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.

The degeneration of large-scale interfacial gravity waves in lakes

2001 ◽  
Vol 434 ◽  
pp. 181-207 ◽  
Author(s):  
D. A. HORN ◽  
J. IMBERGER ◽  
G. N. IVEY
Keyword(s):  
Gravity Waves ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Field Observations ◽  
Layer Model ◽  
Lake Ecology ◽  
Initial Wave ◽  
Basin Scale ◽  
Two Layer Model

Mechanisms for the degeneration of large-scale interfacial gravity waves are identified for lakes in which the effects of the Earth's rotation can be neglected. By assuming a simple two-layer model and comparing the timescales over which each of these degeneration mechanisms act, regimes are defined in which particular processes are expected to dominate. The boundaries of these regimes are expressed in terms of two lengthscale ratios: the ratio of the amplitude of the initial wave to the depth of the thermocline, and the ratio of the depth of the thermocline to the overall depth of the lake. Comparison of the predictions of this timescale analysis with the results from both laboratory experiments and field observations confirms its applicability. The results suggest that, for small to medium sized lakes subject to a relatively uniform windstress, an important mechanism for the degeneration of large-scale internal waves is the generation of solitons by nonlinear steepening. Since solitons are likely to break at the sloping boundaries, leading to localized turbulent mixing and enhanced dissipation, the transfer of energy from an initial basin-scale seiche to shorter solitons has important implications for the lake ecology.

Trapped internal gravity waves in a geostrophic boundary current

1993 ◽  
Vol 247 ◽  
pp. 205-229
Author(s):  
Hong Ma
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Combined Effects ◽  
Kelvin Wave ◽  
Boundary Current ◽  
Trapping Mechanism ◽  
Rossby Radius Of Deformation ◽  
Wave Guides ◽  
Internal Kelvin Wave

The effect of a geostrophic boundary current on internal gravity waves is studied with a reduced-gravity model. We found that the boundary current not only modifies the coastal Kelvin wave, but also forms wave guides for short internal gravity waves. The combined effects of current shear, the boundary, and the slope of the interface create the trapping mechanism. These trapped internal gravity waves appear as groups of discrete zonal modes. They have wavelengths comparable to or shorter than the internal Rossby radius of deformation. Their phase speeds are close to that of the internal Kelvin wave. However, they can propagate both in, or opposite to, the direction of the Kelvin wave. The results of the present work suggest the possibility of finding an energetic internal gravity wave phenomenon with near-inertial frequency in a broad geostrophic boundary current.

Modulation of Internal Gravity Waves in a Multiscale Model for Deep Convection on Mesoscales

2010 ◽  
Vol 67 (8) ◽  
pp. 2504-2519 ◽  
Author(s):  
Daniel Ruprecht ◽  
Rupert Klein ◽  
Andrew J. Majda
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Energy Transport ◽  
Deep Convection ◽  
Potential Temperature ◽  
Internal Gravity Waves ◽  
Small Scale ◽  
Closed Model ◽  
Large Scale Flow ◽  
Effective Stability

Abstract Starting from the conservation laws for mass, momentum, and energy together with a three-species bulk microphysics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multiscale asymptotic techniques. From the leading-order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime on which the analysis is based. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and microscale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and nonsaturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: (i) it reduces vertical energy transport by waves, (ii) it increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) it introduces a new lower horizontal cutoff wavenumber in addition to the well-known high wavenumber cutoff, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime.

Seasonal modulation of trapped gravity waves and their imprints on trade wind clouds

2020 ◽  
Author(s):  
Claudia Stephan
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Climate Models ◽  
Global Climate ◽  
Wave Theory ◽  
Internal Gravity Waves ◽  
Global Climate Models ◽  
Trade Wind ◽  
Trapped Waves ◽  
Convective Boundary

<p>Idealized simulations have shown decades ago that shallow clouds generate internal gravity waves, which under certain atmospheric background conditions become trapped inside the troposphere and influence the development of clouds. These feedbacks, which occur at horizontal scales of up to several tens of km are neither resolved, nor parameterized in traditional global climate models (GCMs), while the newest generation of GCMs is starting to resolve them. The interactions between the convective boundary layer and trapped waves have almost exclusively been studied in highly idealized frameworks and it remains unclear to what degree this coupling affects the organization of clouds and convection in the real atmosphere. Here, the coupling between clouds and trapped waves is examined in storm-resolving simulations that span the entirety of the tropical Atlantic and are initialized and forced by meteorological analyses. The coupling between clouds and trapped waves is sufficiently strong to be detected in these simulations of full complexity.  Stronger upper-tropospheric westerly winds are associated with a stronger cloud-wave coupling. In the simulations this results in a highly-organized scattered cloud field with cloud spacings of about 19 km, matching the dominant trapped wavelength. Based on the large-scale atmospheric state wave theory can reliably predict the regions and times where cloud-wave feedbacks become relevant to convective organization. Theory, the simulations and satellite imagery imply a seasonal cycle in the trapping of gravity waves. </p>

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.

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.

The Generation of Internal Gravity Waves in a Multilayered Moving Fluid by a Flap-Type Wave Maker

1985 ◽  
Vol 52 (2) ◽  
pp. 247-252
Author(s):  
M. R. Mu¨ller ◽  
P. C. Shang
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Low Frequencies ◽  
Type Wave ◽  
Wave Maker ◽  
Moving Fluid

Experiments have examined the waveforms generated by a flap-type wave maker in a moving, three-layer fluid. Results show that the observed modulating waveforms could be predicted accurately for low frequencies and that if the two interfaces are sufficiently close together, both mode-one waves (whose amplitude vary in the vertical such that there is only one maximum) and mode-two waves (with a vertical amplitude structure that contains two relative maxima) are generated of similar amplitude. This results in downstream shifts from sinuous to varicose modes of oscillation.

scholarly journals On pressure perturbations caused by a moving heat source of the frontal type (hydrostatic mode)

2019 ◽  
Vol 55 (5) ◽  
pp. 51-61
Author(s):  
M. V. Kalashnik ◽  
S. N. Kulichkov
Keyword(s):  
Heat Source ◽  
Gravity Waves ◽  
Surface Pressure ◽  
Internal Gravity Waves ◽  
Observation Point ◽  
Time Signal ◽  
Moving Heat Source ◽  
Transfer Energy ◽  
Pressure Perturbations ◽  
Additional Excitation

The problem of perturbations of the surface pressure caused by a moving nonstationary frontal heat source (localized along one horizontal coordinate) is considered. Pressure disturbances are associated with internal gravity waves (IGWs). It is shown that when a source moves in a finite-height atmospheric layer (atmospheric waveguide) when a discrete set of vertical IGW modes is excited, there are three types of temporal variation of surface pressure at a fixed observation point. These types correspond respectively to the time signal with amplitude modulation, the signal with frequency modulated Doppler type and the signal that occurs only after passing through the source. Each type is implemented for specific values of the oscillation frequency of the source and the Mach number (the ratio of the speed of the source to the phase velocity of the IGW). At Mach numbers less than one, an oscillating source always excites wave precursors disturbances observed before the source arrives. The movement of the source in a semi-infinite atmosphere leads to additional excitation of waves that transfer energy to the upper layers of the atmosphere.

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