Nonlinear disintegration of the internal tide

The disintegration of a first-mode internal tide into shorter solitary-like waves is considered. Because observations frequently show both tides and waves with amplitudes beyond the restrictions of weakly nonlinear theory, the evolution is studied using a fully-nonlinear, weakly nonhydrostatic two-layer theory that included the effects of rotation. In the hydrostatic limit, the governing equations have periodic, nonlinear inertia-gravity solutions that are explored as models of the nonlinear internal tide. These are shown to be robust to weak nonhydrostatic effects. Numerical solutions show that the disintegration of an initially sinusoidal, linear internal tide is closely linked to the presence of these periodic waves. The initial tide steepens due to nonlinearity and sheds energy into short solitary waves. The disintegration is halted as the longwave part of the solution settles onto a state close to one of the nonlinear, hydrostatic solutions, with the short solitary waves superimposed. The degree of disintegration depends upon the initial amplitude of the tide and the properties of the underlying nonlinear solutions, which, depending on stratification and tidal frequency, exist only for a finite range of amplitudes (or energies). There is a lower threshold below which no short solitary waves are produced. However, for initial amplitudes above another threshold, given approximately by the energy of the limiting nonlinear inertia-gravity wave, most of the initial tidal energy goes into solitary waves. Recent observations of large amplitude solitary waves in the South China Sea are discussed in the context of these model results

Optimal transient growth in thin-interface internal solitary waves

The dynamics of perturbations to large-amplitude internal solitary waves (ISWs) in two-layered flows with thin interfaces is analysed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough ) of potentially unstable Richardson number, <[CDATA Ri. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with . The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local Wentzel-Kramers-Brillouin (WKB) approximation for spatially growing Kelvin-Helmholtz (K-H) waves through the <[CDATA Ri zone. The WKB approach is able to capture properties (e.g. carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K-H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave. Two-dimensional numerical calculations of the nonlinear evolution of optimal disturbance packets leads to the generation of large-amplitude K-H billows that can emerge on the leading face of the wave and that break down into turbulence in the lee of the wave. The nonlinear calculations are used to derive a slowly varying model of ISW decay due to repeated encounters with optimal or free wave packets. Field observations of unstable ISW by Moum et al. (J. Phys. Oceanogr., vol. 33 (10), 2003, pp. 2093-2112) are consistent with excitation by optimal disturbances

Hard-Sphere Fluids in Contact with Curved Substrates

The properties of a hard-sphere fluid in contact with hard spherical and cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is applied to determine the density profile and surface tension $\gamma$ for wide ranges of radii of the curved walls and densities of the hard-sphere fluid. Particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to $\gamma$ that is proportional to the logarithm of the radius of curvature. Moreover, by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard-sphere fluid close to arbitrary hard convex walls. The agreement between the analytical expression and DFT is good. Our results show no signs for the existence of a logarithmic term in the curvature dependence of $\gamma$.Comment: 15 pages, 6 figure

The formation and fate of internal waves in the South China Sea

Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis1, sediment and pollutant transport2 and acoustic transmission3; they also pose hazards for man-made structures in the ocean4. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking5, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects6,7. For over a decade, studies8-11 have targeted the South China Sea, where the oceans' most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions

MIBiG 3.0: a community-driven effort to annotate experimentally validated biosynthetic gene clusters

Microbial Biotechnolog

Testing the physical oceanographic implications of the suggested sudden Black Sea infill 8400 years ago

We apply a shock-capturing numerical model based on the single-layer shallow water equations to an idealized geometry of the Black Sea and the Sea of Marmara in order to test the implications of a suggested sudden Black Sea infill 8400 years ago. The model resolves the two-dimensional flow upstream and downstream of the hydraulic jump provoked by the cascade of water from the Sea of Marmara into the Black Sea, which would occur during a sudden Black Sea infill. The modeled flow downstream of the hydraulic jump in the Black Sea would consist of a jet that is in part constrained by bathymetric contours. Guided by the Bosporus Canyon, the modeled jet reaches depths of up to 2000 m and could explain the origin of the sediment waves observed at this depth. At a late stage of the infill the modeled jet is attached to the coast and might account for the course of a submerged channel at the mouth of the Bosporus. The preservation of continuous barrier-washover-lagoonal fill systems occurring on the Black Sea shelf is, however, not easily reconcilable with the large flows over the southwest Black Sea shelf predicted by the model. Intensified flow in the upstream basin (Sea of Marmara) is restricted to the immediate vicinity of the Bosporus, suggesting that a sudden reconnection need not have disturbed sediments in the wider Sea of Marmara