Experimental self-generation of axisymmetric internal wave super-harmonics

Triadic resonant instability in confined and unconfined axisymmetric geometries

We present an investigation of the resonance conditions of axisymmetric internal wave sub-harmonics in confined and unconfined domains. In both cases, sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies, of the form $ω_0 = \pm ω_1 \pm ω_2$. We demonstrate that, in an unconfined domain, the sub-harmonics follow three dimensional spatial resonance conditions similar to the ones of Triadic Resonance Instability (TRI) for Cartesian plane waves. In a confined domain, however, the spatial structure of the sub-harm…

On the saturation of non-axisymmetric instabilites of magnetized spherical Couette flow

We numerically investigate the saturation of the hydromagnetic instabilities of a magnetized spherical Couette flow. Previous simulations [Hollerbach, 2009] demonstrated region where the axisymmetric flow, calculated from a 2-D simulation, was linearly unstable to nonaxisymmetric perturbations. Full, nonlinear, 3d simulations [Hollerbach 2009, Travnikov 2011] showed that the saturated state would consist only of harmonics of one azimuthal wave number, though there were bifurcations and transitions as nondimensional parameters (Re, Ha) were varied. Here, the energy transfer between different az…

Collapse of Non-Axisymmetric Cavities

A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.

Collapse of a non-axisymmetric, impact-created air cavity in water

The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single m…

A solvable model of axisymmetric and non-axisymmetric droplet bouncing

We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in t…

旋转斜压环流中局部周边加热的对流流动的线性稳定性分析：一种Floquet-BiGlobal方法

Linear Stability Analysis of convective flows in Rotating Baroclinic Annulus with Localized Peripheral Heating: A Floquet-BiGlobal Approach

本文采用Floquet-Bloch理论与BiGlobal特征值方法，分析了局部加热下旋转流体环的非轴对称基态线性稳定性，揭示了交叉模态斜压能量释放和剪切产生的不稳定机制。