Internal waves generated by the turbulent wake of a sphere

Lin, Qinhao; Boyer, Don L.; Fernando, H. J. S.

doi:10.1007/bf00190954

Cited by 22 publications

(17 citation statements)

References 16 publications

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“…Further comparisons to lee wave models are presented in § 3.4.3. Finally, the transition between the lee wave and the turbulent wake generation regimes agrees with the Fr ≈ 2 location noted by Chomaz et al (1991, Lin et al (1993) and Robey (1997). The large run-to-run variation in PE A at Fr = 2 and 5 (and to some degree at Fr = 1) is due to the presence of wake turbulence-generated IWs, as further discussed in the following section.…”

Section: Variation Of Iw Pe With Froude Numbersupporting

confidence: 63%

“…For a towed sphere, the degree of mixing is substantially less, so that the global collapse of the wake does not contribute substantially to the generation of IWs, as discussed by Bonneton et al (1993). The transition between the lee wave IW regime and the turbulent-wake-generated random wave regime has been found to occur at Fr = 2 by Chomaz et al (1991, Lin, Boyer & Fernando (1993) and Robey (1997). However, the transition between regimes is not precise, as there is a range of Fr where both mechanisms can generate IWs.…”

Section: Stratified Wakesmentioning

confidence: 94%

“…While random IWs are a significant contributor to the IW field at high Fr (Gilreath & Brandt 1985), it was found that both the lee waves and random waves contributed to the resultant IW field. The link between coherent structures in the wake of a sphere and the random IW was shown by Lin et al (1993), Bonneton et al (1993Bonneton et al ( , 1996 and Robey (1997). In particular, Bonneton et al (1993) have shown the presence of random IWs due to the initial wake impulse and to the later-time coherent structures, with amplitudes that both increase proportionally to Fr 2 and decay as (Nt) −1 .…”

mentioning

confidence: 97%

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The internal wavefield generated by a towed sphere at low Froude number

Brandt

Rottier

2015

J. Fluid Mech.

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In highly stratified atmospheric and oceanic environments, a large fraction of energy input by various sources can be manifest as internal waves (IWs). The propagating nature of IWs results in the distribution of the energy over a large fraction of the air/water column. Wakes of translating bodies are one source of input energy that has been of continued interest. To further the understanding of wakes in strongly stratified environments, and particularly the near-field regime where strong coupling to the internal wavefield is evident, an extensive series of experiments on the internal wavefield generated by a towed sphere was performed, wherein the internal wavefield was measured over a Froude number range 0.1 Fr 5 (where Fr = U/ND, U is the tow speed, D the sphere diameter and N the Brunt-Väisälä (BV) frequency). In a second series of experiments, the temporal wavefield evolution was studied over two BV periods. These measurements show that the body generation (lee wave) mechanism dominates at Fr 1, while the random eddies in the turbulent wake become the dominant source at Fr 1. In the low-Fr regime, Fr 1, there is a resonant peak in the coupling of the input wake energy to the internal wavefield at a Froude number of ∼0.5, and at its maximum 70 % of the input energy is coupled into IW potential energy. In this regime it was also found that the spreading angle of the evolving wavefield was considerably broader than predicted by the classical point-source models for the wavefield further downstream, owing to the existence in the near field of a significant energy content in the higher-IW modes that deteriorate at later times. In the low-Fr regime, it was found that, while the IW potential energy increases ∝ Fr 2 , the fraction of the total energy input is a weak function of Fr, varying as Fr 1/2 .

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Section: Variation Of Iw Pe With Froude Numbersupporting

confidence: 63%

Section: Stratified Wakesmentioning

confidence: 94%

mentioning

confidence: 97%

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The internal wavefield generated by a towed sphere at low Froude number

Brandt

Rottier

2015

J. Fluid Mech.

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“…A stratified towed-sphere wake is characterized by its Reynolds number Re ≡ UD/ν and Froude number Fr ≡ 2U/(ND), where U, D, ν and N are the tow speed, sphere diameter, viscosity and buoyancy frequency, respectively. Pioneering and recent experimental studies (Gilreath & Brandt 1985;Hopfinger et al 1991;Bonneton, Chomaz & Hopfinger 1993;Lin, Boyer & Fernando 1993;Robey 1997;Meunier 2012;Brandt & Rottier 2015) revealed at least two types of IWs generated by stratified wakes: the lee waves behind the sphere (or cylinder) which dominates at Fr < 4, and the quasirandom waves emitted by the turbulence in the wake which dominates at Fr 4, the latter wave type being the focus of the present study. Källén (1987) formulated the linear theory for wave generation by the spatially varying mean-flow structure of the wake.…”

Section: Internal Waves Emitted By Localized Stratified Turbulencementioning

confidence: 82%

Surface manifestation of internal waves emitted by submerged localized stratified turbulence

Zhou

Diamessis

2016

J. Fluid Mech.

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The internal waves (IWs) radiated by the turbulent wake of a sphere of diameter $D$ towed at speed $U$ are investigated using three-dimensional fully nonlinear simulations performed in a linearly stratified Boussinesq fluid with buoyancy frequency $N$. The study focuses on a broad range of wave characteristics in the far field of the turbulent wave source, specifically at the sea surface (as modelled by a free-slip rigid lid) where the IWs reflect. Six simulations are performed at Reynolds number $Re\equiv UD/{\it\nu}\in \{5\times 10^{3},10^{5}\}$ and Froude number $Fr\equiv 2U/(ND)\in \{4,16,64\}$, where ${\it\nu}$ is viscosity. The wave-emitting wake is located at a fixed distance of $9D$ below the surface. As the wake evolves for up to $O(300)$ units of buoyancy time scale $1/N$, IW characteristics, such as horizontal wavelength ${\it\lambda}_{H}$ and wave period $T$, are sampled at the sea surface via wavelet transforms of horizontal divergence signals. The statistics of amplitudes and orientations of IW-induced surface strains are also reported. The mean dimensionless observable wavelength $\overline{{\it\lambda}}_{H}/D$ at the sea surface decays in time as $(Nt)^{-1}$, which is due to the waves’ dispersion. This observation is in agreement with a linear propagation model that is independent of the wake $Re$ and $Fr$. This agreement further suggests that the most energetic waves impacting the surface originate from the early-time wake that is adjusting to buoyancy. The most energetic dimensionless wavelength $\hat{{\it\lambda}}_{H}/D$ is found to scale as $Fr^{1/3}$ and decrease with $Re$, which causes the arrival time (in $Nt$ units) of the strongest waves at the surface to scale as $Fr^{-1/3}$ and increase with $Re$. This wavelength $\hat{{\it\lambda}}_{H}$ is also found to correlate with the vertical Taylor scale of the wake turbulence. IW-driven phenomena at the surface that are of interest to an observer, such as the local enrichment of surfactant and the transport of ocean surface tracers, are also examined. The local enrichment ratio of surface scalar scales linearly with the steepness of IWs that reach the surface, and the ratio often exceeds a possible visibility threshold. The Lagrangian drifts of ocean tracers, which are linked to the nonlinear interaction between incident and reflecting IW packets, create a local divergence in lateral mass transport right above the wake centreline, an effect that intensifies strongly with increasing $Fr$. The findings of this study may serve as a platform to investigate the generation and surface manifestation of IWs radiated by other canonical submerged stratified turbulent flows.

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“…When these intrusions, i.e., coherent structures, are fairly periodic, they generate an asymptotic wave field which has been described by both Gilreath and Brandt 5 and Voisin. 6 Furthermore, Lin et al 7 and Sysoeva and Chashechkin 8 have concluded from measurements that the coherent structures of the wake represent the basic source of internal waves in the wake without explaining clearly the wave generation mechanism.…”

Section: Introductionmentioning

confidence: 99%

Internal waves generated by the wake of Gaussian hills

2001

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International audienceDepending on their structure and dynamics, the wakes of various obstacles can generate different kinds of internal waves in stratified fluids. Experiments on waves emitted by three-dimensional Gaussian models towed uniformly in a linearly stratified fluid were carried out. Beyond a critical value Frc of the Froude number Fr, the developed wake was observed to radiate an internal wave field shorter than the lee waves of the hill. The emergence of such waves is correlated with the periodic shedding of three dimensional vortical structures at Fr>Frc. Measurements show that the wavelengths of these short waves are constant in space and time, and proportional to Fr. Their phase and group velocities are proportional to the coherent structure velocity which is estimated from velocity measurements inside the wake. All those spatio-temporal characteristics prove that these short waves are generated by the displacement of the coherent structure inside the wake. © 2001 American Institute of Physics

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Internal waves generated by the turbulent wake of a sphere

Cited by 22 publications

References 16 publications

The internal wavefield generated by a towed sphere at low Froude number

The internal wavefield generated by a towed sphere at low Froude number

Surface manifestation of internal waves emitted by submerged localized stratified turbulence

Internal waves generated by the wake of Gaussian hills

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