Finite-amplitude instabilities of thin internal wave beams: experiments and theory

Fan, Boyu; Akylas, T. R.

doi:10.1017/jfm.2020.682

Cited by 11 publications

(13 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be stressed that the wave vector components can be strictly defined only for spatially monochromatic fields (or approximately monochromatic as in Bourget et al. 2013) while for narrow wave beams the objective measurement of wave vector components raises some problems as discussed in Fan & Akylas (2020). However, experimentally it is often possible to construct the PDFs for the wave vector components measured in a zone of interest and estimate the length of the wave vectors from the positions of PDF's maxima.…”

Section: Numerical Resultsmentioning

confidence: 99%

Vortex cluster arising from an axisymmetric inertial wave attractor

et al. 2021

View full text Add to dashboard Cite

We present an experimental and numerical study of the nonlinear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom and a horizontal wave generator at the top: the vertical cross-section is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully nonlinear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Vortex cluster arising from an axisymmetric inertial wave attractor

et al. 2021

View full text Add to dashboard Cite

show abstract

“…To tackle this complication, we follow the approach taken by Onuki & Tanaka (2019) in their stability analysis of finite-amplitude internal wave beams under oceanic flow conditions. This approach was used earlier for inertial wave beams (Jouve & Ogilvie 2014) and also in a very recent study of finite-amplitude thin internal wave beams under laboratory flow conditions (Fan & Akylas 2020).…”

Section: Locally Confined Beamsmentioning

confidence: 99%

“…It should be noted that three-dimensional (m / = 0) instabilities are possible and may be important at large amplitudes (Onuki & Tanaka 2019). Furthermore, other three-dimensional instability mechanisms such as streaming, which involves the generation of a resonant mean flow due to finite transverse variations of a beam (Kataoka & Akylas 2015;Fan, Kataoka & Akylas 2018;Fan & Akylas 2020;Jamin et al 2021) and thus falls beyond the scope of linear stability analysis, may be important in other contexts.…”

Section: Locally Confined Beamsmentioning

confidence: 99%

“…Following Onuki & Tanaka (2019), we solve (2.5) using the 'monodromy' matrix, which can be easily computed by integrating (2.5) over one period of oscillation of the primary wave, namely T 0 = 2π/ω. The Floquet exponents λ = λ r + iλ i , where λ r > 0 implies instability, as well as the Floquet modes, are then obtained via the eigenvalues and eigenvectors of the monodromy matrix (see Fan (2020) and Fan & Akylas (2020) for details). Finally, we repeat this procedure for various μ in order to find the instability modes with the highest growth rate.…”

Section: Locally Confined Beamsmentioning

confidence: 99%

See 1 more Smart Citation

Instabilities of finite-width internal wave beams: from Floquet analysis to PSI

Fan

Akylas

2021

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…2011; Karimi & Akylas 2014; Chalamalla & Sarkar 2016; Dauxois et al. 2018; Fan & Akylas 2019, 2020; Leclair, Raja & Staquet 2020). The structure of the wave groups is important, e.g.…”

Section: Introductionmentioning

confidence: 99%