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1

Scattering of internal waves by vertical barrier in a channel of stratified fluid

Dolai P.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 3

471--485

EN

The problem of two dimensional internal wave scattering by a vertical barrier in the form of a submerged plate, or a thin wall with a gap in an exponentially stratified fluid of uniform finite depth bounded by a rigid plane at the top, is considered in this paper. Assuming linear theory and the Boussinesq approximation, the problem is formulated in terms of the stream function. In the regions of the two sides of the vertical barrier, the scattered stream function is represented by appropriate eigen function expansions. By the use of appropriate conditions on the barrier and the gap, a dual series relation involving the unknown elements of the scattering matrix is produced. By defining a function with these unknown elements as its Fourier sine expansion series, it is found that this function satisfies a Carleman type integral equation on the barrier whose solution is immediate. The elements of the scattering matrix are then obtained analytically as well as numerically corresponding to any mode of the incident internal wave train for each barrier configuration. A comparison with earlier results available in the literature shows good agreement. To visualize the effect of the barrier on the fluid motion, the stream lines for an incident internal wave train at the lowest mode are plotted.

2

ThermaI stratification effects on nonIinear hydromagnetic flow over a verticaI stretching surface with a power-Iaw velocity

Kandasamy R., Khamis A.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 1

47-54

EN

An analysis has been carried out to obtain the nonlinear MHD flow with heat transfer characteristics of an incompressible, viscous and Boussinesq fluid on a vertical stretching surface with power-Iaw velocity. An approximate numerical solution for the flow problem has been obtained by solving the goveming equations using a numerical technique. A magnetic field is applied transversely to the direction of the flow. Adopting the similarity transformation, goveming nonlinear partial differential equations of the problem are transformed to nonlinear ordinary differential equations. Then the numerical solution of the problem is drawn using the Runge Kutta Gili method. NumericaI caIculations are carried out for different values of the dimensionless parameters in !he problem and an analysis of the results obtained show that the flow field is influenced appreciably by the presence of the magnetic field and thermal stratification effect.

3

The transformational analytical solution for nonlinear convection in the presence of two-way rotation

El-Kholy S. A., Ismail I. A.

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 1

119-130

EN

Steady two-dimensional finite amplitude solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotated about its vertical axis. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. Different boundaries with prescribed constant temperature are assumed and the solutions are obtained. The transform for summing the variables, which reduce the nonlinear partial differential equation into ordinary differential equation of the high order, is used. The existence of steady subcritical finite amplitude solutions is demonstrated for different Prandtl numbers. A strong reduction in the domain of stable rolls that occurs as the rotation rate is increasing. Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of the vertical sidewalls the critical Rayleigh number R is much lower than the classical value of the infinity extended layer.

4

Influence of the method of dry convection in the atmosphere modeling on the dynamic properties of the model

Brojewski R., Jasiński J.

Journal of Technical Physics

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2003

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Vol. 44, no 2

215-233

EN

This paper presents the problem of modeling dry convection in the atmosphere based on scaling of the movement equations resulting from the assumption that convection streams are mainly generated by the Archimedes draught force. This approach leads to description of the atmosphere movement different than in the Boussinesq approximation. The simplest case of Galerkin type equations in 3D phase space was considered. The obtained equations have different dynamics than the equations of the classical Lorenz model of dry convection. Lorenz model dynamics is controlled by the configuration of 2 non-dimensional numbers, while the dynamics of the proposed model is controlled by 3 numbers. It is presented in the language of symbolic dynamics, illustrated with numerous examples - indicating its different character than in the classical Lorenz model, among others: different values of Rayleigh number for which the systems loose structural stability.