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Register a new userFrom waves to convection and back again: The phase space of stably stratified turbulence
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Added by
Nicol\\'as Eduardo Sujovolsky
Publication date
2019
fields
Physics
and research's language is
English
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We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium corresponds to waves, while a global invariant manifold corresponds to the onset of local convection. Using a reduced model derived from the Boussinesq equations, we propose that waves accumulate energy nonlinearly up to a point such that fluid elements escape from the local manifold and evolve fast to the global manifold, where kinetic energy can be more efficiently dissipated. After this, fluid elements return to the first manifold. As the stratification increases, the volume of the first manifold increases, and the second manifold becomes harder to access. This explains recent observations of enhanced intermittency and marginal instability in these flows. The reduced model also allows us to study structure formation, alignment of field gradients in the flow, and to identify balance relations that hold for each fluid element.
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We present an investigation of rapidly rotating (small Rossby number $Roll 1$) and stratified turbulence where the stratification strength is varied from weak (large Froude number $Frgg1$) to strong ($Frll1$). The investigation is set in the context of a reduced model derived from the Boussinesq equations that efficiently retains anisotropic inertia-gravity waves with order-one frequencies and highlights a regime of wave-eddy interactions. Numerical simulations of the reduced model are performed where energy is injected by a stochastic forcing of vertical velocity, which forces wave modes only. The simulations reveal two regimes characterized by the presence of well-formed, persistent and thin turbulent layers of locally-weakened stratification at small Froude numbers, and by the absence of layers at large Froude numbers. Both regimes are characterized by a large-scale barotropic dipole enclosed by small-scale turbulence. When the Reynolds number is not too large a direct cascade of barotropic kinetic energy is observed, leading to total energy equilibration. We examine net energy exchanges that occur through vortex stretching and vertical buoyancy flux and diagnose the horizontal scales active in these exchanges. We find that the baroclinic motions inject energy directly to the largest scales of the barotropic mode, implying that the large-scale barotropic dipole is not the end result of an inverse cascade within the barotropic mode.
We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and enhance kinetic and potential energy dissipation, providing an explanation for the observed variability of the local energy dissipation in the ocean and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in oceans, roughly $10%$ of the domain flow can account for up to $50%$ of the total volume dissipation, consistently with recent estimates based on oceanic models.
Marangoni instabilities can emerge when a liquid interface is subjected to a concentration or temperature gradient. It is generally believed that for these instabilities bulk effects like buoyancy are negligible as compared to interfacial forces, especially on small scales. Consequently, the effect of a stable stratification on the Marangoni instability has hitherto been ignored. Here we report, for an immiscible drop immersed in a stably stratified ethanol-water mixture, a new type of oscillatory solutal Marangoni instability which is triggered once the stratification has reached a critical value. We experimentally explore the parameter space spanned by the stratification strength and the drop size and theoretically explain the observed crossover from levitating to bouncing by balancing the advection and diffusion around the drop. Finally, the effect of the stable stratification on the Marangoni instability is surprisingly amplified in confined geometries, leading to an earlier onset.
We find an instability resulting in generation of large-scale vorticity in a fast rotating small-scale turbulence or turbulent convection with inhomogeneous fluid density along the rotational axis in anelastic approximation. The large-scale instability causes excitation of two modes: (i) the mode with dominant vertical vorticity and with the mean velocity being independent of the vertical coordinate; (ii) the mode with dominant horizontal vorticity and with the mean momentum being independent of the vertical coordinate. The mode with the dominant vertical vorticity can be excited in a fast rotating density stratified hydrodynamic turbulence or turbulent convection. For this mode, the mean entropy is depleted inside the cyclonic vortices, while it is enhanced inside the anti-cyclonic vortices. The mode with the dominant horizontal vorticity can be excited only in a fast rotating density stratified turbulent convection. The developed theory may be relevant for explanation of an origin of large spots observed as immense storms in great planets, e.g., the Great Red Spot in Jupiter and large spots in Saturn. It may be also useful for explanation of an origin of high-latitude spots in rapidly rotating late-type stars.
Stratified turbulence shows scale- and direction-dependent anisotropy and the coexistence of weak turbulence of internal gravity waves and strong turbulence of eddies. Straightforward application of standard analyses developed in isotropic turbulence sometimes masks important aspects of the anisotropic turbulence. To capture detailed structures of the energy distribution in the wave-number space, it is indispensable to examine the energy distribution with non-integrated spectra by fixing the codimensional wave-number component or in the two-dimensional domain spanned by both the horizontal and vertical wave numbers. Indices which separate the range of the anisotropic weak-wave turbulence in the wave-number space are proposed based on the decomposed energies. In addition, the dominance of the waves in the range is also verified by the small frequency deviation from the linear dispersion relation. In the wave-dominant range, the linear wave periods given by the linear dispersion relation are smaller than approximately one third of the eddy-turnover time. The linear wave periods reflect the anisotropy of the system, while the isotropic Brunt-Vaisala period is used to evaluate the Ozmidov wave number, which is necessarily isotropic. It is found that the time scales in consideration of the anisotropy of the flow field must be appropriately selected to obtain the critical wave number separating the weak-wave turbulence.
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