On the Structure of Wave Fronts in Nonlinear Dissipative Media

Баренблатт, Г. И.; Ivanov, M. Ya.; Shapiro, G. I.

doi:10.1007/978-3-642-61634-1_30

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…More recently, Small et al (1999b) observed a smaller bore on the Malin Shelf, just north of the observations that are described here, that subsequently disintegrated into about 5 waves. The number of NIWs that form when an internal bore disintegrates depends on the ratio of the parameters of dispersion, non-linearity and dissipation in the water column (Barenblatt et al, 1985). On the Scotian Shelf, packets of between two and four NIWs have been observed (Sandstrom and Elliott, 1984).…”

Section: Introductionmentioning

confidence: 99%

Mass transport by non-linear internal waves on the Malin Shelf

Inall¹,

Shapiro²,

Sherwin³

2001

Continental Shelf Research

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Packets of non-linear internal waves (NIWs) were observed with a moored ADCP in the seasonal thermocline at the edge of the Malin Shelf, to the west of Scotland, during August 1995. A wide range of wave sizes was encountered including some that were strongly non-linear. The largest waves had a vertical displacement of about 25 m (in 145 m water) and a vertical shear greater than 0.4 m s À1 over a depth of 65 m across the thermocline. In general they propagated toward the ESE, which is south of a line normal to the shelf break, with a phase speed of between 0.54 and 0.60 m s À1. Within each packet the direction of the current flow in successive waves veered at a similar rate to that of waves with a tidal frequency. However, large NIWs were only encountered during neap rather than spring tides, so their relationship with the tide is not entirely clear. The first empirical mode dominated the motion, but its shape was often more convoluted than an equivalent baroclinic mode. A two-layer KdV theory for the mass transport due to the waves, which relates transport to the elevation of the interface and the linear long wave phase speed, is presented. It compares well with the observed transport in the lower layer. None of the waves possessed significant dispersion, so they did not conform to the KdV soliton solution. In a typical NIW packet a lower layer transport of about 5 m 2 s À1 offshore was maintained over a period of about 1.5 h, with a peak of about 20 m 2 s À1. A sustained transport of about 0.3 m 2 s À1 can be attributed to NIWs at the Malin Shelf edge in summer.

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Section: Introductionmentioning

confidence: 99%

Mass transport by non-linear internal waves on the Malin Shelf

Inall¹,

Shapiro²,

Sherwin³

2001

Continental Shelf Research

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“…(5.2) The solution of this equation is presented in [7,14]. In particular, on the example of the numerical inte gration of the problem of arbitrary discontinuity decay, some averaged "turbulent" characteristics of the oscillating solutions implemented (of effective turbulent viscosity and pulsation intensity) are shown.…”

Section: Microstructure Dispersion In Burger's Modelmentioning

confidence: 99%

Simulation of the generation of turbulence motion in edge wakes

Ivanov

2009

Math Models Comput Simul

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The process of generating turbulence in edge wakes has been simulated and the results of the simulation are presented. The proposed mathematical model follows from a special procedure, which aims to average the flow parameters on scales comparable with the free path of molecules. The examined mechanism of generating turbulence is described by an expended set of Euler and Navier-Stokes nonstationary equations, with additional dispersive summands of the third order, which are obtained, if one uses the averaging procedure. The basic hydrodynamic equations are integrated by means of the well known Godunov procedure of the second order. The calculated averaged perfor mances of the turbulent flows agree with the experimental data.

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“…where ǫ ≥ 0, α ≥ 0, β ≥ 0 are constants and c = 1/2 is the velocity of propagation of the steady wave (see also [4]). The problem is to find the value of the parameters in the effective equation which minimizes…”

Section: An Example: the Korteveg-devries-burgers Equationmentioning

confidence: 99%

Problem reduction, renormalization, and memory

Chorin

Stinis

2006

CAMCoS

101

127

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Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for time dependent problem averaging usually fails, and averaged equations must be augmented by appropriate memory and random forcing terms. Approximations are described and examples are given.

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On the Structure of Wave Fronts in Nonlinear Dissipative Media

Cited by 4 publications

References 5 publications

Mass transport by non-linear internal waves on the Malin Shelf

Mass transport by non-linear internal waves on the Malin Shelf

Simulation of the generation of turbulence motion in edge wakes

Problem reduction, renormalization, and memory

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