Swimming of a ludion in a stratified sea

We describe and model experimental results on the dynamics of a ‘ludion’ – a neutrally buoyant body – immersed in a layer of stably stratified salt water. By oscillating a piston inside a cylinder communicating with a narrow (in one of its horizontal dimensions) vessel containing the stably stratified layer of salt water, it is easy to periodically vary the hydrostatic pressure of the fluid. The ludion or Cartesian diver, initially positioned at its equilibrium height and free to move horizontally, can then oscillate vertically when forced by the pressure oscillations. Depending on the ratio of the forcing frequency to the Brunt–Väisälä frequency of the stratified fluid, the ludion can emit its own internal gravity waves that we measure by a classical particle image velocimetry technique. Our experimental results describe first the resonance of the vertical motions of the ludion when excited at different frequencies. A theoretical oscillator model is then derived taking into account added mass and added friction coefficients and its predictions are compared with the experimental data. Then, for the larger oscillation amplitudes, we observe and describe a bifurcation towards free horizontal motions. Although the internal gravity wave frequencies are affected by the Doppler shift induced by the horizontal displacement velocities, it seems that, contrary to surface waves associated with Couder walkers (Couder et al. Nature, vol. 437, 2005, p. 238) they are not the cause of the horizontal swimming. This does not, however, exclude possible interactions between the ludion and internal gravity waves and possible hydrodynamic quantum analogies to be explored in the future.

Dynamic soliton–mean flow interaction with non-convex flux

The interaction of localised solitary waves with large-scale, time-varying dispersive mean flows subject to non-convex flux is studied in the framework of the modified Korteweg–de Vries (mKdV) equation, a canonical model for internal gravity wave propagation and potential vorticity fronts in stratified fluids. The effect of large amplitude, dynamically evolving mean flows on the propagation of localised waves – essentially ‘soliton steering’ by the mean flow – is considered. A recent theoretical and experimental study of this new type of dynamic soliton–mean flow interaction for convex flux has revealed two scenarios where the soliton either transmits through the varying mean flow or remains trapped inside it. In this paper, it is demonstrated that the presence of a non-convex cubic hydrodynamic flux introduces significant modifications to the scenarios for transmission and trapping. A reduced set of Whitham modulation equations is used to formulate a general mathematical framework for soliton–mean flow interaction with non-convex flux. Solitary wave trapping is stated in terms of crossing modulation characteristics. Non-convexity and positive dispersion – common for stratified fluids – imply the existence of localised, sharp transition fronts (kinks). Kinks play dual roles as a mean flow and a wave, imparting polarity reversal to solitons and dispersive mean flows, respectively. Numerical simulations of the mKdV equation agree with modulation theory predictions. The mathematical framework developed is general, not restricted to completely integrable equations like mKdV, enabling application beyond the mKdV setting to other fluid dynamic contexts subject to non-convex flux such as strongly nonlinear internal wave propagation that is prevalent in the ocean.

Optimal perturbation growth on a breaking internal gravity wave

The breaking of internal gravity waves in the abyssal ocean is thought to be responsible for much of the mixing necessary to close oceanic buoyancy budgets. The exact mechanism by which these waves break down into turbulence remains an active area of research and can have significant implications on the mixing efficiency. Recent evidence has suggested that both shear instabilities and convective instabilities play a significant role in the breaking of an internal gravity wave in a high Richardson number mean shear flow. We perform a systematic analysis of the stability of a configuration of an internal gravity wave superimposed on a background shear flow first considered by Howland et al. (J. Fluid Mech., vol. 921, 2021, A24), using direct–adjoint looping to find the perturbation giving maximal energy growth on this evolving flow. We find that three-dimensional, convective mechanisms produce greater energy growth than their two-dimensional counterparts. In particular, we find close agreement with the direct numerical simulations of Howland et al. (J. Fluid Mech., 2021, in press), which demonstrated a clear three-dimensional mechanism causing breakdown to turbulence. The results are shown to hold at realistic Prandtl numbers. At low mean Richardson numbers, two-dimensional, shear-driven mechanisms produce greater energy growth.

Tsunami detection by GPS-derived ionospheric total electron content

To unravel the relationship between earthquake and tsunami using ionospheric total electron content (TEC) changes, we analyzed two Chilean tsunamigenic subduction earthquakes: the 2014 Pisagua Mw 8.1 and the 2015 Illapel Mw 8.3. During the Pisagua earthquake, the TEC changes were detected at the GPS sites located to the north and south of the earthquake epicenter, whereas during the Illapel earthquake, we registered the changes only in the northward direction. Tide-gauge sites mimicked the propagation direction of tsunami waves similar to the TEC change pattern during both earthquakes. The TEC changes were represented by three signals. The initial weaker signal correlated well with Acoustic Rayleigh wave (AWRayleigh), while the following stronger perturbation was interpreted to be caused by Acoustic Gravity wave (AGWepi) and Internal Gravity wave (IGWtsuna) induced by earthquakes and subsequent tsunamis respectively. Inevitably, TEC changes can be utilized to evaluate earthquake occurrence and tsunami propagation within a framework of multi-parameter early warning systems.

Variability and sources of the internal wave continuum examined from global moored velocity records

Energy for ocean turbulence is thought to be transferred from its presumed sources (namely, the mesoscale eddy field, near-inertial internal waves and internal tides) to the internal wave continuum, and through the continuum via resonant triad interactions to breaking scales. To test these ideas, the level and variability of the oceanic internal gravity wave continuum spectrum are examined by computing time-dependent rotary spectra from a global database of 2260 current meter records deployed on 1362 separate moorings. Time series of energy in the continuum and the three “source bands” (near-inertial, tidal and mesoscale) are computed, and their variability and covariability examined. Seasonal modulation of the continuum by factors of up to 5 is seen in the upper ocean, implicating wind-driven near-inertial waves as an important source. The time series of the continuum is found to correlate more strongly with the near-inertial peak than with the semi-diurnal or mesoscale. The use of moored internal-wave kinetic energy frequency spectra as an alternate input to the traditional shear or strain wavenumber spectra in the Gregg-Henyey-Polzin finescale parameterization is explored and compared to traditional strain-based estimates.

Two-dimensional internal gravity wave beam instability

<p>The instability of propagating internal gravity waves is of long-standing interest in geophysical fluid dynamics since breaking gravity waves exchange energy and momentum with the large-scale flow and hence support the large-scale circulation. In this study a low-order gravity wave beam model is used to delineate the linear stability of wave beams and also to study subcritical non-modal transient instability. Assuming that the dissipation of the linearly unstable beam equilibrates with the small-scale turbulence, the model explains the constancy with the height of the amplitude of the wave beam, so that oblique wave beams can reach significant altitudes without disintegrating due to the instability that arises [1]. We further study the robustness of the transient growth when the initial condition for optimal growth is randomly perturbed [2]. It is concluded that for full randomization, in particular, shallow wave beams can show subcritical growth when entering a turbulent background field. Such growing and eventually breaking wave beams might add turbulence to existing background turbulence that originates from other sources of instability.</p><p>[1] Kurgansky and Harlander (2021) Two-dimensional internal gravity wave beam instability. Part I: Linear theory, submitted.</p><p>[2] Harlander and Kurgansky (2021) Two-dimensional internal gravity wave beam instability. Part II: Subcritical instability, submitted.</p>

Spatial and temporal analysis of high-frequency internal gravity wave signatures in brightness temperature satellite images

<p>Highly idealized model studies suggest that convectively generated internal gravity waves in the troposphere with horizontal wavelengths on the order of a few kilometers may affect the lifetime, spacing, and depth of clouds and convection. To answer whether such a convection-wave coupling occurs in the real atmosphere, one needs to find corresponding events in observations. In general, the study of high-frequency internal gravity wave-related phenomena in the troposphere is a challenging task because they are usually small-scale and intermittent. To overcome case-by-case studies, it is desirable to have an automatic method to analyze as much data as possible and provide enough independent and diverse evidence.<br>Here, we focus on brightness temperature satellite images, in particular so-called satellite water vapor channels. These channels measure the radiation at wavelengths corresponding to the energy emitted by water vapor and provide cloud-independent observations of internal gravity waves, in contrast to visible and other infrared satellite channels where one relies on the wave impacts on clouds. In addition, since these water vapor channels are sensitive to certain vertical layers in the troposphere, combining the images also reveals some vertical structure of the observed waves.<br>We propose an algorithm based on local Fourier analyses to extract information about high-frequency wave patterns in given brightness temperature images. This method allows automatic detection and analysis of many wave patterns in a given domain at once, resulting in a climatology that provides an initial observational basis for further research. Using data from the instrument ABI on board the satellite GOES-16 during the field campaign EUREC<sup>4</sup>A, we demonstrate the capabilities and limitations of the method. Furthermore, we present the respective climatology of the detected waves and discuss approaches based on this to address the initial question.</p>

On strongly nonlinear gravity waves in a vertically sheared atmosphere

<p>Internal gravity waves are a well-known mechanism of energy redistribution in stratified fluids such as the atmosphere. They may propagate from their generation region, typically in the Troposphere, up to high altitudes. During their lifetime internal waves couple to the atmospheric background through various processes. Among the most important interactions are the exertion of wave drag on the horizontal mean-flow, the heat generation upon wave breaking, or the mixing of atmospheric tracers such as aerosols or greenhouse gases.</p><p>Many of the known internal gravity wave properties and interactions are covered by linear or weakly nonlinear theories. However, for the consideration of some of the crucial effects, like a reciprocal wave-mean-flow interaction including the exertion of wave drag on the mean-flow, strongly nonlinear systems are required. That is, there is no assumption on the wave amplitude relative to the mean-flow strength such that they may be of the same order.</p><p>Here, we exploit a strongly nonlinear Boussinesq theory to analyze the stability of a stationary internal gravity wave which is refracted at the vertical edge of a horizontal jet. Thereby we assume that the incident wave is horizontally periodic, non-hydrostatic, and vertically modulated. Performing a linear stability analysis in the vicinity of the jet edge we find necessary and sufficient criteria for instabilities to grow. In particular, the refracted wave becomes unstable if its incident amplitude is large enough and both mean-flow horizontal winds, below and above the edge of the jet, do not exceed particular upper bounds.</p>

Slow earthquake signatures in the ratio between acoustic and internal gravity wave amplitudes in coseismic ionospheric disturbances

<p>Frequency spectra of seismic waves from a fault rupture reflects the size of the faults, i.e. relatively large amplitudes of long period waves are excited by larger earthquakes. Anomalies in rise times of the fault movements would also influence the spectra. For example, earthquakes characterized by slow faulting, known as tsunami earthquakes, excite large tsunamis for the amplitudes of short-period seismic waves. In this study, we compare amplitudes of long- and short-period atmospheric waves excited by vertical crustal movements associated with earthquake faulting. Such atmospheric waves often reach the ionospheric F region and cause coseismic ionospheric disturbances (CID) observed as oscillations in ionospheric total electron content (TEC), with ground Global Navigation Satellite System (GNSS) receivers. CID often includes long-period internal gravity wave (IGW) components in addition to short period acoustic wave (AW) components. The latter has a period of ~4 minutes and propagate by 0.8-1.0 km/s, while the former has a period of ~12 minutes and propagate as fast as 0.2-0.3 km/s. Here we compare amplitudes of these two different waves for five earthquakes, 2011 Tohoku-oki (Mw9.0), 2010 Maule (Mw8.8), 1994 Hokkaido-Toho-Oki (Mw8.3), 2003 Tokachi-oki (Mw8.0), and the 2010 Mentawai (Mw7.9) earthquakes, using data from regional dense GNSS networks. We found two important features, i.e. (1) larger earthquakes show larger IGW/AW amplitude ratios, and (2) Mentawai earthquake, a typical tsunami earthquake, exhibits abnormally large IGW amplitudes relative to AW amplitudes. These findings demonstrate that earthquakes with longer durations for faulting, or with longer times for vertical crustal movements, excite longer period atmospheric waves such as IGW more efficiently.</p>