The Generation and Propagation of Ship Internal Waves in a Generally Stratified Ocean at High Densimetric Froude Numbers, Including Nonlinear Effects

2000 ◽  
Vol 44 (03) ◽  
pp. 197-227
Author(s):  
Marshall P. Tulin ◽  
Yitao Yao ◽  
Pei Wang
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Near Field ◽  
Nonlinear Effects ◽  
Wave Pattern ◽  
Small Scale ◽  
Far Field ◽  
Asymptotic Equation ◽  
Densimetric Froude Number ◽  
Central Lobe

A nonlinear theory for internal wave generation and propagation is derived here for slender ships traveling at high densimetric Froude number (Fh >> 1) in water of small density variation. It is based on an asymptotic equation for the evolution of the internal wave vorticity generated under the ship by a known inviscid ship flow and then self-propagating in the wake. In its numerical implementation, arbitrary pycnoclines and slender ship hulls may be used, and boundary conditions on the ship hull are satisfied; the free surface is treated here as rigid, although this may be relaxed. The theory has been implemented by a suitable numerical method and numerous simulations have been carried out. The results have been compared with earlier OEL experiments. In the near field, emphasis is given to a triple-lobe pattern in the pycnocline, an upwelling along the centerline of motion with a trough on either side, forming close behind the ship. Two distinct types of triple lobes are identified:dominant central lobe and very weak troughs, and;weak central lobe and dominant troughs. The former (a) is shown to result in linear propagation into the far field. The latter (b) results in far-field patterns preceded by a deep trough whose propagation is nonlinear. The comparisons of both simulated trends and actual amplitudes with measurements are good, surprisingly so considering the small scale of the experiment and the asymptotic nature of the theory. The effect of the turbulent wake on the internal waves in the experiments is restricted to a very narrow region behind the ship; the bulk of the wave pattern including the leading waves seem unaffected. Simulations show that under certain conditions of stratification, triple-lobe patterns with abnormally large troughs are generated and lead to strong nonlinear effects; these deep troughs propagate sidewards to large distances aft (over 40 ship lengths) with slow decay, and result in much larger surface currents and strain rates than in the normal case. Correspondingly, fast waves of depression, which decay slowly, were discovered through the simulation of two-dimensional initial value problems, where the initial area of depression was significantly less than required of a true soliton; these "quasi-solitons" are briefly studied here.

WAVELET-BASED POSTPROCESSING OF JET LES DATA FOR ACOUSTIC FAR-FIELD EXTRAPOLATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 1350017
Author(s):  
RAMIN KAVIANI ◽  
VAHID ESFAHANIAN ◽  
MOHAMMAD EBRAHIMI
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Near Field ◽  
Flow Simulation ◽  
Computational Time ◽  
Jet Flows ◽  
Small Scale ◽  
Frequency Noise ◽  
Far Field ◽  
Noise Sources

The affordable grid resolutions in conventional large-eddy simulations (LESs) of high Reynolds jet flows are unable to capture the sound generated by fluid motions near and beyond the grid cut-off scale. As a result, the frequency spectrum of the extrapolated sound field is artificially truncated at high frequencies. In this paper, a new method is proposed to account for the high frequency noise sources beyond the resolution of a compressible flow simulation. The large-scale turbulent structures as dominant radiators of sound are captured in LES, satisfying filtered Navier–Stokes equations, while for small-scale turbulence, a Kolmogorov's turbulence spectrum is imposed. The latter is performed via a wavelet-based extrapolation to add randomly generated small-scale noise sources to the LES near-field data. Further, the vorticity and instability waves are filtered out via a passive wavelet-based masking and the whole spectrum of filtered data are captured on a Ffowcs-Williams/Hawkings (FW-H) surface surrounding the near-field region and are projected to acoustic far-field. The algorithm can be implemented as a separate postprocessing stage and it is observed that the computational time is considerably reduced utilizing a hybrid of many-core and multi-core framework, i.e. MPI-CUDA programming. The comparison of the results obtained from this procedure and those from experiments for high subsonic and transonic jets, shows that the far-field noise spectrum agree well up to 2 times of the grid cut-off frequency.

scholarly journals Internal Waves and Mixing near the Kerguelen Plateau

2015 ◽  
Vol 46 (2) ◽  
pp. 417-437 ◽  
Author(s):  
Amelie Meyer ◽  
Kurt L. Polzin ◽  
Bernadette M. Sloyan ◽  
Helen E. Phillips
Keyword(s):  
Internal Wave ◽  
Wave Field ◽  
Internal Waves ◽  
Large Scale ◽  
Polar Front ◽  
Frontal Region ◽  
Small Scale ◽  
Kerguelen Plateau ◽  
Flow Strength ◽  
Internal Wave Field

AbstractIn the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.

A Computational Fluid Dynamics Model for Investigating Air-Pumping Mechanisms in Air-Borne Tire Noise

2016 ◽  
Vol 44 (3) ◽  
pp. 191-211 ◽  
Author(s):  
Prashanta Gautam ◽  
Abhilash J. Chandy
Keyword(s):  
Stokes Equations ◽  
Road Traffic ◽  
Near Field ◽  
Spectral Characteristics ◽  
Small Scale ◽  
Road Traffic Noise ◽  
Far Field ◽  
Noise Generation ◽  
Tire Noise ◽  
Noise Characteristics

ABSTRACT The reduction in power train noise over the past decade has led to an increased focus in reducing tire/road noise, largely due to the environmental concerns related to road traffic noise in industrial countries. Computational fluid dynamic (CFD) simulations conducted using ANSYS FLUENT are presented here with the objective of understanding air-pumping noise-generation mechanisms due to tire/road interaction. The CFD model employs a large eddy simulation turbulence modeling approach, in which the filtered compressible Navier-Stokes equations are solved to obtain temporally and spatially accurate near-field pressure fluctuations for a two-dimensional (2D) tire geometry with (1) one groove and (2) two grooves. In addition, the Ffowcs-Williams and Hawkings (FW-H) acoustic model is used to predict far-field acoustics. The deformation of the grooves, as the tire rotates, is represented by prescribed sidewall movements. Consequently, the solution to the numerical problem is obtained through a single process, thereby enabling the prediction of small-scale air pumping, horn effect, and far-field acoustics in a single simulation. The acoustic characteristics associated with air pumping are studied through spectral analysis tools, and comparisons show that the additional groove on the horn geometry alters the spectral characteristics of air pumping. Validation of the model is conducted through qualitative and quantitative comparisons with previous studies. These simulations are intended to provide a deeper understanding about the small-scale noise generation as well as the near-field and far-field acoustics, thereby paving the way for the automotive manufacturer to compare a variety of air-related tire noise characteristics without spending time and money for vehicle pass-by tests.

Spectra and Coherence of Wind-Generated Internal Waves

1976 ◽  
Vol 33 (10) ◽  
pp. 2323-2328 ◽  
Author(s):  
R. H. Käse ◽  
C. L. Tang
Keyword(s):  
Energy Density ◽  
Internal Wave ◽  
Internal Waves ◽  
Wind Stress ◽  
Wave Mode ◽  
Wave Number ◽  
Small Scale ◽  
Two Dimensional ◽  
Scale Turbulence ◽  
Main Thermocline

On the basis of a model for an internal wave field that is generated by a randomly varying isotropic wind stress and in which energy is transferred to small-scale turbulence, we derive the two-dimensional energy density function. The coherence scales are determined by the highest order internal wave mode that is not affected by virtual friction in the main thermocline, provided the curl of the wind stress has a white noise wave number spectrum. In general, this mode number scale is increasing monotonically with frequency. As a result of such a frequency dependent mode bandwidth, the vertical coherence drops with increasing frequency.

Upscale Energy Transfer by the Vortical Mode and Internal Waves

2014 ◽  
Vol 44 (9) ◽  
pp. 2446-2469 ◽  
Author(s):  
Anne-Marie E. G. Brunner-Suzuki ◽  
Miles A. Sundermeyer ◽  
M.-Pascale Lelong
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Internal Waves ◽  
Numerical Experiments ◽  
Large Scale ◽  
Vertical Shear ◽  
Small Scale ◽  
Driving Mechanism ◽  
Vortex Interaction ◽  
Vertical Scale

Abstract Diapycnal mixing in the ocean is sporadic yet ubiquitous, leading to patches of mixing on a variety of scales. The adjustment of such mixed patches can lead to the formation of vortices and other small-scale geostrophic motions, which are thought to enhance lateral diffusivity. If vortices are densely populated, they can interact and merge, and upscale energy transfer can occur. Vortex interaction can also be modified by internal waves, thus impacting upscale transfer. Numerical experiments were used to study the effect of a large-scale near-inertial internal wave on a field of submesoscale vortices. While one might expect a vertical shear to limit the vertical scale of merging vortices, it was found that internal wave shear did not disrupt upscale energy transfer. Rather, under certain conditions, it enhanced upscale transfer by enhancing vortex–vortex interaction. If vortices were so densely populated that they interacted even in the absence of a wave, adding a forced large-scale wave enhanced the existing upscale transfer. Results further suggest that continuous forcing by the main driving mechanism (either vortices or internal waves) is necessary to maintain such upscale transfer. These findings could help to improve understanding of the direction of energy transfer in submesoscale oceanic processes.

Tensor CSAMT survey over the Sulphur Springs thermal area, Valles Caldera, New Mexico, United States of America, Part II: Implications for CSAMT methodology

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 466-476 ◽  
Author(s):  
Philip E. Wannamaker
Keyword(s):  
Near Field ◽  
Skin Depth ◽  
Small Scale ◽  
Far Field ◽  
Survey Area ◽  
Wave Regime ◽  
Low Frequencies ◽  
Field Source ◽  
Source Field ◽  
Sulphur Springs

The resistivity model for the Sulphur Springs area in the companion paper (Part I) plus the availability of overlapping controlled‐source audiomagnetotelluric (CSAMT) and magnetotelluric (MT) data has allowed study of far‐field to near‐field transitions, source field geometries over the survey area, and scalar‐tensor impedance discrepancies. The regional setting of conductive Paleozoic sediments over resistive basement seriously reduced depth of exploration within the plane‐wave regime to about 1/20th of the transmitter‐receiver separation, rather than the traditional 1/3rd to 1/5th based on half‐space models. As frequency falls to where skin depth in the sedimentary layer exceeds its thickness, transmitter electromagnetic (EM) fields enter the resistive basement and may diffuse to the receiver with relatively little attenuation, promoting near‐field behavior. Comparisons are made of observed electric (E) and magnetic (H) fields inside and outside the caldera with EM fields computed from layered resistivity models derived from local 1-D inversion of the ρa and θ, and from simple 3-D models. First, the comparisons indicate that small‐scale structure near the transmitter does not lead to overprint effects in the impedance data at the receiver but, instead, acts as an equivalent far‐field source. Second, at both high and low frequencies, the observed E and H fields can depart substantially from those predicted by local layered models. In fact, an effective regional layering appears to control the magnetic field amplitudes and the far‐to near‐field transition in this survey area. The observed electric fields, on the other hand, are controlled by all scales of geology. When heterogeneity is important, significant departures between scalar and tensor CSAMT data can be expected, and are exacerbated when the source field is poorly coupled to the sensors. The problem is much reduced for vector CSAMT measurements where all horizontal field components are measured and the maximally coupled results are defined, but mode identification is more difficult for multidimensional structures.

INTERNAL GRAVITY-SHEAR WAVES IN THE TROPOSPHERE: III. PERTURBATION OF SMOKE TRAILS

1966 ◽  
Vol 44 (10) ◽  
pp. 2287-2291
Author(s):  
Keikichi Naito ◽  
D. R. Hay
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Shear Waves ◽  
Vertical Plane ◽  
Lower Troposphere ◽  
Scale Structure ◽  
Small Scale ◽  
Small Scale Structure ◽  
Air Motion ◽  
Large Eddies

Experimental observations on vertical smoke trails and smoke puffs in the lower troposphere have shown several interesting features of the small-scale structure of the air. The perturbation velocities of wavelengths of several hundred meters have relatively simple contour patterns in the vertical plane. Isolated deformations of the trails occur with small, semicircular motions of the air. The air motion is turbulent at heights below about 300 m, while above this level it is principally laminar. Perturbations of the smoke trails may be attributed either to large eddies or to internal waves, but the theory of internal waves and the experimental observations lend greater support to the internal–wave explanation.

scholarly journals Downstream Propagation and Remote Dissipation of Internal Waves in the Southern Ocean

2019 ◽  
Vol 49 (7) ◽  
pp. 1873-1887 ◽  
Author(s):  
Kaiwen Zheng ◽  
Maxim Nikurashin
Keyword(s):  
Energy Dissipation ◽  
Southern Ocean ◽  
Internal Wave ◽  
Linear Theory ◽  
Internal Waves ◽  
Turbulent Energy ◽  
Wave Radiation ◽  
Small Scale ◽  
Length Scale ◽  
Geostrophic Flows

AbstractRecent microstructure observations in the Southern Ocean report enhanced internal gravity waves and turbulence in the frontal regions of the Antarctic Circumpolar Current extending a kilometer above rough bottom topography. Idealized numerical simulations and linear theory show that geostrophic flows impinging on rough small-scale topography are very effective generators of internal waves and estimate vigorous wave radiation, breaking, and turbulence within a kilometer above bottom. However, both idealized simulations and linear theory assume periodic and spatially uniform topography and tend to overestimate the observed levels of turbulent energy dissipation locally at the generation sites. In this study, we explore the downstream evolution and remote dissipation of internal waves generated by geostrophic flows using a series of numerical, realistic topography simulations and parameters typical of Drake Passage. The results show that significant levels of internal wave kinetic energy and energy dissipation are present downstream of the rough topography, internal wave generation site. About 30%–40% of the energy dissipation occurs locally over the rough topography region, where internal waves are generated. The rest of the energy dissipation takes place remotely and decays downstream of the generation site with an e-folding length scale of up to 20–30 km. The model we use is two-dimensional with enhanced viscosity coefficients, and hence it can result in the underestimation of the remote wave dissipation and its decay length scale. The implications of our results for turbulent energy dissipation observations and mixing parameterizations are discussed.

Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Application to the Southern Ocean

2010 ◽  
Vol 40 (9) ◽  
pp. 2025-2042 ◽  
Author(s):  
Maxim Nikurashin ◽  
Raffaele Ferrari
Keyword(s):  
Southern Ocean ◽  
Internal Wave ◽  
Internal Waves ◽  
Acoustic Doppler Current Profiler ◽  
Drake Passage ◽  
Internal Tides ◽  
Wave Radiation ◽  
Small Scale ◽  
Region Theory ◽  
Abyssal Mixing

Abstract Recent estimates from observations and inverse models indicate that turbulent mixing associated with internal wave breaking is enhanced above rough topography in the Southern Ocean. In most regions of the ocean, abyssal mixing has been primarily associated with radiation and breaking of internal tides. In this study, it is shown that abyssal mixing in the Southern Ocean can be sustained by internal waves generated by geostrophic motions that dominate abyssal flows in this region. Theory and fully nonlinear numerical simulations are used to estimate the internal wave radiation and dissipation from lowered acoustic Doppler current profiler (LADCP), CTD, and topography data from two regions in the Southern Ocean: Drake Passage and the southeast Pacific. The results show that radiation and dissipation of internal waves generated by geostrophic motions reproduce the magnitude and distribution of dissipation previously inferred from finescale measurements in the region, suggesting that it is one of the primary drivers of abyssal mixing in the Southern Ocean.

Stability and mixing of a vertical plane buoyant jet in confined depth

1979 ◽  
Vol 94 (2) ◽  
pp. 275-304 ◽  
Author(s):  
Gerhard H. Jirka ◽  
Donald R. F. Harleman
Keyword(s):  
Hydraulic Jump ◽  
Near Field ◽  
Vertical Plane ◽  
Convective Transport ◽  
Relative Depth ◽  
Far Field ◽  
Buoyant Jet ◽  
Densimetric Froude Number ◽  
Mixing Characteristics ◽  
The Stability

A plane turbulent buoyant jet discharging vertically into a two-dimensional channel of confined depth is considered. The channel opens at both ends into a large outside reservoir, thus defining a steady symmetrical flow field within the channel. The analysis is aimed at two aspects, the stability and the bulk mixing characteristics of the discharge. A stable discharge configuration is defined as one in which a buoyant surface layer is formed which spreads horizontally and does not communicate with the initial buoyant jet region. On the other hand, the discharge configuration is unstable when a recirculating cell exists on both sides of the jet efflux.It is shown that discharge stability is only dependent on the dynamic interaction of three near-field regions, a buoyant jet region, a surface impingement region and an internal hydraulic jump region. The buoyant jet region is analysed with the assumption of a variable entrainment coefficient in a form corresponding to an approximately constant jet-spreading angle as confirmed by different experimental sources. The properties of surface impingement and internal jump regions are determined on the basis of control volume analyses. Under the Boussinesq approximation, only two dimensionless parameters govern the near-field interaction; these are a discharge densimetric Froude number and a relative depth. For certain parameter combinations, namely those implying low buoyancy and shallow depth, there is no solution to the conjugate downstream condition in the hydraulic jump which would satisfy both momentum and energy conservation principles. Arguments are given which interpret this condition as one which leads to the establishment of a near-field recirculation cell and, thus, discharge instability.The far-field boundary conditions, while having no influence on discharge stability, determine the bulk mixing characteristics of the jet discharge. The governing equations for the two-layered counterflow system in the far field are solved. The strength of the convective transport, and hence the related dilution ratio, is governed by another non-dimensional parameter, the product of the relative channel length and the boundary friction coefficient.Experiments in a laboratory flume, covering a range of the governing parameters, are in excellent agreement with the theoretical predictions, both the stability criterion and the bulk mixing characteristics.

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