scholarly journals Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

2014 ◽  
Vol 745 ◽  
pp. 223-250 ◽  
Author(s):  
Laurène Jouve ◽  
Gordon I. Ogilvie
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Dissipation Rate ◽  
Laboratory Experiments ◽  
Rotation Axis ◽  
Internal Gravity Waves ◽  
Direct Numerical Simulations ◽  
Inertial Wave ◽  
Linear And Nonlinear ◽  
Nonlinear Regimes

AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

Study on the influence of linear and nonlinear distribution of crosswind on the motion of aircraft wake vortex

2021 ◽  
pp. 095441002098743
Author(s):  
Dong Li ◽  
Ziming Xu ◽  
Ke Zhang ◽  
Zeyu Zhang ◽  
Jinxin Zhou ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Dissipation Rate ◽  
Vortex Pair ◽  
Vertical Shear ◽  
Wake Vortex ◽  
Analysis Method ◽  
Velocity Magnitude ◽  
Aircraft Wake ◽  
Linear And Nonlinear ◽  
Nonlinear Distribution

Environmental crosswind can greatly affect the development of aircraft wake vortex pair. Previous numerical simulations and experiments have shown that the nonlinear vertical shear of the crosswind velocity can affect the dissipation rate of the aircraft wake vortex, causing each vortex of the vortex pair descent with different velocity magnitude, which will lead to the asymmetrical settlement and tilt of the wake vortex pair. Through numerical simulations, this article finds that uniform crosswind convection and linear vertical shear crosswind convection can also have an effect on the strength of the vortex. This effect is inversely proportional to the cube of the vortex spacing, so it is more intense on small separation vortex pair. In addition, the superposition of crosswind and vortex-induced velocities will lead to the asymmetrical pressure distribution around the vortex pair, which will also cause the tilt of the vortex pair. Furthermore, a new analysis method for wake vortex is proposed, which can be used to predict the vortex trajectory.

Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow

1995 ◽  
Vol 286 ◽  
pp. 1-23 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag ◽  
Ilya Staroselsky
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Channel Flow ◽  
Gravity Waves ◽  
Open Channel ◽  
Open Channel Flow ◽  
Surface Region ◽  
Direct Numerical Simulations ◽  
Turbulence Production ◽  
Wind Sea

We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.

K–ϵ model for rotating homogeneous decaying turbulence

2016 ◽  
Vol 94 (11) ◽  
pp. 1200-1204 ◽  
Author(s):  
Hamed Marzougui
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Decay Rate ◽  
Rate Equation ◽  
Rotation Rate ◽  
Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Uniform Rotation ◽  
Axis Of Rotation ◽  
Decaying Turbulence

In the present work, we propose a modification to the standard K–ϵ model for simulating homogeneous decaying turbulence subjected to uniform rotation. In this modification, the dissipation rate equation is formulated in terms of the rotation rate Ω, the integral length scales along the axis of rotation [Formula: see text], and its isotropic value [Formula: see text]. The comparison of our results with the corresponding direct numerical simulations proves that the new model reproduces in an excellent way the decay rate of the turbulent kinetic energy.

scholarly journals Analysis of the atmosphere behaviour in the proximities of an orographic obstacle

1995 ◽  
Vol 2 (1) ◽  
pp. 30-48 ◽  
Author(s):  
E. Hernández ◽  
J. Díaz ◽  
L. C. Cana ◽  
A. García
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Critical Points ◽  
Complex Terrain ◽  
Laboratory Experiments ◽  
Real Experiment ◽  
The Real ◽  
Linear And Nonlinear ◽  
Atmospheric Variables

Abstract. The atmospheric behaviour near an orographic obstacle has been thoroughly studied in the last decades. The first papers in this field were mainly theoretical, being more recent the laboratory experiments which represented that behaviour in ideal conditions. The numerical simulations have been addressed lately thanks to the development of computers. But the study of meteorology in complex terrain has lacked experiments in the atmosphere to understand the real influence the relief has on it. In this paper the problem has been considered from the last perspective, and so, seasons of measure of the atmospheric variables within the boundary layer have been organized with the goal of checking existing theories and bringing right conclusions from real experiment in the atmosphere. Controverted aspects of linear and nonlinear theories, as the location of critical points upwind and downwind of an orographic obstacle, will be analyzed. The results obtained show a large adequacy between the forecasted behaviour and the experimentally detected.

scholarly journals Observations of Near-Inertial Internal Gravity Waves Radiating from a Frontal Jet

2013 ◽  
Vol 43 (6) ◽  
pp. 1225-1239 ◽  
Author(s):  
Matthew H. Alford ◽  
Andrey Y. Shcherbina ◽  
Michael C. Gregg
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Shear Layers ◽  
Adjustment Process ◽  
Vertical Wavelength ◽  
The North ◽  
Inertial Wave ◽  
The North Pacific

Abstract Shipboard ADCP and towed CTD measurements are presented of a near-inertial internal gravity wave radiating away from a zonal jet associated with the Subtropical Front in the North Pacific. Three-dimensional spatial surveys indicate persistent alternating shear layers sloping downward and equatorward from the front. As a result, depth-integrated ageostrophic shear increases sharply equatorward of the front. The layers have a vertical wavelength of about 250 m and a slope consistent with a wave of frequency 1.01f. They extend at least 100 km south of the front. Time series confirm that the shear is associated with a downward-propagating near-inertial wave with frequency within 20% of f. A slab mixed layer model forced with shipboard and NCEP reanalysis winds suggests that wind forcing was too weak to generate the wave. Likewise, trapping of the near-inertial motions at the low-vorticity edge of the front can be ruled out because of the extension of the features well south of it. Instead, the authors suggest that the wave arises from an adjustment process of the frontal flow, which has a Rossby number about 0.2–0.3.

Collective instability of salt fingers

1969 ◽  
Vol 35 (2) ◽  
pp. 209-218 ◽  
Author(s):  
Melvin E. Stern
Keyword(s):  
Gravity Waves ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Asymptotic Dependence ◽  
Salinity Gradients ◽  
Salt Fingers ◽  
Order Of Magnitude ◽  
Ocean Observations ◽  
Molecular Salt ◽  
Steady Laminar

We first consider a steady laminar model of salt fingers and show that the latter become unstable with respect to internal gravity waves when the finger Reynolds number exceeds a critical value. The criterion is then used in speculations about the statistically steady state in a fully developed similarity model where horizontally averaged temperature and salinity gradients are constant at all depths. Dimensional reasoning is used to obtain the asymptotic dependence of the turbulent flux on the molecular salt diffusivity. From this and other relationships order-of-magnitude estimates are obtained and compared with laboratory experiments and ocean observations.

An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid

2014 ◽  
Vol 742 ◽  
pp. 308-339 ◽  
Author(s):  
Hugo N. Ulloa ◽  
Alberto de la Fuente ◽  
Yarko Niño
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Kelvin Wave ◽  
Nonlinear Processes ◽  
Transfer Energy ◽  
Type Wave ◽  
Basin Scale ◽  
Layer Flow

AbstractThe temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of $\eta _{i}$, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré wave can transfer energy to higher or lower frequencies than the frequency of the fundamental Kelvin wave, as a function of the background rotation. In particular, a specific normal mode in the off-shore region could be energized by this interaction. Finally, the bulk decay rate of the fundamental Kelvin wave, $\tau _{dk}$, was investigated. The results exhibit that $\tau _{dk}$ is concordant with the Ekman damping time scale when there is no evidence of steepening in the basin-scale waves. However, as nonlinear processes increase, $\tau _{dk}$ shows a strong decrease. In this context, the nonlinear processes play an important role in the decay of the fundamental Kelvin wave, via the energy radiation to other modes. The results reported demonstrate that the background rotation and nonlinear processes are essential aspects in understanding the degeneration and the decay of large-scale internal gravity waves on enclosed basins.

A new approach to modelling near-wall turbulence energy and stress dissipation

2002 ◽  
Vol 459 ◽  
pp. 139-166 ◽  
Author(s):  
S. JAKIRLIĆ ◽  
K. HANJALIĆ
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Transport Equation ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Turbulence Energy ◽  
Viscous Term ◽  
Dissipation Equation ◽  
Near Wall

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than εij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using εh instead of ε, agree well with the direct numerical simulations.

Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations

2001 ◽  
Vol 444 ◽  
pp. 199-221 ◽  
Author(s):  
MITSUHIRO TANAKA
Keyword(s):  
Energy Transfer ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Direct Numerical Simulations ◽  
Rate Of Change ◽  
Surface Gravity ◽  
Primitive Equations ◽  
Surface Gravity Waves ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

The temporal evolution of nonlinear wave fields of surface gravity waves is studied by large-scale direct numerical simulations of primitive equations in order to verify Hasselmann's theory for nonlinear energy transfer among component gravity waves. In the simulations, all the nonlinear interactions, including both resonant and non-resonant ones, are taken into account up to the four-wave processes. The initial wave field is constructed by combining more than two million component free waves in such a way that it has the JONSWAP or the Pierson–Moskowitz spectrum. The nonlinear energy transfer is evaluated from the rate of change of the spectrum, and is compared with Hasselmann's theory. It is shown that, in spite of apparently insufficient duration of the simulations such as just a few tens of characteristic periods, the energy transfer obtained by the present method shows satisfactory agreement with Hasselmann's theory, at least in their qualitative features.

Sign in / Sign up

Export Citation Format

Share Document