Viscoelastic models for turbulence are derived by modeling the Reynolds stress as a space-time fu... more Viscoelastic models for turbulence are derived by modeling the Reynolds stress as a space-time functional depending on the entire past of the mean field. This well known approach has a long history in turbulence modeling literature (E.g: Monin & Yaglom, Statistical Methods in fluid mechanics-I, MIT Press, 1971). Similar equations also arise in non-Newtonian fluid dynamics. We will present certain rigorous results for a particular model in 3-D. One of the interesting theorems concerns with finite speed of propagation. Namely, if the initial data (initial mean field) is non-zero in a confined region in the 3-D space then at any other time, the solution (mean field) will again be confined to (a bigger) region dictated by the speed of propagation. This striking property not shared by the original Navier-Stokes equation is due to the hereditary viscous term in the viscoelastic turbulence model. The finite speed of propagation also provides some heuristics in to confined regions of turbulence such as clear air turbulence.
Impulse control corresponds to forcing the fluid at strategic times where the optimal instances o... more Impulse control corresponds to forcing the fluid at strategic times where the optimal instances of time as well as the strengths of the control are to be determined by control theory of Navier-Stokes equation. This subject can also be exactly rephrased as an optimal weather prediction problem where the initial data is updated at strategic times (in current variational data assimilation literature in meteorology one obtains the optimal initial data just once). The underlying mathematical structure is precisely resolved with very elegant explanations using infinite dimensional free boundary problems where the boundaries of the free boundary correspond to optimal instances.
A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence ... more A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.
This paper presents a new formulation and computational solution of an optimal control problem co... more This paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation. The adjoint system of equations for the unsteady Euler system in 1D is derived and utilized in an adjoint-based solution procedure for the ...
Viscoelastic models for turbulence are derived by modeling the Reynolds stress as a space-time fu... more Viscoelastic models for turbulence are derived by modeling the Reynolds stress as a space-time functional depending on the entire past of the mean field. This well known approach has a long history in turbulence modeling literature (E.g: Monin & Yaglom, Statistical Methods in fluid mechanics-I, MIT Press, 1971). Similar equations also arise in non-Newtonian fluid dynamics. We will present certain rigorous results for a particular model in 3-D. One of the interesting theorems concerns with finite speed of propagation. Namely, if the initial data (initial mean field) is non-zero in a confined region in the 3-D space then at any other time, the solution (mean field) will again be confined to (a bigger) region dictated by the speed of propagation. This striking property not shared by the original Navier-Stokes equation is due to the hereditary viscous term in the viscoelastic turbulence model. The finite speed of propagation also provides some heuristics in to confined regions of turbulence such as clear air turbulence.
Impulse control corresponds to forcing the fluid at strategic times where the optimal instances o... more Impulse control corresponds to forcing the fluid at strategic times where the optimal instances of time as well as the strengths of the control are to be determined by control theory of Navier-Stokes equation. This subject can also be exactly rephrased as an optimal weather prediction problem where the initial data is updated at strategic times (in current variational data assimilation literature in meteorology one obtains the optimal initial data just once). The underlying mathematical structure is precisely resolved with very elegant explanations using infinite dimensional free boundary problems where the boundaries of the free boundary correspond to optimal instances.
A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence ... more A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.
This paper presents a new formulation and computational solution of an optimal control problem co... more This paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation. The adjoint system of equations for the unsteady Euler system in 1D is derived and utilized in an adjoint-based solution procedure for the ...
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Papers by Sivaguru S Sritharan