Figure 3 - uploaded by K. Balaje
Content may be subject to copyright.
Reflection and Transmission Coefficient as a function of complex frequencies. The white dots indicate the poles which are points where there is an abrupt change in color. The poles correspond to the resonance frequencies of the shelf/cavity system. The color denotes the phase angle and the brightness, the magnitude of the complex number (Wegert, 2012).
Context in source publication
Context 1
... implements the method to solve the vibration problem for complex valued incident frequencies which are useful to study resonances in the complex plane (B. Kalyanaraman et al., 2020), shown in Figure 3. While a priori knowledge of finite elements are useful to write scripts using iceFEM, some macros which yield the essential stiffness matrix and load vector are available. ...
Similar publications
Вибухові роботи при видобуванні корисних копалин у Криворізькому залізорудному басейні є причиною численних просадок основ, руйнування фундаментів та несучих елементів будівель та споруд Кривого Рогу. Вона посилюється водоносними пісками, що відклалися здебільшого території міста. Вони залягають на глибинівід 1,5 до 30 метрів і перекриті пластичним...
Citations
... Models have reached the sophistication of incorporating idealized geometrical variations, such as seabed undulations and shoaling (Ilyas et al., 2018;Meylan et al., 2021;Papathanasiou et al., 2019), and ice thickening away from the shelf front (Kalyanaraman et al., 2020;Meylan et al., 2021;Papathanasiou et al., 2015). Sergienko (2017) and Kalyanaraman et al. (2021) incorporated measured ice shelf and seabed geometries from Bedmap2 (Fretwell et al., 2013). Kalyanaraman et al. (2021)'s model is two-dimensional and the solution method is restricted to shelves up to tens of kilometers long. ...
... Sergienko (2017) and Kalyanaraman et al. (2021) incorporated measured ice shelf and seabed geometries from Bedmap2 (Fretwell et al., 2013). Kalyanaraman et al. (2021)'s model is two-dimensional and the solution method is restricted to shelves up to tens of kilometers long. Sergienko (2017)'s model is three-dimensional, solved numerically using a commercial software that limited her study to only two frequencies, and applies wave forcing via a simplified boundary condition at the interface between the open ocean and sub-shelf water cavity, so that ocean wave to shelf transfer is not modeled. ...
An efficient mathematical model is presented for predicting the transfer of ocean waves to ice shelf flexure along two‐dimensional transects. The model incorporates varying ice shelf thickness and seabed bathymetry profiles, and is able to predict responses of large ice shelves over a broad frequency spectrum. The model is used to generate displacement and strain transfer functions for the Ross Ice Shelf (RIS) using geometries from the Bedmap2 data set. The transfer functions are validated against recent observations and used to study the influence of geometrical variations on strain transfer close to the shelf front. Predictions of RIS strain in response to example irregular incident swell and infragravity waves are generated over a wide region, and show similar maximum strains but contrasting spatial strain patterns. The model and results provide a basis for studying destabilizing impacts of ocean waves on the RIS.
A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water–ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime.
