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The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10−4) m2 s−1 and above 1000-m depth is O(10−5) m2 s−1. The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depth-integrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins.

Recent microstructure observations in the Southern Ocean report enhanced internal gravity waves and turbulence in the frontal regions of the Antarctic Circumpolar Current extending a kilometer above rough bottom topography. Idealized numerical simulations and linear theory show that geostrophic flows impinging on rough small-scale topography are very effective generators of internal waves and estimate vigorous wave radiation, breaking, and turbulence within a kilometer above bottom. However, both idealized simulations and linear theory assume periodic and spatially uniform topography and tend to overestimate the observed levels of turbulent energy dissipation locally at the generation sites. In this study, we explore the downstream evolution and remote dissipation of internal waves generated by geostrophic flows using a series of numerical, realistic topography simulations and parameters typical of Drake Passage. The results show that significant levels of internal wave kinetic energy and energy dissipation are present downstream of the rough topography, internal wave generation site. About 30%–40% of the energy dissipation occurs locally over the rough topography region, where internal waves are generated. The rest of the energy dissipation takes place remotely and decays downstream of the generation site with an e -folding length scale of up to 20–30 km. The model we use is two-dimensional with enhanced viscosity coefficients, and hence it can result in the underestimation of the remote wave dissipation and its decay length scale. The implications of our results for turbulent energy dissipation observations and mixing parameterizations are discussed.

The Kuroshio and tides significantly influence the oceanic environment off the Japanese mainland and promote mass/heat transport. However, the interaction between the Kuroshio and tides/internal waves has not been examined in previous works. To investigate this phenomenon, the two-dimensional high-resolution nonhydrostatic oceanic Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) model was employed. The results show that strong internal tides propagating upstream in the Kuroshio are generated at a near-critical internal Froude number (Fr i = 0.91). The upstream internal wave energy flux reaches a magnitude of 12 kW m −1 , which is approximately 3 times higher than that of internal waves without the Kuroshio. On the other hand, under supercritical conditions, the Kuroshio suppresses the internal wave energy flux. The interaction of internal tides and the Kuroshio also generates upstream propagating high-frequency internal waves and solitary wave packets. The high-frequency internal waves contribute to the increase in the total internal wave energy flux up to 40% at the near-critical Fr i value. The results of this study suggest that the interaction of internal tides and the Kuroshio enhances the upstream propagating internal tides under the specified conditions (Fr i ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

Internal waves are predominantly generated by winds, tide/topography interactions and balanced flow/topography interactions. Observations of vertical shear of horizontal velocity ( u z , v z ) from LADCP profiles conducted during GO-SHIP hydrographic surveys, as well as vessel-mounted sonars, are used to interpret these signals. Vertical directionality of intermediate-wavenumber [λ z ~ (100 m)] internal waves is inferred in this study from rotary-with-depth shears. Total shear variance and vertical asymmetry ratio (Ω), i.e. the normalized difference between downward- and upward-propagating intermediate wavenumber shear variance, where Ω > 0 (< 0) indicates excess downgoing (upgoing) shear variance, are calculated for three depth ranges: 200-600 m, 600 m to 1000 mab (meters above bottom), and below 1000 mab. Globally, downgoing (clockwise-with-depth in the northern hemisphere) exceeds upgoing (counterclockwise-with-depth in the northern hemisphere) shear variance by 30% in the upper 600 m of the water column (corresponding to the globally averaged asymmetry ratio of = 0.13), with a near-equal distribution below 600-m depth ( ~ 0). Downgoing shear variance in the upper water column dominates at all latitudes. There is no statistically significant correlation between the global distribution of Ω and internal wave generation, pointing to an important role for processes that re-distribute energy within the internal wave continuum on wavelengths of (100 m).

Based on the analytical and numerical solutions as well as unexpected observed damages to the buildings and long-span structures in the epicentral zone of large shallow earthquakes, structural engineers have concluded that coseismic vertical ground motion play a major role in the damages. Recent researches have revealed the generation of high frequency Rayleigh wave with large amplitude in the epicentral zone of shallow earthquakes. Further, there is meta-response of a building at its longitudinal resonance frequency as compared to flexural resonance frequency during interaction with the Rayleigh waves. This paper presents the physics behind Rayleigh wave generation in the homogeneous half-space due to an incident SV-wave at the free surface and numerical quantification of variation of dominant frequency and spectral amplitudes of the generated Rayleigh waves with focal depth, Poisson's ratio and the rise-time of the point earthquake. It is concluded that the coupling of evanescence P-wave with the critically reflected SV-wave at/just after the critical point generates Rayleigh waves. Further, generation process is not immediate just after the critical point, but, it occurs over a span at least equal to one wavelength. A relation is established between depth of point earthquake and dominant wavelength of Rayleigh wave and this relation is unaffected by the change of Poisson’s ratio, rise-time and depth of point earthquake source. There is an exponential decrease of percentage conversion of the critically incident SV-wave energy in to the Rayleigh wave energy with an increase of focal-depth. Further, this percentage conversion increases with decrease of Poisson’s ratio and an increase of rise-time of the earthquake.

Only limited information is currently available on the evolution of waves generated by wind that varies in time, and in particular on the initial stages of wind–wave growth from rest under a suddenly applied wind forcing. The emerging wind–wave field varies in time as well as in space. Detailed knowledge of wave parameter distributions under those conditions contributes to a better understanding of the mechanisms of wind wave generation. In the present study, the instantaneous surface elevation and two components of the instantaneous surface slope were recorded at various fetches in a small-scale experimental facility under nearly impulsive wind forcing. Numerous independent realizations have been recorded for each selection of operational conditions. Sufficient data at a number of fetches were accumulated to calculate reliable ensemble-averaged statistical parameters of the evolving random wind–wave field as a function of the time elapsed from activation of wind forcing. Distinct stages in the wave evolution process from appearance of initial ripples to emergence of a quasi-steady wind–wave field were identified. The experimental results during each stage of evolution were analysed in view of the viscous instability theory by Kawai (J. Fluid Mech., vol. 93, 1979, pp. 661–703) and the resonance model by Phillips (J. Fluid Mech., vol. 2, 1957, pp. 417–445).

In this paper, we use asymptotic theory and numerical methods to study resonant triad interactions among discrete internal wave modes at a fixed frequency ($\\omega$) in a two-dimensional, uniformly stratified shear flow. Motivated by linear internal wave generation mechanisms in the ocean, we assume the primary wave field as a linear superposition of various horizontally propagating vertical modes at a fixed frequency $\\omega$. The weakly nonlinear solution associated with the primary wave field is shown to comprise superharmonic (frequency $2\\omega$) and zero frequency wave fields, with the focus of this study being on the former. When two interacting primary modes $m$ and $n$ are in triadic resonance with a superharmonic mode $q$, it results in the divergence of the corresponding superharmonic secondary wave amplitude. For a given modal interaction $(m, n)$, the superharmonic wave amplitude is plotted on the plane of primary wave frequency $\\omega$ and Richardson number $Ri$, and the locus of divergence locations shows how the resonance locations are influenced by background shear. In the limit of weak background shear ($Ri\\to \\infty$), using an asymptotic theory, we show that the horizontal wavenumber condition $k_m + k_n = k_q$ is sufficient for triadic resonance, in contrast to the requirement of an additional vertical mode number condition ($q = |m-n|$) in the case of no shear. As a result, the number of resonances for an arbitrarily weak shear is significantly larger than that for no shear. The new resonances that occur in the presence of shear include the possibilities of resonance due to self-interaction and resonances that occur at the seemingly trivial limit of $\\omega \\approx 0$, both of which are not possible in the no shear limit. Our weak shear limit conclusions are relevant for other inhomogeneities such as non-uniformity in stratification as well, thus providing an understanding of several recent studies that have highlighted superharmonic generation in non-uniform stratifications. Extending our study to finite shear (finite $Ri$) in an ocean-like exponential shear flow profile, we show that for cograde–cograde interactions, a significant number of divergence curves that start at $Ri\\to \\infty$ will not extend below a cutoff $Ri$ $\\sim O(1)$. In contrast, for retrograde–retrograde interactions, the divergence curves extend all the way from $Ri\\to \\infty$ to $Ri = 0.5$. For mixed interactions, new divergence curves appear at $\\omega = 0$ for $Ri\\sim O(10)$ and extend to other primary wave frequencies for smaller $Ri$. Consequently, the total ($\\text {cograde} + \\text {retrograde} + \\text {mixed}$) number of resonant triads is of the same order for small $Ri\\approx 0.5$ as in the limit of weak shear ($Ri\\to \\infty$), although it attains a maximum at $Ri\\sim O(10)$.

Strong bidirectional internal solitary waves (ISWs) generate from a shallow channel between Car Nicobar and Chowra Islands of Nicobar Islands, India, and propagate toward the Andaman Sea (eastward) and Bay of Bengal (westward). Batti Malv Island separates this shallow channel into two ridges, north of Batti Malv (NBM) and south of Batti Malv (SBM). First, this study identifies the prominent mode-1 and mode-2 ISWs emerging from NBM and SBM using synthetic aperture radar images and then explores their generation mechanism(s) using a nonlinear, unstructured, and nonhydrostatic model, SUNTANS. During spring tide, flow over NBM is supercritical with respect to mode-1 internal wave. Model simulations reveal that mode-1 ISWs are generated at NBM by a “lee wave mechanism” and propagate both in the east and west directions depending on the tidal phases. However, the flow over SBM is subcritical with respect to mode-1 internal wave. The bidirectional propagating mode-1 ISWs evolve from a long-wave disturbance induced by “upstream influence.” But, during spring tide, with an increased tidal flow over SBM, it is observed that the westward propagating ISWs are formed by a dispersed hydraulic jump observed over the ridge. Moreover, the bidirectional mode-2 waves from SBM are generated by a lee wave mechanism. An energy budget comparison reveals that the region surrounding NBM is efficient in radiating low-mode baroclinic energy (0.98 GW), while SBM is highly efficient in converting barotropic to baroclinic energy (4.1 GW).

Using a nonlinear model of the general circulation of the middle and upper atmosphere (MUAM), spatio-temporal structures of planetary waves (PWs) during boreal winter were studied. Modeling of global atmospheric circulation was performed for January–February. Despite the tropospheric PW sources shaped in the model, the phenomenon of 16-day PW excitation arise out of internal atmospheric sources in the southern lower thermosphere was discovered. To explain the observed phenomenon, a number of numerical experiments were carried out according to different scenarios with a selective turning (on/off) tropospheric sources of PW individual modes (having periods of 4–16 days) in the model. Also, the evolution of perturbed potential enstrophy for a 16-day PW, as well as the contribution of nonlinear interactions between individual PW to it, was studied. This made it possible for the first time to demonstrate explicitly the process of generation a secondary 16-day PW as a result of the nonlinear interconnection of 4-day and 5-day PWs. Graphical Abstract

Direct observations in the Southern Ocean report enhanced internal wave activity and turbulence in a kilometer-thick layer above rough bottom topography collocated with the deep-reaching fronts of the Antarctic Circumpolar Current. Linear theory, corrected for finite-amplitude topography based on idealized, two-dimensional numerical simulations, has been recently used to estimate the global distribution of internal wave generation by oceanic currents and eddies. The global estimate shows that the topographic wave generation is a significant sink of energy for geostrophic flows and a source of energy for turbulent mixing in the deep ocean. However, comparison with recent observations from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean shows that the linear theory predictions and idealized two-dimensional simulations grossly overestimate the observed levels of turbulent energy dissipation. This study presents two- and three-dimensional, realistic topography simulations of internal lee-wave generation from a steady flow interacting with topography with parameters typical of Drake Passage. The results demonstrate that internal wave generation at three-dimensional, finite bottom topography is reduced compared to the two-dimensional case. The reduction is primarily associated with finite-amplitude bottom topography effects that suppress vertical motions and thus reduce the amplitude of the internal waves radiated from topography. The implication of these results for the global lee-wave generation is discussed.