This study presents the turbulent flow field in submerged plane wall-jets on horizontal fully rou... more This study presents the turbulent flow field in submerged plane wall-jets on horizontal fully rough walls detected by a Vectrino velocimeter. For the comparison between the fully rough and smooth submerged wall-jets, the smooth submerged wall-jet case was also revisited. The two-dimensional Reynolds averaged boundary layer equations of a steady turbulent flow are analyzed to determine the velocity and Reynolds shear stress profiles in the fully developed zone of smooth and fully rough submerged wall-jets. The response of the turbulent flow characteristics in submerged wall-jets to wall roughness is examined from the point of view of similarity characteristics, growth of the length scale, and decay of the velocity and turbulence characteristics scales; and compared with the response of those to smooth and transitionally rough walls. The significant observation is that with an appropriate scaling, the velocity, Reynolds shear stress and turbulence intensities in the fully developed zo...
Open Access Journal of Mathematical and Theoretical Physics
might have been the course taken up by mathematics during the long journey, since ancient times. ... more might have been the course taken up by mathematics during the long journey, since ancient times. A very early method necessitated for counting of objects (enumeration) was the Tally Marks used in the late Stone Age. In some parts of Europe, Africa and Australia the system consisted of simple vertical bars:
In this paper, we study the exact controllability and boundary stabilization of the torsional vib... more In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.
Page 1. Proc. Indian Acad. Sci. (Math. Sci.), Vol. 107, No. 4, November 1997, pp. 411-423. 9 Prin... more Page 1. Proc. Indian Acad. Sci. (Math. Sci.), Vol. 107, No. 4, November 1997, pp. 411-423. 9 Printed in India Transformation of chaotic nonlinear polynomial difference systems through Newton iterations SUJIT K BOSE s N Bose ...
The Green's function solution of the Helmholtz's equation for acoustic scattering by hard surface... more The Green's function solution of the Helmholtz's equation for acoustic scattering by hard surfaces and radiation by vibrating surfaces, lead in both the cases, to a hyper singular surface boundary integral equation. Considering a general open surface, a simple proof has been given to show that the integral is to be interpreted like the Hadmard finite part of a divergent integral in one variable. The equation is reformulated as a Cauchy principal value integral equation, but also containing the potential at the control point. It is amenable to numerical treatment by conventional methods. An alternative formulation in the better known form, containing the tangential derivative of the potential is also given. The two dimensional problem for an open arc is separately treated for its simpler feature.
ABSTRACT The boundary stabilization of the problem satisfying the differential equation y &#3... more ABSTRACT The boundary stabilization of the problem satisfying the differential equation y '' +λy ''' =c 2 (Δy+μΔy ' ),0<λ<μ, in a bounded domain Ω in ℝ n with smooth boundary Γ is studied. Such equations arise in the vibrations of flexible structures possessing internal material damping and modeled by the “standard linear model” of viscoelasticity. Explicit exponential energy decay rate is obtained for the solution of the above problem subject to mixed boundary conditions.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Sep 1, 2009
Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity eq... more Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter.
Instability Theory of Sand Ripples Formed by Turbulent Shear Flows. [Journal of Hydraulic Enginee... more Instability Theory of Sand Ripples Formed by Turbulent Shear Flows. [Journal of Hydraulic Engineering 1, 335 (2012)]. Sujit K. Bose, Subhasish Dey. Abstract. A theory of turbulent shear flow over a sand bed is developed addressing ...
A new theoretical approach is presented for the derivation of free surface profiles of two-dimens... more A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide.
Abstract An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude n... more Abstract An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady‐state flow equation. ...
This study presents the turbulent flow field in submerged plane wall-jets on horizontal fully rou... more This study presents the turbulent flow field in submerged plane wall-jets on horizontal fully rough walls detected by a Vectrino velocimeter. For the comparison between the fully rough and smooth submerged wall-jets, the smooth submerged wall-jet case was also revisited. The two-dimensional Reynolds averaged boundary layer equations of a steady turbulent flow are analyzed to determine the velocity and Reynolds shear stress profiles in the fully developed zone of smooth and fully rough submerged wall-jets. The response of the turbulent flow characteristics in submerged wall-jets to wall roughness is examined from the point of view of similarity characteristics, growth of the length scale, and decay of the velocity and turbulence characteristics scales; and compared with the response of those to smooth and transitionally rough walls. The significant observation is that with an appropriate scaling, the velocity, Reynolds shear stress and turbulence intensities in the fully developed zo...
Open Access Journal of Mathematical and Theoretical Physics
might have been the course taken up by mathematics during the long journey, since ancient times. ... more might have been the course taken up by mathematics during the long journey, since ancient times. A very early method necessitated for counting of objects (enumeration) was the Tally Marks used in the late Stone Age. In some parts of Europe, Africa and Australia the system consisted of simple vertical bars:
In this paper, we study the exact controllability and boundary stabilization of the torsional vib... more In this paper, we study the exact controllability and boundary stabilization of the torsional vibrations of a flexible space structure (such as a solar cell array) modeled by a rectangular panel, incorporating the material damping of the structure. The panel is hoisted at one end by a rigid hub and the other end is totally free. For the attachment of this hub on one side of the panel, the hub dynamics leads to a nonstandard boundary condition. To incorporate internal damping of the material, we assume Voigt-type viscoelasticity of the structure. Exact controllability theory is established using the Hilbert uniqueness method by means of a control torque applied only on the rigid hub of the panel. At the same time, uniform exponential energy decay rate is obtained directly for the solution of this problem.
Page 1. Proc. Indian Acad. Sci. (Math. Sci.), Vol. 107, No. 4, November 1997, pp. 411-423. 9 Prin... more Page 1. Proc. Indian Acad. Sci. (Math. Sci.), Vol. 107, No. 4, November 1997, pp. 411-423. 9 Printed in India Transformation of chaotic nonlinear polynomial difference systems through Newton iterations SUJIT K BOSE s N Bose ...
The Green's function solution of the Helmholtz's equation for acoustic scattering by hard surface... more The Green's function solution of the Helmholtz's equation for acoustic scattering by hard surfaces and radiation by vibrating surfaces, lead in both the cases, to a hyper singular surface boundary integral equation. Considering a general open surface, a simple proof has been given to show that the integral is to be interpreted like the Hadmard finite part of a divergent integral in one variable. The equation is reformulated as a Cauchy principal value integral equation, but also containing the potential at the control point. It is amenable to numerical treatment by conventional methods. An alternative formulation in the better known form, containing the tangential derivative of the potential is also given. The two dimensional problem for an open arc is separately treated for its simpler feature.
ABSTRACT The boundary stabilization of the problem satisfying the differential equation y &#3... more ABSTRACT The boundary stabilization of the problem satisfying the differential equation y '' +λy ''' =c 2 (Δy+μΔy ' ),0<λ<μ, in a bounded domain Ω in ℝ n with smooth boundary Γ is studied. Such equations arise in the vibrations of flexible structures possessing internal material damping and modeled by the “standard linear model” of viscoelasticity. Explicit exponential energy decay rate is obtained for the solution of the above problem subject to mixed boundary conditions.
Physical Review E Statistical Nonlinear and Soft Matter Physics, Sep 1, 2009
Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity eq... more Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter.
Instability Theory of Sand Ripples Formed by Turbulent Shear Flows. [Journal of Hydraulic Enginee... more Instability Theory of Sand Ripples Formed by Turbulent Shear Flows. [Journal of Hydraulic Engineering 1, 335 (2012)]. Sujit K. Bose, Subhasish Dey. Abstract. A theory of turbulent shear flow over a sand bed is developed addressing ...
A new theoretical approach is presented for the derivation of free surface profiles of two-dimens... more A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide.
Abstract An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude n... more Abstract An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady‐state flow equation. ...
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