Instability in the oscillations of a moving oscillator while it radiates surface and internal waves

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

“…Substituted into a dispersion relation, the Cerenkov condition transforms the former into an expression defining a surface in the space of wavenumbers that determines the wake pattern behind the source (Schulkes et al 1987; Carusotto & Rousseaux 2013). For the supercritical velocities the surface in the space of wavenumbers develops a conical singularity known as the Cerenkov cone (Nemtsov 1985; Carusotto & Rousseaux 2013) with the angular aperture The anomalous Doppler effect (ADE) is the change in the sign of the field frequency radiated into the Cerenkov cone as compared with the field radiated outside this cone (Nezlin 1976; Gaponov-Grekhov et al 1983; Nemtsov 1985; Abramovich et al 1986; Carusotto & Rousseaux 2013). It is exactly the slow surface gravity wave that satisfies this condition …”

“…It was shown that the oscillator becomes excited due to radiation of internal gravity waves if it moves sufficiently fast. In Abramovich, Mareev & Nemtsov (1986) the ADE for such an oscillator was demonstrated due to radiation of surface gravity waves in a layer of an incompressible fluid. Nemtsov (1985) was the first who considered flutter of an elastic membrane resting at the bottom of a uniform horizontal flow of an inviscid and incompressible fluid as an anomalous Doppler effect due to emission of long surface gravity waves.…”

“…It was shown that the oscillator becomes excited due to radiation of internal gravity waves if it moves sufficiently fast. In Abramovich, Mareev & Nemtsov (1986) the ADE for such an oscillator was demonstrated due to radiation of surface gravity waves in a layer of an incompressible fluid.…”

Radiation-induced instability of a finite-chord Nemtsov membrane

“…In particular, from (39) we easily obtain the growth rate of the perturbed simple real eigenvalue ω n…”

“…In a related set of problems on the stability of oscillations of moving wave emitters (e.g. radiation of elastic waves in rails by high-speed trains [37] and emission of internal or surface gravity waves by a spherical body on an elastic spring moving parallel to the interface of two liquids [38,39]), the theory of Cherenkov radiation for structureless particles [10,40] and its extension by Ginzburg and Frank [41] to the particles having internal degrees of freedom, provides important clues both for derivation of necessary and sufficient criteria for instability and for better understanding radiation-induced instabilities in the general physical context [42].…”