Kinetic Wave Turbulence Research Articles

Identification of weakly to strongly-turbulent three-wave processes in a micro-scale system

We find capillary wave turbulence (WT) spanning multiple dynamical regimes and geometries, all within a 40μL volume microfluidic system. This study is made viable with recent advances in ultra-high-speed digital holographic microscopy, providing 10μs time and 10nm spatial resolutions for images across the entire field at speeds sufficient to capture the salient wave phenomena. The observed WT types are: (i) discrete wave turbulence (DWT) dominated by finite domain effects, (ii) kinetic wave turbulence (KWT) that approximately satisfies weak wave turbulence (WWT) theory, and (iii) intermediate wave turbulence (IWT) that exhibits features from both DWT and KWT. We show that WT regime depends on input power and wavenumber, and we provide simple nondimensional parameters – derived from WWT theory – for intra-spectrum regime classification. Using the nondimensional parameters, a bulk nonlinearity metric is defined that employs bicoherence-based weighting. Analysis of experimental results reveals a correspondence between the theoretical regime classifiers and the observed phenomena. At sufficiently high input powers, the phenomena substantially depart from the WWT theory and reveal a regime of strongly nonlinear wave turbulence (SWT) defined by shallower spectral slopes that achieve a constant slope value over a range of input powers. This may suggest a corresponding power-law solution to the governing equations. This work augments current understanding of WT regimes and behaviors, and directly applies to many fields beyond fluid mechanics. For example, SWT appears upon the fluid interface at powers less than required for atomization, indicating that further study of SWT is needed to properly understand ultrasound-driven fuel spray atomization and drug and agricultural nebulization.

4-wave dynamics in kinetic wave turbulence

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an “interaction representation” and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman–Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Finite-dimensional turbulence of planetary waves

Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave "clusters" consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finite-dimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wave-kinetic equations that account for interactions with overlapping quasiresonances of finite amplitude waves. The present results are directly applicable to finite-dimensional wave turbulence in any wave system in finite domains with three-mode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.