Vertical spectra of stratified turbulence at large horizontal scales

Maffioli, Andrea

doi:10.1103/physrevfluids.2.104802

Cited by 31 publications

(44 citation statements)

References 32 publications

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“…In the laminar case, a specific forcing F u and F b is chosen which is explained case-by-case in the next sections. In the turbulent case, a specific spectral statistical forcing (explained in [28]) is used, with the advantage of limiting the increase of VSHF. It consists in forcing velocity only (F b = 0) with a forcing term F u chosen in Fourier space to ensure a constant injected power P =< F u • u >, where < * > is a statistical volume average.…”

Section: Methodsmentioning

confidence: 99%

“…In the first stage, the VSHF flow is obtained from a direct numerical simulation of the linearized Navier-Stokes-Boussinesq Equation (1). The VSHF mode is directly forced using a stochastic forcing of velocity explained in [28]. The force is only imposed on the velocity component F u (k h = 0, k z ) with k z = ±1 and an injected power P =< F u • u >= 10 −6 ; as a result, the forcing only operates on the large-scales of the flow.…”

Section: Sweeping By a Sheared Convective Mean Flowmentioning

confidence: 99%

“…To understand the link between the two methods, by analogy with the total energy defined previously in Equation 5, we define the vertical energy by: The second technique, which is more computationally expensive, starts with the time Fourier transform of the flow component, then summing them in the θ ∈ I θ domain and finally computing the energy density. As shown in [23], the difference between the two formulations of vertical density of energy is:…”

Section: Application To the Sweeping By Horizontal Velocity Of Saint-mentioning

confidence: 99%

“…However, in a fully turbulent flow, the wave-vortex decomposition can be questioned for assessing the exact wave contents, since it is based on spatial criteria only and does not explicitly account for the space-time coherence of waves, an essential feature in their dispersion relation. Recent investigations show that this technique overestimates the wave energy as it does not take into account the temporal dependence [23]. In addition, it does not directly apply to other flow types such as rotating or rotating-stratified turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Partitioning Waves and Eddies in Stably Stratified Turbulence

2020

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We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

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Section: Methodsmentioning

confidence: 99%

Section: Sweeping By a Sheared Convective Mean Flowmentioning

confidence: 99%

Section: Application To the Sweeping By Horizontal Velocity Of Saint-mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Partitioning Waves and Eddies in Stably Stratified Turbulence

2020

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“…Recent modelling results on stratified turbulence, mainly from Direct Numerical Simulations DNS with output commonly in vertical wavenumber (kz) spectra, indicate a sharp transition in spectral scaling, e.g., for the vertical kinetic energy from kz-scaling kz -3 of a buoyancy-inertial subrange to kz -5/3 (e.g., Kimura and Herring, 2012;Augier et al, 2015;Maffioli, 2017). The results confirmed open ocean observations (Gregg, 1977), of which temperature frequency spectra showed an extensive super-buoyancy range scaling with  -3 before dropping into  -5/3 (van Haren and Gostiaux, 2009).…”

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confidence: 99%

Deep-ocean inertial subrange small bandwidth coherence and Ozmidov-frequency separation

Haren

2019

Physics of Fluids

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The inertial subrange of turbulence in a density stratified environment is the transition from internal waves to isotropic turbulence, but it is unclear how to interpret its extension to anisotropic 'stratified' turbulence. Knowledge about stratified turbulence is relevant for the dispersal of suspended matter in geophysical flows, such as in most of the ocean. For studying internal-wave-induced ocean-turbulence moored highresolution temperature (T-)sensors are used. Spectra from observations on episodic quasi-convective internal wave breaking above a steep slope of large seamount Josephine in the Northeast-Atlantic demonstrate an inertial subrange that can be separated in two parts: A large-scale part with relatively coherent portions adjacent to less coherent portions, and a small-scale part that is smoothly continuous (to within standard error). The separation is close to the Ozmidov frequency, and coincides with the transition from anisotropic/quasi-deterministic stratified turbulence to isotropic/stochastic inertial convective motions as inferred from a comparison of vertical and horizontal co-spectra. These observations contrast with T-sensor observations of shear-dominated internal wave breaking in an equally turbulent environment above the slope of a small Mid-Atlantic ridge-crest, which demonstrate a stochastic inertial subrange throughout.

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Asymmetry of vertical buoyancy gradient in stratified turbulence

Maffioli

2019

J. Fluid Mech.

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We consider the asymmetry of the buoyancy field in the vertical direction in stratified turbulence. While this asymmetry is known, its causes are not well understood, and it has not been systematically quantified previously. Using theoretical arguments, it is shown that both stratified turbulence and isotropic turbulence in the presence of a mean scalar gradient will become positively skewed, as a direct consequence of the presence of stratification and mean scalar gradient, respectively. Assuming a rapid adjustment of isotropic turbulence to a stable stratification on a time scale $\unicode[STIX]{x1D70F}\sim N^{-1}$, where $N$ is the Brunt–Väisälä frequency, a scaling for the skewness of the vertical buoyancy gradient is obtained. Direct numerical simulations of stratified turbulence with forcing are performed and the positive skewness of $\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z$ is confirmed ($b$ is the buoyancy). Both the volume-averaged dimensional skewness, $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, and the non-dimensional skewness, $S$, are computed and compared against the theoretical predictions. There is a good agreement for $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, while there is a discrepancy in the behaviour of $S$. The theory predicts $S\sim 1$ and a constant skewness, while the direct numerical simulations confirm that the skewness is $O(1)$ but with a remaining dependence on the Froude number. The results are interpreted as being due to the concurrent action of linear and nonlinear processes in stratified turbulence leading to $S>0$ and to the formation of layers and interfaces in vertical profiles of buoyancy.

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Vertical spectra of stratified turbulence at large horizontal scales

Cited by 31 publications

References 32 publications

Partitioning Waves and Eddies in Stably Stratified Turbulence

Partitioning Waves and Eddies in Stably Stratified Turbulence

Deep-ocean inertial subrange small bandwidth coherence and Ozmidov-frequency separation

Asymmetry of vertical buoyancy gradient in stratified turbulence

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