with hydrodynamic models in terms of development and calculation time by capturing hydrodynamics in an effective manner, employing, for instance, added mass and damping coefficients. While several studies investigated the efficacy of these models, currently no satisfactory effective fluid model exists. The main goal of this thesis is to further the understanding of how hydrodynamics affects the interaction between ice and a sloping structure and to assess whether it is possible to create an effective model that can replicate the observed effects. The full scope encompasses three smaller studies. First, the surface-wave-based coupling between an elastic ice sheet and nearby floater structure is investigated. This interaction has not been studied before and the solution method that is developed for this problem is also used in the subsequent two studies. Second, a thorough study of the effects of hydrodynamics on the interaction between a sloping structure and level ice is accomplished. This study resulted in the identification of the parameter range wherein hydrostatic models are valid, which is essential given that they constitute the majority of all models. In addition, this study improved the understanding of the effects of hydrodynamics by means of investigating the importance of various components such as the rotational inertia of the ice, axial compression, and the nonlinear hydrodynamic pressure. Furthermore, the relation was analyzed between the temporal development of the contact force and the velocity dependence of the breaking length. Lastly, based on the findings of the second study, an attempt was made to develop an effective fluid model for ice-slope interaction. The efficacy of this model was studied in this thesis for a range of parameters. The main findings of the three studies are summarized next. In the first part of this thesis, the interaction is investigated between an ice floe and a floater through surface waves. This problem is considered first as the Green's functions that are derived for this problem are required for the subsequent studies on ice-slope interaction. The floater is modeled in-plane as a thin rigid body that floats on the surface of a fluid layer of finite depth. On one side of the floater, an ice floe is present which is modeled as a semi-infinite Kirchhoff-Love plate. The floater is excited by external loads and the resulting motions generate waves. Those waves hitting the ice edge are partly transmitted into the ice floe and partly reflected back towards the floater. The reflected waves exert pressure on the floater, altering its response. The resulting motions of the floater were analyzed, revealing several interesting facts. The study showed that below a certain onset frequency, the waves are almost fully transmitted into the ice floe and, consequently, the response of the floater is unaffected by the presence of the ice. The susceptibility of a floater to the waves reflected by a nearby ice floe can thus be estimated by checking how much of its open water response occurs above or below the onset frequency. The onset frequency is sensitive to changes of the ice thickness and insensitive to changes of the Young's modulus and water depth. Above the onset frequency, the waves reflected by the ice have a pronounced effect on the response of the floater. In certain frequency ranges, quasi-standing waves occur within the gap between ice floe and floater. Within these frequency ranges, the response of the floater is significantly altered. Depending on the phasing between the reflected waves and the floater's motions, resonance or anti-resonance can occur which can greatly amplify or reduce the floater's motions when compared to the case when no ice is present. Even when there is no gap between ice and floater, the amplitude of the floater can still be amplified and its natural frequency somewhat increased. The second study of this thesis focuses on the effect of hydrodynamics on the bending failure of an elastic ice floe due to the interaction with a downward-sloping floater, i.e. the effects of hydrodynamics on ice-slope interaction (ISI). A novel, semi-analytical in-plane ISI model is proposed that is based on potential theory in conjunction with the nonlinear Bernoulli equation to describe the fluid pressure. The ice is modeled as a semi-infinite Kirchhoff-Love plate. The predictions of the hydrodynamic model are compared with those of a hydrostatic ISI model, thereby obtaining a quantitative measure of the effect of hydrodynamics on ISI. The comparison revealed several interesting facts. First, the importance of several components of the model was investigated to determine which ones are essential for ISI. It was found that the contribution of the rotational inertia of the ice, axial compression and the nonlinear hydrodynamic pressure is insignificant. Being able to ignore the last two components greatly simplifies the modeling of ISI as it removes all sources of spatial nonlinearity. The terms that were found to be essential for ISI, listed in the order of importance, are: bending of the ice floe, linear hydrodynamic pressure, hydrostatic pressure and the inertia of the ice floe. The contribution of the fluid's inertia is on average four to ten times bigger than that of the inertia of the ice. The study also demonstrated that the effect of wave radiation on ISI is minimal. Second, the relation between the temporal development of the contact force and the velocity-dependence of the breaking length was studied. The study showed that the breaking length has two regimes which are separated by a transition velocity. When the ice velocity is below the transition velocity, the ice fails during the initial impact. Alternatively, when the ice velocity is above the transition velocity, the ice floe survives the impact and fails with a breaking length that is close to the static breaking length. The transition velocity of the hydrodynamic model is much lower than the transition velocity of the hydrostatic model, 0.0725 m/s compared to 0.275 m/s. This major difference in transition velocity is the primary reason for the limited applicability of the hydrostatic model. The results show that the hydrostatic model should not be used when the ice velocity is higher than 0.6 times the transition velocity of the hydrodynamic model as its predictions will deviate significantly, with errors ranging from 30% to 100%. This upper bound corresponds to values between 0.02 m/s and 0.1 m/s for the parameters considered. Lastly, this study underlined the stochastic nature of the breaking length of the ice floe. When the floe fails, a relatively large segment of the floe is, in fact, close to failure. A defect in the ice can locally amplify the stresses, causing the ice to fail at the defect rather than at the location predicted by a homogeneous model. This can cause the breaking length to vary by 10% to 30%. The last part of this thesis builds on the knowledge gained in part two by attempting to create a simple effective fluid model (EFM) that captures the effects of hydrodynamics on ISI as observed in part two. Based on the observations, an EFM is proposed that uses frequency-independent added mass and damping coefficients. This EFM was added to the hydrostatic model, thereby obtaining an ISI model that contains all four essential components of the ISI model. The resulting effective ISI model is very simple and, consequently, its implementation is trivial compared to a true hydrodynamic model such as the one proposed in part two. Its simplicity should help to improve the adoption of hydrodynamics in ISI. The performance of the effective ISI model is assessed. Investigated are the velocity-dependent breaking length, the maximum contact force that occurred during the interaction, and the contact force as a function of time. The predictions of the effective model are far more accurate than those of the hydrostatic model. The coefficients of the EFM were found to be relatively insensitive to changes in the parameters, allowing the effective model to be used for a fairly broad range of parameters.