Flexural-gravity wave motion in the presence of shear current: Wave blocking and negative energy waves

Abstract

Flexural-gravity wave propagation under the action of a compressive force and in the presence of flow vorticity is studied under the framework of linear water wave theory. The occurrences of wave blocking which is analogous to the free surface gravity wave propagation against an opposing current as well as light wave propagation in curved space-time near a black hole are shown to exist. Moreover, negative energy waves that are responsible for making the total energy of the fluid flow less than that without the waves are also analyzed. The effects of compressive force, Froude number, and vorticity on the existence of negative energy waves as well as the occurrence of flexural-gravity wave blocking are graphically illustrated. The variation in group velocity for different flow parameters such as the vorticity, the Froude number, and the compressive force is analyzed. Time-dependent simulations of the propagation of wave packets are calculated.

Membrane flutter induced by radiation of surface gravity waves on a uniform flow

“…Surface gravity waves on a motionless fluid of finite depth are a classical subject as well, going back to the seminal studies of Russell and Kelvin (Carusotto & Rousseaux 2013). Numerous generalizations are known taking into account, for instance, a uniform or a shear flow and surface tension (Maissa, Rousseaux & Stepanyants 2016), submerged solids (Smorodin 1972; Arzhannikov & Kotelnikov 2016) and hydrofoils (Faltinsen & Semenov 2008), a flexible bottom (Mohapatra & Sahoo 2011) or a flexible plate resting on a free surface (Greenhill 1886; Schulkes, Hosking & Sneyd 1987; Bochkarev, Lekomtsev & Matveenko 2016; Das, Sahoo & Meylan 2018 a , b ; Das et al 2018). The latter setting has a straightforward motivation in the dynamics of sea ice and a less obvious application in the analogue gravity experiments (Barcelo, Liberati & Visser 2011; Weinfurtner et al 2011; Carusotto & Rousseaux 2013).…”

Waves on a compressed floating ice plate caused by motion of a dipole in water

“…It has been partially studied in the linear approximation in the papers by Das et al. (2018 a , b , c ); it is worthy of further study, taking into consideration nonlinear effects arising in the vicinity of a blocking point (Liu & Mollo-Christensen 1988).…”

“…The problem becomes very non-trivial from the theoretical point of view as it leads to a big variety of possible cases due to the rather complex dispersion relation (see, for example, Das et al. 2018 a , Das, Sahoo & Meylan 2018 b , c ).…”

“…This makes topical the study of flexural-gravity waves in the oceans covered by a compressed/stretched ice. The problem becomes very non-trivial from the theoretical point of view as it leads to a big variety of possible cases due to the rather complex dispersion relation (see, for example, Das et al 2018a, Das, Sahoo & Meylan 2018b.…”

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

“…As a result, the study of FGWs in oceans covered by compressed ice is a topical and important problem. However, this problem becomes rather complex from the theoretical point of view since it leads to a wide variety of possible cases due to a rather complex dispersion relation for this type of waves (see, e.g., [15][16][17][18]). The recently published work by the current authors [18] contains a study of FGWs generated by a dipole moving horizontally at some depth under the ice and oscillating along the direction of motion.…”