“…The comparison with theory, shown in figures 3 and 4, does not exhibit any systematic effect of . Indeed, Vasil'ev & Chashechkin (2009) presented statistical averages over experiments for different values of , keeping all other parameters constant; the averages were spline-interpolated then resampled. Some experiments belonged to the earlier series by Levitskii, Prikhod'ko and Chashechkin, while others were performed specially by Y. Prikhod'ko for the purpose of the study (A. Vasil'ev, personal communication).…”
Section: Free Oscillationsmentioning
confidence: 92%
“…Parameters values are given in table 1.Figure 4.Same as figure 3 for the data in figures 2 and 7 of Levitskii & Chashechkin (1999), figure 5 of Chashechkin & Levitskii (2003) and figure 2 of Prikhod'ko & Chashechkin (2006). Figure 5.Same as figure 3 for the data in figures 1 and 2 of Vasil'ev & Chashechkin (2009). …”
Section: Free Oscillationsmentioning
confidence: 96%
“…The viscous damping of the oscillations of the sphere was considered by Vasil'ev, Kistovich &Chashechkin (2009). Using a no-slip boundary condition, the oscillations were obtained as a series…”
Section: Viscous Analysismentioning
confidence: 99%
“…For a linearly stratified fluid, the experiments of Larsen (1969) and Winant (1974) for a buoyant sphere had been focused on the motion of the sphere. Further attention was paid to the flow around it by , , ) and Vasil'ev & Chashechkin (2009, while Prikhod'ko & and also considered a finite-length horizontal or vertical circular cylinder, and Biró et al (2008) a smaller sphere dropped at the surface and observed over hundreds of oscillation periods. Finally, Hurlen (2006) and Hurlen & Llewellyn Smith (2024) considered theoretically, experimentally and numerically the free translational and rotational oscillations of a horizontal elliptic cylinder.…”
Section: Introductionmentioning
confidence: 99%
“…For a linearly stratified fluid, the experiments of Larsen (1969) and Winant (1974) for a buoyant sphere had been focused on the motion of the sphere. Further attention was paid to the flow around it by Levitskii & Chashechkin (1999), Chashechkin & Levitskii (1999, 2003), Prikhod'ko & Chashechkin (2006), Chashechkin & Prikhod'ko (2006, 2007) and Vasil'ev & Chashechkin (2009), while Prikhod'ko & Chashechkin (2006) and Chashechkin & Prikhod'ko (2006) also considered a finite-length horizontal or vertical circular cylinder, and Biró et al. (2008) a smaller sphere dropped at the surface and observed over hundreds of oscillation periods.…”
The oscillations of buoyant bodies in stratified fluids are deduced from the variations of their added mass. Three configurations are considered: a body displaced from its neutral level then released; a Cartesian diver set into oscillation by a modulation of the hydrostatic pressure, then released; and a body attached to a pendulum to which an impulse is applied. The first configuration is related to the dynamics of Lagrangian floats in the ocean. Two particular bodies are considered: an elliptic cylinder of horizontal axis, typical of two-dimensional bodies; and a spheroid of vertical axis, typical of three-dimensional bodies. The ultimate motion of the body consists of oscillations at the buoyancy frequency with an amplitude decaying algebraically with time. Before that, the resonant response of the system is observed, either aperiodic exponential decay when the system has no intrinsic dynamics, or exponentially damped oscillation otherwise. Comparison with available measurements demonstrates the need to include viscous dissipation in the analysis. At high Stokes number, dissipation comes from the Basset–Boussinesq memory force and is affected negligibly by the stratification; at low Stokes number, dissipation comes from Stokes resistance and exhibits a significant effect of the stratification.
“…The comparison with theory, shown in figures 3 and 4, does not exhibit any systematic effect of . Indeed, Vasil'ev & Chashechkin (2009) presented statistical averages over experiments for different values of , keeping all other parameters constant; the averages were spline-interpolated then resampled. Some experiments belonged to the earlier series by Levitskii, Prikhod'ko and Chashechkin, while others were performed specially by Y. Prikhod'ko for the purpose of the study (A. Vasil'ev, personal communication).…”
Section: Free Oscillationsmentioning
confidence: 92%
“…Parameters values are given in table 1.Figure 4.Same as figure 3 for the data in figures 2 and 7 of Levitskii & Chashechkin (1999), figure 5 of Chashechkin & Levitskii (2003) and figure 2 of Prikhod'ko & Chashechkin (2006). Figure 5.Same as figure 3 for the data in figures 1 and 2 of Vasil'ev & Chashechkin (2009). …”
Section: Free Oscillationsmentioning
confidence: 96%
“…The viscous damping of the oscillations of the sphere was considered by Vasil'ev, Kistovich &Chashechkin (2009). Using a no-slip boundary condition, the oscillations were obtained as a series…”
Section: Viscous Analysismentioning
confidence: 99%
“…For a linearly stratified fluid, the experiments of Larsen (1969) and Winant (1974) for a buoyant sphere had been focused on the motion of the sphere. Further attention was paid to the flow around it by , , ) and Vasil'ev & Chashechkin (2009, while Prikhod'ko & and also considered a finite-length horizontal or vertical circular cylinder, and Biró et al (2008) a smaller sphere dropped at the surface and observed over hundreds of oscillation periods. Finally, Hurlen (2006) and Hurlen & Llewellyn Smith (2024) considered theoretically, experimentally and numerically the free translational and rotational oscillations of a horizontal elliptic cylinder.…”
Section: Introductionmentioning
confidence: 99%
“…For a linearly stratified fluid, the experiments of Larsen (1969) and Winant (1974) for a buoyant sphere had been focused on the motion of the sphere. Further attention was paid to the flow around it by Levitskii & Chashechkin (1999), Chashechkin & Levitskii (1999, 2003), Prikhod'ko & Chashechkin (2006), Chashechkin & Prikhod'ko (2006, 2007) and Vasil'ev & Chashechkin (2009), while Prikhod'ko & Chashechkin (2006) and Chashechkin & Prikhod'ko (2006) also considered a finite-length horizontal or vertical circular cylinder, and Biró et al. (2008) a smaller sphere dropped at the surface and observed over hundreds of oscillation periods.…”
The oscillations of buoyant bodies in stratified fluids are deduced from the variations of their added mass. Three configurations are considered: a body displaced from its neutral level then released; a Cartesian diver set into oscillation by a modulation of the hydrostatic pressure, then released; and a body attached to a pendulum to which an impulse is applied. The first configuration is related to the dynamics of Lagrangian floats in the ocean. Two particular bodies are considered: an elliptic cylinder of horizontal axis, typical of two-dimensional bodies; and a spheroid of vertical axis, typical of three-dimensional bodies. The ultimate motion of the body consists of oscillations at the buoyancy frequency with an amplitude decaying algebraically with time. Before that, the resonant response of the system is observed, either aperiodic exponential decay when the system has no intrinsic dynamics, or exponentially damped oscillation otherwise. Comparison with available measurements demonstrates the need to include viscous dissipation in the analysis. At high Stokes number, dissipation comes from the Basset–Boussinesq memory force and is affected negligibly by the stratification; at low Stokes number, dissipation comes from Stokes resistance and exhibits a significant effect of the stratification.
In this paper, we study the motion of a spheroid of a moderate aspect ratio in a viscous fluid under the action of an external harmonic force. We first derive the dynamics equation of the particle oscillating along one of its axes and subject to damping, Basset memory, and second history integral forces at small Reynolds numbers, and then, we proceed to obtain an analytical solution of this equation at resonance. With graphical representation, we observe that for a prolate spheroid, the conventional Q-curves show a greater variation with respect to the particle aspect ratio, particle–fluid density ratio, and natural frequency; the variation is significantly larger for the curve corresponding to the second history force. Furthermore, we find that all three forces affect the amplitude of motion: the amplitude increases with the strength of damping as well as the second history integral forces, whereas the presence of Basset memory decreases it. Remarkably, Basset memory causes a phase-shift in the oscillations, while the other two forces have no effect on the phase. Since our solutions are analytical, they may have valuable application in experiments involving more complex systems, in particular, to understand the effect of external force on the transport of micro-particles.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
