Collective instability of salt fingers

1969 ◽  
Vol 35 (2) ◽  
pp. 209-218 ◽  
Author(s):  
Melvin E. Stern
Keyword(s):  
Gravity Waves ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Asymptotic Dependence ◽  
Salinity Gradients ◽  
Salt Fingers ◽  
Order Of Magnitude ◽  
Ocean Observations ◽  
Molecular Salt ◽  
Steady Laminar

We first consider a steady laminar model of salt fingers and show that the latter become unstable with respect to internal gravity waves when the finger Reynolds number exceeds a critical value. The criterion is then used in speculations about the statistically steady state in a fully developed similarity model where horizontally averaged temperature and salinity gradients are constant at all depths. Dimensional reasoning is used to obtain the asymptotic dependence of the turbulent flux on the molecular salt diffusivity. From this and other relationships order-of-magnitude estimates are obtained and compared with laboratory experiments and ocean observations.

An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid

2014 ◽  
Vol 742 ◽  
pp. 308-339 ◽  
Author(s):  
Hugo N. Ulloa ◽  
Alberto de la Fuente ◽  
Yarko Niño
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Kelvin Wave ◽  
Nonlinear Processes ◽  
Transfer Energy ◽  
Type Wave ◽  
Basin Scale ◽  
Layer Flow

AbstractThe temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of $\eta _{i}$, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré wave can transfer energy to higher or lower frequencies than the frequency of the fundamental Kelvin wave, as a function of the background rotation. In particular, a specific normal mode in the off-shore region could be energized by this interaction. Finally, the bulk decay rate of the fundamental Kelvin wave, $\tau _{dk}$, was investigated. The results exhibit that $\tau _{dk}$ is concordant with the Ekman damping time scale when there is no evidence of steepening in the basin-scale waves. However, as nonlinear processes increase, $\tau _{dk}$ shows a strong decrease. In this context, the nonlinear processes play an important role in the decay of the fundamental Kelvin wave, via the energy radiation to other modes. The results reported demonstrate that the background rotation and nonlinear processes are essential aspects in understanding the degeneration and the decay of large-scale internal gravity waves on enclosed basins.

scholarly journals Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

2014 ◽  
Vol 745 ◽  
pp. 223-250 ◽  
Author(s):  
Laurène Jouve ◽  
Gordon I. Ogilvie
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Dissipation Rate ◽  
Laboratory Experiments ◽  
Rotation Axis ◽  
Internal Gravity Waves ◽  
Direct Numerical Simulations ◽  
Inertial Wave ◽  
Linear And Nonlinear ◽  
Nonlinear Regimes

AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

scholarly journals Convective differential rotation in stars and planets – II. Observational and numerical tests

2020 ◽  
Vol 498 (3) ◽  
pp. 3782-3806
Author(s):  
Adam S Jermyn ◽  
Shashikumar M Chitre ◽  
Pierre Lesaffre ◽  
Christopher A Tout
Keyword(s):  
Gravity Waves ◽  
Differential Rotation ◽  
Internal Gravity Waves ◽  
Companion Paper ◽  
General Picture ◽  
Giant Stars ◽  
Numerical Tests ◽  
Rotating Systems ◽  
Order Of Magnitude ◽  
Red Giant

ABSTRACT Differential rotation is central to a great many mysteries in stars and planets. In part I, we predicted the order of magnitude and scaling of the differential rotation in both hydrodynamic and magnetohydrodynamic convection zones. Our results apply to both slowly and rapidly rotating systems, and provide a general picture of differential rotation in stars and fluid planets. We further calculated the scalings of the meridional circulation, entropy gradient, and baroclinicity. In this companion paper, we compare these predictions with a variety of observations and numerical simulations. With a few exceptions, we find that these are consistent in both the slowly rotating and rapidly rotating limits. Our results help to localize core–envelope shear in red giant stars, suggest a rotation-dependent frequency shift in the internal gravity waves of massive stars, and potentially explain observed deviations from von Zeipel’s gravity darkening in late-type stars.

On the breaking of standing internal gravity waves

1972 ◽  
Vol 54 (4) ◽  
pp. 577-598 ◽  
Author(s):  
Isidoro Orlanski
Keyword(s):  
Gravity Waves ◽  
Laboratory Experiments ◽  
Gravitational Instability ◽  
Perturbation Expansion ◽  
Standing Waves ◽  
Maximum Amplitude ◽  
Internal Gravity Waves ◽  
Numerical Results ◽  
Critical Amplitude ◽  
Transient Behaviour

A solution has been found for the transient behaviour of resonant growing standing waves by using a perturbation expansion. Comparison with laboratory experiments as well as a numerical nonlinear solution of the same problem leads to the conclusion that: (i) the transient behaviour and the nonlinear tendency of the standing waves are described well by the analytic expression; (ii) the numerical results describe the solution very well until the wave starts to break; (iii) from the laboratory experiments and the numerical results, the standing internal gravity waves break owing to local gravitational instability at a critical amplitude which is similar to the one predicted by the expansion theory; (iv) the critical amplitude seems to be the maximum amplitude that a wave can reach; (v) when the generation of turbulence is violent, the small eddies begin forcing a secondary flow characterized by layers of strong jets separated by patches of turbulence.

scholarly journals Biharmonic Attractors of Internal Gravity Waves

2021 ◽  
Vol 56 (3) ◽  
pp. 403-412
Author(s):  
D. A. Ryazanov ◽  
M. I. Providukhina ◽  
I. N. Sibgatullin ◽  
E. V. Ermanyuk
Keyword(s):  
Gravity Waves ◽  
High Frequency ◽  
Large Time ◽  
Internal Gravity Waves ◽  
Wave Pattern ◽  
Mean Value ◽  
Order Of Magnitude ◽  
The Mean ◽  
Low Amplitude ◽  
Large Time Scale

Abstract— The hydrodynamic system that admits the development of internal wave attractors under biharmonic forcing is investigated. It is shown that in the case of low amplitude of external forcing the wave pattern consists of two attractors that interact between themselves only slightly: the total energy of the system is equal to the sum of energies of the components with high accuracy. In the nonlinear case the attractors interact in the more complex way which leads to the development of a cascade of triad interactions generating a rich set of time scales. In the case of closely adjacent frequencies of the components of a biharmonic perturbation, the nonlinear “beating” regime develops, namely, the mean energy of the system of coupled attractors performs oscillations at a large time scale that corresponds to the beating period. It is found that the high-frequency energy fluctuations corresponding to the same mean energy can differ by an order of magnitude depending on whether the envelope of the mean value increases or decreases.

Model of the internal gravity waves excited by lithospheric greenhouse effect gases

2001 ◽  
Vol 7 (2s) ◽  
pp. 26-33 ◽  
Author(s):  
O.E. Gotynyan ◽  
◽  
V.N. Ivchenko ◽  
Yu.G. Rapoport ◽  
◽  
...  
Keyword(s):  
Gravity Waves ◽  
Greenhouse Effect ◽  
Internal Gravity Waves

scholarly journals Shear-induced breaking of internal gravity waves

2021 ◽  
Vol 921 ◽  
Author(s):  
Christopher J. Howland ◽  
John R. Taylor ◽  
C.P. Caulfield
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves

Abstract

scholarly journals Rolls of the internal gravity waves in the Earth's atmosphere

2014 ◽  
Vol 32 (2) ◽  
pp. 181-186 ◽  
Author(s):  
O. Onishchenko ◽  
O. Pokhotelov ◽  
W. Horton ◽  
A. Smolyakov ◽  
T. Kaladze ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
Closed System ◽  
Wind Shear ◽  
Internal Gravity Waves ◽  
Temperature Gradients ◽  
System Of Equations ◽  
Vertical Temperature ◽  
Earth’S Atmosphere ◽  
Earth's Atmosphere

Abstract. The effect of the wind shear on the roll structures of nonlinear internal gravity waves (IGWs) in the Earth's atmosphere with the finite vertical temperature gradients is investigated. A closed system of equations is derived for the nonlinear dynamics of the IGWs in the presence of temperature gradients and sheared wind. The solution in the form of rolls has been obtained. The new condition for the existence of such structures was found by taking into account the roll spatial scale, the horizontal speed and wind shear parameters. We have shown that the roll structures can exist in a dynamically unstable atmosphere.

scholarly journals Hydraulic transmissivity inferred from ice-sheet relaxation following Greenland supraglacial lake drainages

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ching-Yao Lai ◽  
Laura A. Stevens ◽  
Danielle L. Chase ◽  
Timothy T. Creyts ◽  
Mark D. Behn ◽  
...  
Keyword(s):  
Laboratory Experiments ◽  
Ice Sheet ◽  
Drainage System ◽  
Greenland Ice Sheet ◽  
Field Observations ◽  
Surface Uplift ◽  
Drainage Networks ◽  
Order Of Magnitude ◽  
Lake Drainage ◽  
Magnitude Increase

AbstractSurface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of-magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 $${\rm{m}}{{\rm{m}}}^{3}$$ m m 3 to 215 ± 90.2 $${\rm{m}}{{\rm{m}}}^{3}$$ m m 3 ) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.

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