The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for ...The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.展开更多
The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity ...The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity function of TLA is presented in this paper. An algorithm for precisely determning the coordinates of each element by means of the inverse elliptic function is derived. A fast approximation of recursive formula for solving distorted array shape is given. According to the comparison between ideal directivity and the directivity of distorted array, the criterion for making decision of operational mode of TLA sonar is presented. So that the performance prediction problem in TLA is solved. The results of system simulation in computer show a good agreement with the theoretical analysis.展开更多
基金supported by the Scientific and Research Council of Turkey (No.106T337)the ISF Grant (No.120/6)+1 种基金the BSF Grant (No.2004271)the National Science Foundation (Nos.DMS-0504619,DMS-0708832)
文摘The authors investigate the long-term dynamics of the three-dimensional Navier- Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous （inviscid） regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes- Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient v →0.
文摘The distortion of the array shape is one of the main factors which result the performance degeneration from the ideal situation of towed line array (TLA). Based on the ordinary array shape distortion, the directivity function of TLA is presented in this paper. An algorithm for precisely determning the coordinates of each element by means of the inverse elliptic function is derived. A fast approximation of recursive formula for solving distorted array shape is given. According to the comparison between ideal directivity and the directivity of distorted array, the criterion for making decision of operational mode of TLA sonar is presented. So that the performance prediction problem in TLA is solved. The results of system simulation in computer show a good agreement with the theoretical analysis.
