Turbulent Dissipation Rate
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Abstract We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber – frequency (m – w) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a ‘local’ and a ‘scale-separated’ contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed ‘no-flux’ solutions are reinstated to the status of ‘constant-downscale-flux’ solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of ‘Oceanic Ultraviolet Catastrophe’.

Md Mizanur Rahman ◽  
Khalid Hasan ◽  
Wenchang Liu ◽  
Xinming Li

A new zero-equation model (ZEM) is devised with an eddy-viscosity formulation using a stress length variable which the structural ensemble dynamics (SED) theory predicts. The ZEM is distinguished by obvious physical parameters, quantifying the underlying flow domain with a universal multi-layer structure. The SED theory is also utilized to formulate an anisotropic Bradshaw stress-intensity factor, parameterized with an eddy-to-laminar viscosity ratio. Bradshaw’s structure function is employed to evaluate the kinetic energy of turbulence k and turbulent dissipation rate epsilon  . The proposed ZEM is intrinsically plausible, having a dramatic impact on the prediction of wall-bounded turbulence. 

2021 ◽  
Vol 926 ◽  
A.F. Wienkers ◽  
L.N. Thomas ◽  
J.R. Taylor

In Part 1 (Wienkers, Thomas & Taylor, J. Fluid Mech., vol. 926, 2021, A6), we described the theory for linear growth and weakly nonlinear saturation of symmetric instability (SI) in the Eady model representing a broad frontal zone. There, we found that both the fraction of the balanced thermal wind mixed down by SI and the primary source of energy are strongly dependent on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Strong fronts with steep isopycnals develop a flavour of SI we call ‘slantwise inertial instability’ by extracting kinetic energy from the background flow and rapidly mixing down the thermal wind profile. In contrast, weak fronts extract more potential energy from the background density profile, which results in ‘slantwise convection.’ Here, we extend the theory from Part 1 using nonlinear numerical simulations to focus on the adjustment of the front following saturation of SI. We find that the details of adjustment and amplitude of the induced inertial oscillations depend on the front strength. While weak fronts develop narrow frontlets and excite small-amplitude vertically sheared inertial oscillations, stronger fronts generate large inertial oscillations and produce bore-like gravity currents that propagate along the top and bottom boundaries. The turbulent dissipation rate in these strong fronts is large, highly intermittent and intensifies during periods of weak stratification. We describe each of these mechanisms and energy pathways as the front evolves towards the final adjusted state, and in particular focus on the effect of varying the dimensionless front strength.

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Younes Menni ◽  
Giulio Lorenzini ◽  
Ravinder Kumar ◽  
Babak Mosavati ◽  
Saeed Nekoonam

A numerical study of an especial heat exchanger (HE) equipped with complicated geometry baffles was performed in this research study. This shell-and-tube HE could be applied in various engineering applications like solar collectors. It can be acknowledged that generating longitudinal vortices in the flow results in enhancing the turbulent convective heat transfer. In order to generate these vortices, S-shaped baffles can be applied. It should be noted that computational analysis of shell-and-tube HEs is considered a challenging task due to these vortices. So, in this study, a commercial CFD software has been used for solving the problem and important equation and numerical approach used in the simulation have been explained. The aerodynamic aspect with respect to stream function, mean, axial, and transverse velocities, dynamic pressure, turbulent dissipation rate, turbulence kinetic energy, turbulent viscosity, and turbulence intensity fields was included in this research. This study reports many physical phenomena, such as the turbulence, instability, flow separation, and the appearance of reverse secondary currents. The average speed changed in different areas, where it is low next to the baffles. Velocity amounts are paramount around the upper channel’s wall, starting from the upper left side of the last baffle to the exit. This increase in velocity can be justified by a reduction in flow area and pressure augmentation.


AbstractThe finescale parameterization, formulated on the basis of a weak nonlinear wave–wave interaction theory, is widely used to estimate the turbulent dissipation rate, ε. However, this parameterization has previously been found to overestimate ε in the Antarctic Circumpolar Current (ACC) region. One possible reason for this overestimation is that vertical wavenumber spectra of internal wave energy are distorted from the canonical Garrett-Munk spectrum and have a spectral “hump” at low vertical wavenumbers. Such distorted vertical wavenumber spectra were also observed in other mesoscale eddy-rich regions. In this study, using eikonal simulations, in which internal wave energy cascades are evaluated in the frequency-wavenumber space, we examine how the distortion of vertical wavenumber spectra impacts on the accuracy of the finescale parameterization. It is shown that the finescale parameterization overestimates ε for distorted spectra with a low-vertical-wavenumber hump because it incorrectly takes into account the breaking of these low-vertical-wavenumber internal waves. This issue is exacerbated by estimating internal wave energy spectral levels from the low-wavenumber band rather than from the high-wavenumber band, which is often contaminated by noise in observations. Thus, in order to accurately estimate the distribution of ε in eddy-rich regions like the ACC, high-vertical-wavenumber spectral information free from noise contamination is indispensable.

AIP Advances ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 025125
Weiyang Zhao ◽  
Hang Wang ◽  
Ruidi Bai ◽  
Wangru Wei ◽  
Hongtao Wang

2020 ◽  
Zoé Koenig ◽  
Eivind Kolås ◽  
Kjersti Kalhagen ◽  
Ilker Fer

<p></p><p>North of Svalbard is a key region for the Arctic Ocean heat and salt budget as it is the gateway for one of the main branches of Atlantic Water in the Arctic. As the Atlantic Water layer advances into the Arctic Ocean, its core deepens from about 250 m depth around the Yermak Plateau to 350 m in the Laptev Sea, and gets colder and less saline due to mixing with surrounding waters. The complex topography in the region facilitates vertical and horizontal exchanges between the water masses and, together with strong shear and tidal forcing driving increased mixing rates, impacts the heat and salt content of the Atlantic Water layer that will circulate the Arctic Ocean.</p><p></p><p>In summer 2018, 6 moorings organized in 2 arrays were deployed across the Atlantic Water Boundary current for a year, within the framework of the Nansen Legacy project. In parallel, turbulence structure in the Atlantic Water boundary current was measured north of Svalbard in two different periods (July and September), using a Vertical Microstructure Profiler (Rockland Scientific) in both cruises and a Microrider (Rockland Scientific) mounted on a Slocum glider in September.</p><p></p><p>Using mooring observations, we investigated the background properties of the Atlantic Water boundary current (transport, vertical structure, seasonal variations) and the possible sources of the low-frequency variations (period of more than 2 weeks).</p><p></p><p> Using observations during the cruise periods, we investigated changes in the mixed layer through the summer and the sources of vertical mixing in the water column. In the mixed layer, depth-integrated turbulent dissipation rate is about 10<sup>-4</sup> W m<sup>-2</sup>. Variations in the turbulent heat, salinity and buoyancy fluxes are strong, and hypothesized to be affected by the evolution of the surface meltwater layer through summer. When integrated over the Atlantic Water layer, the turbulent dissipation rate is about 3.10<sup>-3</sup> W m<sup>-2</sup>. Whilst the wind work exerted in the mixed layer accounts for most of the variability in the mixed layer, tidal forcing plays an important role in setting the dissipation rates deeper in the water column.</p><p></p>

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