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Register a new userInertial and gravity wave transmissions near radiative-convective boundaries
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In this paper, we study the inertial and gravity wave transmissions near the radiative-convective boundaries in the {it f}-plane. Two configurations have been considered: waves propagate from the convective layer to the radiative stratified stable layer, or In this paper, we study inertial and gravity wave transmissions near radiative-convective boundaries on the {it f}-plane. Two configurations have been considered: waves propagate from the convective layer to the radiative stratified stable layer, or the other way around. It has been found that waves prefer to survive at low latitudes when the stable layer is strongly stratified ($N^2/(2Omega)^2>1$). When the stable layer is weakly stratified ($N^2/(2Omega)^2<1$), however, waves can survive at any latitude if the meridional wavenumber is large. Then we have discussed transmission ratios for two buoyancy frequency structures: the uniform stratification, and the continuously varying stratification. For the uniform stratification, we have found that the transmission is efficient when the rotation is rapid, or when the wave is near the critical colatitude. For the continuously varying stratification, we have discussed the transmission ratio when the square of buoyancy frequency is an algebraic function $N^2propto z^{ u} ( u >0)$. We have found that the transmission can be efficient when the rotation is rapid, or when the wave is near the critical colatitude, or when the thickness of the stratification layer is far greater than the horizontal wave length. The transmission ratio does not depend on the configurations (radiative layer sits above convective layer, or vice versa; wave propagates outward or inward), but only on characteristics of the wave (frequency and wavenumber) and the fluid (degree of stratification).
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In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunneling occurs. We find that efficient wave transmission can be achieved by `resonant propagation or `resonant tunneling, even when stable layers are strongly stratified, and we call this phenomenon `enhanced wave transmission. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable layers are alternatingly embedded within clamping convective layers, or vise versa). For wave propagation, the occurrence of enhanced wave transmission requires that clamping layers have similar properties, the thickness of each clamping layer is close to a multiple of the half wavelength of the corresponding propagative wave, and the total thickness of embedded layers is close to a multiple of the half wavelength of the corresponding propagating wave (resonant propagation). For wave tunneling, we have considered two cases: tunneling of gravity waves and tunneling of inertial waves. In both cases, efficient tunneling requires that clamping layers have similar properties, the thickness of each embedded layer is much smaller than the corresponding e-folding decay distance, and the thickness of each clamping layer is close to a multiple-and-a-half of half wavelength (resonant tunneling).
We propose a numerical method to compute the inertial modes of a container with near-spherical geometry based on the fully spectral discretisation of the angular and radial directions using spherical harmonics and Gegenbauer polynomial expansion respectively. This allows to solve simultaneously the Poincare equation and the no penetration condition as an algebraic polynomial eigenvalue problem. The inertial modes of an exact oblate spheroid are recovered to machine precision using an appropriate set of spheroidal coordinates. We show how other boundaries that deviate slightly from a sphere can be accommodated for with the technique of equivalent spherical boundary and we demonstrate the convergence properties of this approach for the triaxial ellipsoid.
We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using DNS and find that its emerging butterfly-type structure -- a spatio-temporal variation in the form of upward and downward traveling waves -- is in a very good agreement with the linear stability analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern.
Stellar radiative zones are typically assumed to be motionless in standard models of stellar structure but there is sound theoretical and observational evidence that this cannot be the case. We investigate by direct numerical simulations a three-dimensional and time-dependent model of stellar radiation zones consisting of an electrically-conductive and stably-stratified anelastic fluid confined to a rotating spherical shell and driven by a baroclinic torque. As the baroclinic driving is gradually increased a sequence of transitions from an axisymmetric and equatorially-symmetric time-independent flow to flows with a strong poloidal component and lesser symmetry are found. It is shown that all flow regimes characterised with significant non-axisymmetric components are capable of generating self-sustained magnetic field. As the value of the Prandtl number is decreased and the value of the Ekman number is decreased flows become strongly time-dependent with progressively complex spatial structure and dynamos can be generated at lower values of the magnetic Prandtl number.
We present an experimental study of the saturated non-linear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The experiments are carried out in a rotating ring-shaped fluid domain delimited by two vertical coaxial cylinders, a conical bottom, and a horizontal deformable upper lid as wave generator: the meridional cross-section of the fluid volume is a trapezium, while the horizontal cross-section is a ring. First, the fluid is set into a rigid-body rotation. Thereafter, forcing is introduced into the system via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. After a short transient of about 10 forcing periods, a quasi-linear regime is established, with an axisymmetric inertial wave attractor. The attractor is prone to instability: at long time-scale (order 100 forcing periods) a saturated fully non-linear regime develops as a consequence of an energy cascade draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially-oriented cyclonic vortices that are slowly precessing around the inner cylinder. We show that this slow two-dimensional manifold manifests a persistent slow prograde motion and a strong cyclonic-anticyclonic asymmetry quantified by the time-evolution of the probability density function of the vertical vorticity.
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