Fully dispersive models for moving loads on ice sheets

Dinvay, Evgueni; Kalisch, Henrik; Părău, Emilian

doi:10.1017/jfm.2019.530

Cited by 48 publications

(36 citation statements)

References 53 publications

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“…Schulkes and Sneyd, 1988). Further studies have shown that the buildup of large enough deflections to break the ice may be limited by two-dimensional spreading (Nugroho et al, 1999), viscous effects (Wang et al, 2004), acceleration/deceleration through the critical speed (Miles and Sneyd, 2003) and/or non-linearities (Dinvay et al, 2019). Interestingly, a complementary field of study also exists that focuses on leveraging the resonant flexural waves produced by moving hovercraft to enhance their effectiveness as icebreakers (Hinchey and Colbourne, 1995;Kozin et al, 2017).…”

Section: A General Theory -Moving Loads On Floating Platesmentioning

confidence: 99%

Sea ice thickness from air-coupled flexural waves

et al. 2021

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Abstract. Air-coupled flexural waves (ACFWs) appear as wave trains of constant frequency that arrive in advance of the direct air wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering yet unwieldy analytical efforts of the 1950s. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a real and measurable component of the total wave field of floating ice sheets excited by impulsive sources, and we present a simple closed-form estimator for the ice thickness based on observable properties of the air-coupled flexural waves. Our study is focused on first-year sea ice of ∼ 20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural wave for the sea ice system considered in this study occurs at a constant frequency thickness product of ∼ 48 Hz m. Our field data include ice ranging from ∼ 20–80 cm thickness with corresponding air-coupled flexural frequencies from 240 Hz for the thinnest ice to 60 Hz for the thickest ice. While air-coupled flexural waves for thick sea ice have received little attention, the readily audible, higher frequencies associated with thin ice on freshwater lakes and rivers are well known to the ice-skating community and have been reported in popular media. The results of this study and further examples from lake ice suggest the possibility of non-contact estimation of ice thickness using simple, inexpensive microphones located above the ice sheet or along the shoreline. While we have demonstrated the use of air-coupled flexural waves for ice thickness monitoring using an active source acquisition scheme, naturally forming cracks in the ice are also shown as a potential impulsive source that could allow passive recording of air-coupled flexural waves.

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Section: A General Theory -Moving Loads On Floating Platesmentioning

confidence: 99%

Sea ice thickness from air-coupled flexural waves

et al. 2021

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“…Solution of such a problem cannot easily be obtained by analytical methods; however, contemporary numerical packages such as ANSYS CFD can be used. It is also worth mentioning that, as shown in [28], the influence of nonlinearity in the problem of moving loads on ice sheets becomes notable for rather big-amplitude FGWs. The influence of viscosity and nonlinearity in the general problem of ocean waves and ice interaction is reviewed in [1].…”

Section: Discussionmentioning

confidence: 93%

Hydrodynamic Forces Exerting on an Oscillating Cylinder under Translational Motion in Water Covered by Compressed Ice

Stepanyants

Sturova

2021

Water

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This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion.

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“…For a weakly nonlinear regime and two-dimensional problems, Parau & Dias (2002) derived a forced nonlinear Schrodinger equation for the envelope of ice sheet deflections caused by a load moving at a critical speed. Dinvay, Kalisch & Parau (2019) developed a fully dispersive weakly nonlinear model describing flexural-gravity waves in a floating elastic plate, excited by a moving load. For larger amplitudes, both forced and free steady waves were computed by Guyenne & Parau (2012) using direct numerical simulations with a boundary integral method.…”

Section: Numerical Resultsmentioning

confidence: 99%