VALIDATING RANGE-DEPENDENT, FULL-FIELD MODELS OF THE ACOUSTIC VECTOR FIELD IN SHALLOW WATER ENVIRONMENTS

2008 ◽  
Vol 16 (04) ◽  
pp. 471-486 ◽  
Author(s):  
KEVIN B. SMITH
Keyword(s):  
Parabolic Equation ◽  
Normal Mode ◽  
Numerical Algorithms ◽  
Analytic Solutions ◽  
Equation Model ◽  
Propagation Model ◽  
Full Field ◽  
Benchmark Solutions ◽  
Fourier Algorithm ◽  
Good Agreement

Numerical algorithms for computing acoustic particle velocity from a pressure propagation model are introduced. Implementation using both a parabolic equation and normal mode approach are considered. The parabolic equation model employed uses a split-step Fourier algorithm, although application of the technique is general to other parabolic equation models. Expressions for the normal mode equations are also presented, for both coupled and adiabatic mode models. Results for a Pekeris waveguide are presented for a point source, prompting a brief discussion of multipath influence on the estimation of the direction of energy flow. Approximate analytic solutions are used to validate the general results of both the models. Results for the range-dependent benchmark wedge are then presented, which show generally good agreement between the two types of models. The results from the two-way, coupled normal mode model provide potential benchmark solutions for the wedge and a means of confirming the accuracy of other models.

CONVERGENCE, STABILITY, AND VARIABILITY OF SHALLOW WATER ACOUSTIC PREDICTIONS USING A SPLIT-STEP FOURIER PARABOLIC EQUATION MODEL

2001 ◽  
Vol 09 (01) ◽  
pp. 243-285 ◽  
Author(s):  
KEVIN B. SMITH
Keyword(s):  
Parabolic Equation ◽  
Shallow Water ◽  
Acoustic Field ◽  
Equation Model ◽  
Single Frequency ◽  
Test Case ◽  
Flat Bottom ◽  
Parameter Variations ◽  
Interface Boundary Conditions ◽  
Fourier Algorithm

The Shallow Water Acoustic Modeling (SWAM'99) Workshop was organized to examine the ability of various acoustic propagation models to accurately predict sound transmission in a variety of shallow water environments designed with realistic perturbations. In order to quantify this, tests of reciprocity, convergence, and stability must be considered. This paper presents the results of an established parabolic equation model based on the split-step Fourier algorithm. The test cases examined in this paper include a simple isospeed water column over a flat bottom with geoacoustic parameter variations, a randomly sloping bottom with geoacoustic parameter variations, and a canonical shallow water profile perturbed by internal waves over a flat, homogeneous bottom. Source configurations were generally held constant but numerous single frequency and broadband runs were performed. Model testing is emphasized with specific criteria for accurate solutions being specified. Random perturbations are added to one test case to examine the influence of environmental uncertainty on the details of the propagation. The results indicate that point-wise accurate solutions to the acoustic field in shallow water cannot be achieved beyond a few kilometers. This is partly due to the inaccuracies of the split-step Fourier algorithm employed in these shallow water scenarios and the treatment of the bottom interface boundary conditions, but also due to the inherent variability caused by uncertain environmental specification. Thus, more general features of the acoustic field should be emphasized at longer ranges.

PECAN: A CANADIAN PARABOLIC EQUATION MODEL FOR UNDERWATER SOUND PROPAGATION

2001 ◽  
Vol 09 (01) ◽  
pp. 69-100 ◽  
Author(s):  
G. H. BROOKE ◽  
D. J. THOMSON ◽  
G. R. EBBESON
Keyword(s):  
Parabolic Equation ◽  
Sound Propagation ◽  
Nonlocal Boundary ◽  
Fourier Method ◽  
Propagation Model ◽  
Finite Difference Approximation ◽  
Single Frequency ◽  
Difference Approximation ◽  
Underwater Sound ◽  
Benchmark Solutions

PECan is a Canadian N× 2D/3D parabolic equation (PE) underwater sound propagation model that was developed for matched-field processing applications. It is based on standard square-root operator and/or propagator approximations that lead to an alternating direction solution of the 3-D problem. A 2-D split-step Padé approximation is employed for propagation in range. The 3-D azimuthal corrections are computed using either a split-step Fourier method or a Crank–Nicolson finite-difference approximation. It features a heterogeneous formulation of the differential operators on an offset vertical grid, energy conservation, a choice of initial field including self-starter, and both absorbing and nonlocal boundary conditions. Losses due to shear wave conversion in an elastic bottom are handled in the context of a complex density approximation. In this paper, PECan is described and validated against some standard benchmark solutions to underwater acoustics problems. Subsequently, PECan is applied to several single-frequency test cases that were offered for numerical consideration at the SWAM'99 Shallow Water Acoustic Modeling workshop.

Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Numerical Algorithms ◽  
Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

Heat transport by parallel-roll convection in a rectangular container

1987 ◽  
Vol 185 ◽  
pp. 205-234 ◽  
Author(s):  
R. W. Walden ◽  
Paul Kolodner ◽  
A. Passner ◽  
C. M. Surko
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Critical Rayleigh Number ◽  
Equation Model ◽  
Onset Of Convection ◽  
Infinite Layer ◽  
Lateral Extent ◽  
Prandtl Numbers ◽  
Rayleigh Numbers ◽  
Good Agreement

Heat-transport measurements are reported for thermal convection in a rectangular box of aspect’ ratio 10 x 5. Results are presented for Rayleigh numbers up to 35Rc, Prandtl numbers between 2 and 20, and wavenumbers between 0.6 and 1.0kc, where Rc and kc are the critical Rayleigh number and wavenumber for the onset of convection in a layer of infinite lateral extent. The measurements are in good agreement with a phenomenological model which combines the calculations of Nusselt number, as a function of Rayleigh number and roll wavenumber for two-dimensional convection in an infinite layer, with a nonlinear amplitude-equation model developed to account for sidewell attenuation. The appearance of bimodal convection increases the heat transport above that expected for simple parallel-roll convection.

ACOUSTIC THREE-DIMENSIONAL EFFECTS AROUND THE TAIWAN STRAIT: COMPUTATIONAL RESULTS

1999 ◽  
Vol 07 (01) ◽  
pp. 15-26 ◽  
Author(s):  
CHI-FANG CHEN ◽  
JANG-JIA LIN ◽  
DING LEE
Keyword(s):  
Field Data ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Propagation Model ◽  
Computational Results ◽  
Submarine Canyons ◽  
Offshore Area ◽  
Ocean Environment ◽  
The Taiwan Strait ◽  
Good Agreement

A set of experiments were performed in the offshore area off the coasts of Taiwan and three-dimensional (3-D) measurements recorded. The 3-D effect on underwater propagation due to azimuthal variation of bottom topography is studied for the offshore regions southwest of Taiwan, where submarine canyons exist. A 3-D acoustic propagation model, FOR3D, is used to detect the 3-D effect. Computational results show that the 3-D effect is more prominent along the axis of the canyon than across it. Calculations show a very good agreement with field data, which indicate that the 3-D effect exists in this realistic ocean environment.

scholarly journals Distribution and Source Sites of Nonlinear Internal Waves Northeast of Hainan Island

2022 ◽  
Vol 10 (1) ◽  
pp. 55
Author(s):  
Jianjun Liang ◽  
Xiao-Ming Li ◽  
Kaiguo Fan
Keyword(s):  
Internal Waves ◽  
Hainan Island ◽  
Luzon Strait ◽  
Satellite Observations ◽  
Propagation Model ◽  
Tidal Period ◽  
S Waves ◽  
Nonlinear Internal Waves ◽  
Type D ◽  
Good Agreement

The distribution and source sites of nonlinear internal waves (NLIWs) northeast of Hainan Island were investigated using satellite observations and a wavefront propagation model. Satellite observations show two types of NLIWs (here referred to as type-S and type-D waves). The type-S waves are spaced at a semidiurnal tidal period and the type-D waves are spaced at a diurnal tidal period. The spatial distribution of the two types of NLIWs displays a sandwich structure in which the middle region is influenced by both types of NLIWs, and the northern and southern regions are governed by the type-S and type-D waves, respectively. Solving the wavefront model yields good agreement between simulated and observed wavefronts from the Luzon Strait to Hainan Island. We conclude that the NLIWs originate from the Luzon Strait.

scholarly journals ESTIMATING THE PROPAGATION OF A UNIFORMLY ACCELERATED JET

2021 ◽  
Vol 57 (2) ◽  
pp. 297-309
Author(s):  
J. I. Castorena ◽  
A. C. Raga ◽  
A. Esquivel ◽  
A. Rodríguez-González ◽  
L. Hernández-Martínez ◽  
...  
Keyword(s):  
Loss Rate ◽  
Mass Loss Rate ◽  
Center Of Mass ◽  
Analytic Solutions ◽  
Pressure Balance ◽  
Working Surface ◽  
Ram Pressure ◽  
Balance Solution ◽  
Analytic Models ◽  
Good Agreement

We study the problem of a Herbig-Haro jet with a uniformly accelerating ejection velocity, travelling into a uniform environment. For the ejection density we consider two cases: a time-independent density, and a time-independent mass loss rate. For these two cases, we obtain analytic solutions for the motion of the jet head using a ram-pressure balance and a center of mass equation of motion. We also compute axisymmetric numerical simulations of the same flow, and compare the time-dependent positions of the leading working surface shocks with the predictions of the two analytic models. We find that if the jet is over-dense and over-pressured (with respect to the environment) during its evolution, a good agreement is obtained with the analytic models, with the flow initially following the center of mass analytic solution, and (for the constant ejection density case) at later times approaching the ram-pressure balance solution.

A New Computational Model for Expiratory Flow From Nonhomogeneous Human Lungs

1989 ◽  
Vol 111 (3) ◽  
pp. 200-205 ◽  
Author(s):  
R. K. Lambert
Keyword(s):  
Mechanical Properties ◽  
Model Simulation ◽  
Homogeneous Model ◽  
Equation Model ◽  
Alveolar Pressure ◽  
Mechanical Problem ◽  
Peripheral Airways ◽  
Human Lungs ◽  
Experimental Findings ◽  
Good Agreement

A model has been developed for expiration from human lungs in which the mechanical properties of the airways and parenchyma can be varied between regions. The model is based on an existing homogeneous model. The fluid mechanical problem of the merging of dissimilar flows from adjacent regions is underspecified by the conservation laws of mass and energy. An existing, empirically derived result, provides the required extra equation. Model simulation of a nonhomogeneously distributed mild constriction of the peripheral airways gives results for maximal flows and alveolar pressure differences which are in good agreement with recent experimental findings.

scholarly journals Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 810
Author(s):  
Jade Gesare Abuga ◽  
Tiri Chinyoka
Keyword(s):  
Finite Volume ◽  
Numerical Algorithm ◽  
Numerical Study ◽  
Fluid Model ◽  
Shear Banding ◽  
Numerical Algorithms ◽  
Viscoelastic Fluids ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

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