Wyniki wyszukiwania - BazTech

1

The New Extended KdV Equation for the Case of an Uneven Bottom

Karczewska A., Rozmej P.

Computational Methods in Science and Technology

|

2018

|

Vol. 24, No. 4

221--225

EN

The consistent derivation of the extended KdV equation for an uneven bottom for the case of α = O(β) and δ = O(β 2 ) is presented. This is the only one case when second order KdV type nonlinear wave equation can be derived for arbitrary bounded bottom function.

2

Evolution of a random field of surface gravity waves in a two fluid domain

Senapati S., Debsarma S., Das K. P.

International Journal of Applied Mechanics and Engineering

|

2012

|

Vol. 17, no. 2

481-493

EN

A spectral transport equation is derived here that governs the evolution of a random field of surface gravity waves in a two layer fluid model. This equation is used to study the stability of an initially homogeneous Lorentz spectrum under long wave length perturbations. It is observed that the effect of randomness is to reduce the growth rate of instability. An increase in the thickness of the upper fluid results in an increase in the extent of instability. It is also found that the extent of instability becomes less for a smaller density difference of the two fluids.

3

Stability analysis from fourth order nonlinear evolution equation for two stokes wave trains in deep water in the presence of air flowing over water

Majumder D. P., Dhar A. K.

International Journal of Applied Mechanics and Engineering

|

2009

|

Vol. 14, no 4

989-1008

EN

Fourth order nonlinear evolution equations are derived for two Stokes wave trains in deep water in the presence of air flowing over water. The importance of the fourth order term in the evolution equation was pointed out by Dysthe (1979). Stability analysis is then made for uniform two Stokes wave trains in the presence of air flowing over water. From these evolution equations the expressions for the maximum growth rate of instability, the wave number at marginal stability and the wave number separation of fastest growing side band are derived and graphs are plotted for the above three expressions against the wave steepness. Significant improvements can be achieved from the results obtained from the two coupled third order nonlinear Schrödinger equations.

4

The effect of randomness on stability of surface gravity waves from fourth order nonlinear evolution equation

Dhar A. K., Das K. P.

International Journal of Applied Mechanics and Engineering

|

2001

|

Vol. 6, no 1

11-34

EN

A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves of wave-steepness up to 0.25, is used here to investigate the effect of randomness on stability of deep-water surface gravity waves in the presence of wind blowing over water. A spectral transport equation for narrow band Gaussian surface wave is derived. With the use of this transport equation stability analysis is made for an initial homogeneous wave spectrum having a very simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained, in which higher order contribution comes from only one of the fourth order terms in the evolution equation, which is responsible for wave-induced mean flow. This higher order contribution in this expression for growth rate of instability produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and ultimately the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order terms in the evolution equation.