scholarly journals The energy flux spectrum of internal waves generated by turbulent convection

2018 ◽  
Vol 854 ◽  
Author(s):  
Louis-Alexandre Couston ◽  
Daniel Lecoanet ◽  
Benjamin Favier ◽  
Michael Le Bars
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
Three Dimensional ◽  
Turbulent Convection ◽  
Reynolds Stresses ◽  
Wave Energy Flux ◽  
Flux Spectrum ◽  
The Waves ◽  
Good Agreement

We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of mixed convective and stably stratified fluids. We demonstrate that in the limit of large Rayleigh number ($Ra\in [4\times 10^{7},10^{9}]$) and large stratification (Brunt–Väisälä frequencies$f_{N}\gg f_{c}$, where$f_{c}$is the convective frequency), simulations are in good agreement with a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region as described in Lecoanet & Quataert (Mon. Not. R. Astron. Soc., vol. 430 (3), 2013, pp. 2363–2376). Specifically, we demonstrate that the wave energy flux spectrum scales like$k_{\bot }^{4}\,f^{-13/2}$for weakly damped waves (with$k_{\bot }$and$f$the waves’ horizontal wavenumbers and frequencies, respectively), and that the total wave energy flux decays with$z$, the distance from the convective region, like$z^{-13/8}$.

Diapycnal diffusivity induced by the breaking of lee waves

2020 ◽  
Author(s):  
Thomas Eriksen ◽  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
Diapycnal Mixing ◽  
Overturning Circulation ◽  
Lee Waves ◽  
Lee Wave ◽  
Wave Energy Flux ◽  
Diapycnal Diffusivity

<p>A key component in setting the large scale ocean circulation is the process of diapycnal mixing, since this can drive the meridional overturning circulation. Diapycnal mixing in the interior ocean is predominantly associated with the breaking of internal waves. Traditionally, diapycnal mixing has been represented in ocean models by a diapycnal diffusivity either constant or exponentially decreasing with depth. This approach, however, does not take into account the actual physics behind the breaking of internal waves. The energetically consistent internal wave model IDEMIX (Internal wave Dissipation, Energetics and MIXing), on the other hand, computes diffusivities directly on the basis of internal wave energetics. One such type of internal waves are lee waves. These are generated and subsequently dissipated when geostrophic currents interact with bottom topography and are therefore believed to be a source of energy for deep ocean mixing. In this study IDEMIX is coupled to a 1/12<sup>th</sup> degree regional model of the Atlantic. The lee wave energy flux is calculated and used as a bottom flux at each time step effectively allowing lee waves to propagate, interact with mean flow and waves, and subsequently dissipate. This setup enables not only an estimate of the lee wave energy flux but also a direct investigation of the influence of lee waves on dissipation, stratification and horizontal and overturning circulation.</p>

scholarly journals Strong Internal Waves Generated by the Interaction of the Kuroshio and Tides over a Shallow Ridge

2019 ◽  
Vol 49 (11) ◽  
pp. 2917-2934 ◽  
Author(s):  
Eiji Masunaga ◽  
Yusuke Uchiyama ◽  
Hidekatsu Yamazaki
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Energy Flux ◽  
Wave Energy ◽  
High Frequency ◽  
Deep Ocean ◽  
Internal Tides ◽  
Navier Stokes ◽  
Wave Energy Flux ◽  
The Kuroshio

AbstractThe 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 (Fri = 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 Fri 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 (Fri ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

scholarly journals Energetics of Seamount Wakes. Part II: Wave Fluxes

2020 ◽  
Vol 50 (5) ◽  
pp. 1383-1398 ◽  
Author(s):  
B. Perfect ◽  
N. Kumar ◽  
J. J. Riley
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Parameter Space ◽  
Energy Flux ◽  
Wave Energy ◽  
Wave Model ◽  
Barotropic Flow ◽  
Unsteady Wake ◽  
Lee Wave ◽  
Wave Energy Flux

AbstractSeamounts are thought to facilitate ocean mixing through unsteady wake processes, and through the generation of internal waves, which propagate away from the seamount and later break. The relative importance of these processes is examined for idealized, isolated seamounts (with characteristic width D and height H) in uniform barotropic flow U. A range of Coriolis parameters f and buoyancy frequencies N are used such that a broad parameter space of low Froude numbers (U/NH) and low Rossby numbers (U/fD) is considered. Results indicate that eddy processes energetically dominate the internal wave energy flux in this range of parameter space. The internal wave field is specifically examined and partitioned into steady lee waves and unsteady, wake-generated waves. It is found that the lee wave energy flux cannot be explained by existing analytical theories. A lee wave model by Smith is then extended into the low-Froude-number regime and the effect of rotation is included. While strongly stratified experiments have previously indicated that only the top U/N of an obstacle generates internal waves, the effect of rotation appears to modify this wavemaking height. Once the U/N height is revised to account for rotation, the lee wave energy flux can be reasonably accurately reproduced by the extended Smith model.

scholarly journals Joint Modelling of Wave Energy Flux and Wave Direction

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 460
Author(s):  
Takvor H. Soukissian ◽  
Flora E. Karathanasi
Keyword(s):  
Energy Flux ◽  
Wave Energy ◽  
Goodness Of Fit ◽  
North Atlantic Ocean ◽  
Wave Climate ◽  
Western Mediterranean ◽  
Wave Direction ◽  
Bivariate Model ◽  
The North ◽  
Wave Energy Flux

In the context of wave resource assessment, the description of wave climate is usually confined to significant wave height and energy period. However, the accurate joint description of both linear and directional wave energy characteristics is essential for the proper and detailed optimization of wave energy converters. In this work, the joint probabilistic description of wave energy flux and wave direction is performed and evaluated. Parametric univariate models are implemented for the description of wave energy flux and wave direction. For wave energy flux, conventional, and mixture distributions are examined while for wave direction proven and efficient finite mixtures of von Mises distributions are used. The bivariate modelling is based on the implementation of the Johnson–Wehrly model. The examined models are applied on long-term measured wave data at three offshore locations in Greece and hindcast numerical wave model data at three locations in the western Mediterranean, the North Sea, and the North Atlantic Ocean. A global criterion that combines five individual goodness-of-fit criteria into a single expression is used to evaluate the performance of bivariate models. From the optimum bivariate model, the expected wave energy flux as function of wave direction and the distribution of wave energy flux for the mean and most probable wave directions are also obtained.

Horizontal energy flux of wind-driven intraseasonal waves in the tropical Atlantic by a unified diagnosis

2021 ◽  
Author(s):  
Qingyang Song ◽  
Hidenori Aiki
Keyword(s):  
Energy Flux ◽  
Wave Energy ◽  
Horizontal Distribution ◽  
Kelvin Waves ◽  
Asymmetric Distribution ◽  
Central Basin ◽  
Tropical Atlantic ◽  
Equatorial Wave ◽  
Wave Energy Flux ◽  
Velocity Anomalies

AbstractIntraseasonal waves in the tropical Atlantic Ocean have been found to carry prominent energy that affects interannual variability of zonal currents. This study investigates energy transfer and interaction of wind-driven intraseasonal waves using single-layer model experiments. Three sets of wind stress forcing at intraseasonal periods of around 30 days, 50 days and 80 days with a realistic horizontal distribution are employed separately to excite the second baroclinic mode in the tropical Atlantic. A unified scheme for calculating the energy flux, previously approximated and used for the diagnosis of annual Kelvin and Rossby waves, is utilized in the present study in its original form for intraseasonal waves. Zonal velocity anomalies by Kelvin waves dominate the 80-day scenario. Meridional velocity anomalies by Yanai waves dominate the 30-day scenario. In the 50-day scenario, the two waves have comparable magnitudes. The horizontal distribution of wave energy flux is revealed. In the 30-day and 50-day scenarios, a zonally alternating distribution of cross-equatorial wave energy flux is found. By checking an analytical solution excluding Kelvin waves, we confirm that the cross-equatorial flux is caused by the meridional transport of geopotential at the equator. This is attributed to the combination of Kelvin and Yanai waves and leads to the asymmetric distribution of wave energy in the central basin. Coastally-trapped Kelvin waves along the African coast are identified by along-shore energy flux. In the north, the bend of the Guinea coast leads the flux back to the equatorial basin. In the south, the Kelvin waves strengthened by local wind transfer the energy from the equatorial to Angolan regions.

scholarly journals Another Note on Rossby Wave Energy Flux

2020 ◽  
Vol 50 (2) ◽  
pp. 531-534
Author(s):  
Theodore S. Durland ◽  
J. Thomas Farrar
Keyword(s):  
Group Velocity ◽  
Energy Flux ◽  
Rossby Wave ◽  
Wave Energy ◽  
Energy Equation ◽  
Divergent Part ◽  
Pressure Work ◽  
Wave Energy Flux ◽  
The Difference ◽  
Definition Of

AbstractLonguet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.

scholarly journals Probabilistic forecasting of the wave energy flux

2012 ◽  
Vol 93 ◽  
pp. 364-370 ◽  
Author(s):  
P. Pinson ◽  
G. Reikard ◽  
J.-R. Bidlot
Keyword(s):  
Energy Flux ◽  
Wave Energy ◽  
Probabilistic Forecasting ◽  
Wave Energy Flux

scholarly journals Rotational Effects on Reynolds Stresses in the Solar Convection Zone

1991 ◽  
Vol 130 ◽  
pp. 98-100
Author(s):  
P. Pulkkinen ◽  
I. Tuominen ◽  
A. Brandenburg ◽  
Å. Nordlund ◽  
R.F. Stein
Keyword(s):  
Reynolds Stress ◽  
Convection Zone ◽  
Rotation Axis ◽  
Three Dimensional ◽  
External Parameter ◽  
Reynolds Stresses ◽  
Solar Convection Zone ◽  
Hydrodynamic Simulations ◽  
Solar Convection ◽  
Good Agreement

AbstractThree-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the ∧-effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement is found.

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