6 results
Surface manifestation of internal waves emitted by submerged localized stratified turbulence
- Qi Zhou, Peter J. Diamessis
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- Journal:
- Journal of Fluid Mechanics / Volume 798 / 10 July 2016
- Published online by Cambridge University Press:
- 06 June 2016, pp. 505-539
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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.
Turbulent/non-turbulent interfaces in wakes in stably stratified fluids
- Tomoaki Watanabe, James J. Riley, Stephen M. de Bruyn Kops, Peter J. Diamessis, Qi Zhou
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- Journal:
- Journal of Fluid Mechanics / Volume 797 / 25 June 2016
- Published online by Cambridge University Press:
- 16 May 2016, R1
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We report on a study, employing direct numerical simulations, of the turbulent/non-turbulent interface of a wake in a stably stratified fluid. It is found that thresholds for both enstrophy and potential enstrophy are needed to identify the interface. Using conditional averaging relative to the location of the interface, various quantities of interest are examined. The thickness of the interface is found to scale with the Kolmogorov scale. From an examination of the Ozmidov and Kolmogorov length scales as well as the buoyancy Reynolds number, it is found that the buoyancy Reynolds number decreases and becomes of order 1 near the interface, indicating the suppression of the turbulence there by the stable stratification. Finally the overall rate of loss of energy due to internal wave radiation is found to be comparable to the overall rate of loss due to turbulent kinetic energy dissipation.
The internal gravity wave field emitted by a stably stratified turbulent wake
- Ammar M. Abdilghanie, Peter J. Diamessis
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- Journal:
- Journal of Fluid Mechanics / Volume 720 / 10 April 2013
- Published online by Cambridge University Press:
- 27 February 2013, pp. 104-139
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The internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers, $\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $ and internal Froude numbers, $\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $ ($U$, $D$ are characteristic body velocity and length scales, and $N$ is the buoyancy frequency) is examined. At the higher $\mathit{Re}$ examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to $Nt\approx 100$. In contrast, IGW emission at the lower $\mathit{Re}$ investigated does not continue beyond $Nt\approx 50$ for the three $\mathit{Fr}$ values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with $\mathit{Fr}$ and appear to be smaller at the higher $\mathit{Re}$, especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower $\mathit{Re}$, consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher $\mathit{Re}$, wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.
Boundary-layer-separation-driven vortex shedding beneath internal solitary waves of depression
- Payam Aghsaee, Leon Boegman, Peter J. Diamessis, Kevin G. Lamb
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- Journal:
- Journal of Fluid Mechanics / Volume 690 / 10 January 2012
- Published online by Cambridge University Press:
- 24 November 2011, pp. 321-344
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We investigate global instability and vortex shedding in the separated laminar boundary layer beneath internal solitary waves (ISWs) of depression in a two-layer stratified fluid by performing high-resolution two-dimensional direct numerical simulations. The simulations were conducted with waves propagating over a flat bottom and shoaling over relatively mild and steep slopes. Over a flat bottom, the potential for vortex shedding is shown to be directly dependent on wave amplitude, for a particular stratification, owing to increase of the adverse pressure gradient ( for leftward propagating waves) beneath the trailing edge of larger amplitude waves. The generated eddies can ascend from the bottom boundary to as high as 33 % of the total depth in two-dimensional simulations. Over sloping boundaries, global instability occurs beneath all waves as they steepen. For the slopes considered, vortex shedding begins before wave breaking and the vortices, shed from the bottom boundary, can reach the pycnocline, modifying the wave breaking mechanism. Combining the results over flat and sloping boundaries, a unified criterion for vortex shedding in arbitrary two-layer continuous stratifications is proposed, which depends on the momentum-thickness Reynolds number and the non-dimensionalized ISW-induced pressure gradient at the point of separation. The criterion is generalized to a form that may be readily computed from field data and compared to published laboratory experiments and field observations. During vortex shedding events, the bed shear stress, vertical velocity and near-bed Reynolds stress were elevated, in agreement with laboratory observations during re-suspension events, indicating that boundary layer instability is an important mechanism leading to sediment re-suspension.
Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes
- PETER J. DIAMESSIS, GEOFFREY R. SPEDDING, J. ANDRZEJ DOMARADZKI
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- Journal:
- Journal of Fluid Mechanics / Volume 671 / 25 March 2011
- Published online by Cambridge University Press:
- 07 March 2011, pp. 52-95
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The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers, Re = UD/ν ∈ [5 × 103, 105] and internal Froude numbers, Fr = 2U/(ND) ∈ [4, 64] (U, D are characteristic velocity and length scales, and N is the buoyancy frequency) is examined. The maximum value of Re and the range of Fr values considered allow extrapolation of the results to geophysical and naval applications.
At higher Re, the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lower Re. At Re = 5 × 103, vertical fluid motions are rapidly suppressed, but at Re = 105, secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up to Nt ≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy.
These results agree with existing scaling of buoyancy-driven shear on Re/Fr2 and suggest that, in the field, the NEQ regime may last up to Nt ≈ 1000. At a given high Re value, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent of Fr. This first systematic numerical investigation of stratified turbulence (as defined by Lilly, J. Atmos. Sci. vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.
The structure and dynamics of overturns in stably stratified homogeneous turbulence
- PETER J. DIAMESSIS, KEIKO K. NOMURA
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- Journal:
- Journal of Fluid Mechanics / Volume 499 / 25 January 2004
- Published online by Cambridge University Press:
- 27 January 2004, pp. 197-229
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Direct numerical simulations of stably stratified homogeneous turbulence, with and without mean shear, are used to investigate the three-dimensional structure, evolution and energetic significance of density overturns. Although the flow conditions are idealized, examination of the full-field simulation data provides insight into flow energetics and mixing which may assist in the interpretation of physical measurements, typically limited to one-dimensional vertical profiles. Overturns, defined here through the density field as contiguous regions of non-zero Thorpe displacement, are initially generated by the stirring action of coherent vortex structures present in the flow and further develop through merging with adjacent overturns. During this growth phase, overturns exhibit irregular spatial structure in unsheared flow and elongated structure with distinct orientation in shear flow. Although most of the available potential energy (APE) and buoyancy flux are associated with stable (non-overturning) regions in the flow, young overturns actively contribute to the flow energetics. In particular, overturn peripheries are sites of high levels of APE, buoyancy flux and diapycnal mixing. A collapse phase may follow the growth phase in the absence of adequately strong mean shear. During this phase, buoyancy gradually assumes control of the overturns and their vertical scale steadily decreases. The energetic significance of the overturns diminishes, although high APE and diapycnal mixing continue to occur near their boundaries. In the final phase of their evolution, overturns contribute negligibly to the energetics. The remaining overturns are characterized by a viscous–buoyant balance which maintains their vertical scale. The overturns eventually vanish due to homogenization of their internal density distribution by diffusion. Activity diagrams, sampled at different points of flow evolution, show significant variation in overturn Reynolds and Froude numbers which may have implications for vertical sampling of a turbulent event.