MONOCHROMATIC WAVE PROPAGATION IN KP-TYPE EQUATION

A class of ocean acoustic propagation problems can be solved efficiently by the Parabolic Equation (PE) approximation method. The application of the PE method for the prediction of wave propagation introduces a new parameter, the reference wavenumber k0. This requires selection of the most appropriate k0, which is related to the reference sound speed c0. The influence on the acoustic field by the choice of c0 is rarely visible under weak range-dependent environments. Even if it is visible, the difference is small and is usually negligible since the present judicious choice of the c0 seems to provide acceptable results. When the environment is not weakly range-dependent, the choice of c0 will likely affect the computation of acoustic results. This paper examines a few different choices of c0 and analyzes how these different choices can influence the acoustic results. An application is given where the farfield wave equation represents a realistic range-dependent environment. Different choices of c0 were made for the computation of the acoustic field; as a consequence, different choices of c0 produce different acoustic results. These numerical results are not in agreement with a known reference exact solution. The differences are not too small and may be considered non-negligible. So, there is a need to make an appropriate choice of c0 in order to produce reasonable results. For the purpose of achieving satisfactory and acceptable acoustic results dealing with a PE-type equation, the requirements of the reference wavenumber will be discussed both mathematically and physically. Then, a number of computational choices of c0 will be examined, especially the k0-formula. An analysis as well as an assessment of the k0-formula will be given.

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Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup

Computation ◽

10.3390/computation9040047 ◽

2021 ◽

Vol 9 (4) ◽

pp. 47

Author(s):

Lucas Calvo ◽

Diana De Padova ◽

Michele Mossa ◽

Paulo Rosman

Keyword(s):

Finite Element ◽

Wave Propagation ◽

Type Equation ◽

Element Model ◽

Galerkin Finite Element ◽

Quadrilateral Elements ◽

Discontinuous Galerkin Finite Element ◽

Slope Limiter ◽

Continuous Galerkin ◽

Poisson Type

This paper presents a new depth-integrated non-hydrostatic finite element model for simulating wave propagation, breaking and runup using a combination of discontinuous and continuous Galerkin methods. The formulation decomposes the depth-integrated non-hydrostatic equations into hydrostatic and non-hydrostatic parts. The hydrostatic part is solved with a discontinuous Galerkin finite element method to allow the simulation of discontinuous flows, wave breaking and runup. The non-hydrostatic part led to a Poisson type equation, where the non-hydrostatic pressure is solved using a continuous Galerkin method to allow the modeling of wave propagation and transformation. The model uses linear quadrilateral finite elements for horizontal velocities, water surface elevations and non-hydrostatic pressures approximations. A new slope limiter for quadrilateral elements is developed. The model is verified and validated by a series of analytical solutions and laboratory experiments.

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Monochromatic Wave Propagation

Introduction to Optical Microscopy ◽

10.1017/9781108552660.004 ◽

2019 ◽

pp. 14-32

Keyword(s):

Wave Propagation ◽

Monochromatic Wave

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A Vlasov equation for pressure wave propagation in bubbly fluids

Journal of Fluid Mechanics ◽

10.1017/s002211200100708x ◽

2002 ◽

Vol 454 ◽

pp. 287-325 ◽

Cited By ~ 21

Author(s):

PETER SMEREKA

Keyword(s):

Wave Propagation ◽

Vlasov Equation ◽

Pressure Wave ◽

Bubble Dynamics ◽

Type Equation ◽

Nonlinear Effects ◽

Single Bubble ◽

Pressure Waves ◽

General Description ◽

Bubbly Fluids

The derivation of effective equations for pressure wave propagation in a bubbly fluid at very low void fractions is examined. A Vlasov-type equation is derived for the probability distribution of the bubbles in phase space instead of computing effective equations in terms of averaged quantities. This provides a more general description of the bubble mixture and contains previously derived effective equations as a special case. This Vlasov equation allows for the possibility that locally bubbles may oscillate with different phases or amplitudes or may have different sizes. The linearization of this equation recovers the dispersion relation derived by Carstensen & Foldy. The initial value problem is examined for both ideal bubbly flows and situations where the bubble dynamics have damping mechanisms. In the ideal case, it is found that the pressure waves will damp to zero whereas the bubbles continue to oscillate but with the oscillations becoming incoherent. This damping mechanism is similar to Landau damping in plasmas. Nonlinear effects are considered by using the Hamiltonian structure. It is proven that there is a damping mechanism due to the nonlinearity of single-bubble motion. The Vlasov equation is modified to include effects of liquid viscosity and heat transfer. It is shown that the pressure waves have two damping mechanisms, one from the effects of size distribution and the other from single-bubble damping effects. Consequently, the pressure waves can damp faster than bubble oscillations.

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