摘要:

Internal vortex patterns and the corresponding free surface signatures generated in the late wakes by a submerged sphere moving in a stratified fluid are numerically simulated by a three‐dimensional time‐dependent model. The flow is assumed to be incompressible and hydrostatic with the Boussinesq approximation. A free surface is included to admit barotropic modes and to investigate the surface signature of internal vortices. The turbulent mixing is modeled using the Smagorinsky formula for horizontal fluxes and a Richardson number closure for vertical fluxes. The numerical techniques include a second‐order finite difference scheme with a staggered and stretched grid system. A split‐explicit method is used to separately integrate the fast barotropic modes and the slow baroclinic modes in time. This method allows us to economically simulate the time history of the slowly evolving vortices. Preliminary results for the velocity field, the flow pattern, the density distribution, and the induced surface signature are presented. They consistently reveal the existence of coherent structures in the stratified flow field. Sensitivity studies are performed to examine how the depth of submerged objects, the depth of channel floors, and the size of moving objects affect the evolution of the horizontal vortices. A mechanism based on the interaction of the wake vorticity and the buoyancy induced oscillation is proposed for the generation and growth of the horizontal vortices in stratified fluids. The vorticity stretching thus produced in the direction of stratification is responsible for the generation and evolution of concentrated vortices in stratified fluids. This mechanism explains why the horizontal vortices appear long after the initial disturbances generated by a submerged moving body have dissipated, and why they exist only in stratified fluids but not in homogeneous media. In view of the proposed mechanism, the horizontal vortices are buoyancy‐induced and a model with the stratification properly represented is required to adequately describe the organized vortex motion in stratified wakes. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869078

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Simulations of a fluid rotating inside a partially open cylindrical cavity, performed by numerical solution of the unsteady axisymmetric Navier–Stokes equations, are presented. The configuration consists of a cylindrical vessel holding the fluid, which is entrained into motion by a rotating lid. This one is a coaxial disk in contact with the fluid surface but without covering it entirely. The study focuses on the occurrence of time‐dependent flow, more specifically, the first transition to unsteadiness, by considering cavity cases with different amounts of free surface, for a fixed aspect ratio. By following the time evolution of a few arbitrarily chosen dynamical variables as a function of the Reynolds number, the location of this first Hopf bifurcation is obtained for a collection of cavity cases. Results show a rather strong influence of the free surface both on the onset of the unsteadiness and on the dynamical features of the flow. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869079

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Numerical experimentation is used to examine the onset of axisymmetric vortex breakdown in a completely closed, cylindrical environment. Modification of the boundary motion allows one to compute a state ofincipientvortexbreakdown. The numerically determined states are used to test a recently posed hypothesis for the occurrence of vortex breakdown. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869080

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Velocity structure functions (up′−up)mare calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two‐point field from a volume‐orientation average for a specific solution of the Navier–Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for (up′−up)mas a function of ordermand of the scalar separationr. Special forms of the operator are then obtained for rectilinear stretched vortex models of the Townsend–Lundgren type. Numerical results are given for the Burgers vortex and also for a realization of the Lundgren‐strained spiral vortex, and comparison with experimental measurement is made. In an Appendix, we calculate values of the velocity‐derivative moments for the Townsend–Burgers model. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869081

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Relationships are derived between pressure–velocity–velocity (PVV) statistics, fourth‐order velocity structure functions, and the pressure structure function. The PVV statistics are related to the correlation of pressure at one point with the product of two velocity components at another point. The Navier–Stokes equation, isotropy, and incompressibility are used; no other assumption is used. Thus the relationships apply for all Reynolds numbers and can be used as a benchmark to determine how well turbulence models mimic pressure fluctuations in Navier–Stokes turbulence. A necessary condition limiting compressibility is given. The inertial‐range and viscous‐range formulas of the PVV statistics are obtained. The results are compared with previous theories that used the joint Gaussian approximation. Data from grid turbulence are used to evaluate the statistics.

ISSN:1070-6631    

DOI:10.1063/1.869082

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869083

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The previously established similarity between the temperature spectrum and the spectrum corresponding to the mean turbulent energy in a wide variety of turbulent (shear) flows is re‐examined within the framework of second‐order velocity and temperature structure functions. Measurements in a turbulent wake indicate thatDq, the sum of the three second‐order velocity structure functions bears close similarity toD&thgr;, the second‐order temperature structure function, whenDqandD&thgr;are normalized by the mean turbulent energy and temperature variance, respectively. This similarity also applies to other flows. In the limit of small separations, the Kolmogorov‐normalized structure functions differ only by the value of the molecular Prandtl number. In the inertial range, the Obukhov–Corrsin constant differs from theDqKolmogorov constant by a factor equal to the dissipation time scale ratio. This ratio is typically about 0.5. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869084

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Homogeneous shear flows with an imposed mean velocityU=Syxˆare studied in a period box of sizeLx×Ly×Lz, in the statistically stationary turbulent state. In contrast with unbounded shear flows, the finite size of the system constrains the large‐scale dynamics. The Reynolds number, defined by Re≡SL2y/&ngr; varies in the range 2600⩽Re⩽11300. The total kinetic energy and enstrophy in the volume of numerical integration have large peaks, resulting in fluctuations of kinetic energy of order 30%–50%. The mechanism leading to these fluctuations is very reminiscent of the ‘‘streaks’’ responsible for the violent bursts observed in turbulent boundary layers. The large scale anisotropy of the flow, characterized by the two‐point correlation tensor ⟨uiuj⟩ depends on the aspect ratio of the system. The probability distribution functions (PDF) of the components of the velocity are found to be close to Gaussian. The physics of the Reynolds stress tensor,uv, is very similar to what is found experimentally in wall bounded shear flows. The study of the two‐point correlation tensor of the vorticity ⟨&ohgr;i&ohgr;j⟩ suggests that the small scales become isotropic when the Reynolds number increases, as observed in high Reynolds number turbulent boundary layers. However, the skewness of thezcomponent of vorticity is independent of the Reynolds number in this range, suggesting that some small scale anisotropy remains even at very high Reynolds numbers. An analogy is drawn with the problem of turbulent mixing, where a similar anisotropy is observed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869100

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Mixing of a passive scalar in statistically homogeneous, isotropic, and stationary turbulence with a mean scalar gradient is investigated via direct numerical simulation, for Taylor‐scale Reynolds numbers,R&lgr;, from 28 to 185. Multiple independent simulations are performed to get confidence intervals, and local regression smoothing is used to further reduce statistical fluctuations. The scalar fluctuation field, &fgr;(x,t), is initially zero, and develops to a statistically stationary state after about four eddy turnover times. Quantities investigated include the dissipation of scalar flux, which is found to be significant; probability density functions (pdfs) and joint‐pdfs of the scalar, its derivatives, scalar dissipation, and mechanical dissipation; and conditional expectations of scalar mixing, ∇2&fgr;. A linear model for scalar mixing jointly conditioned on the scalar andv‐velocity is developed, and reproduces the data quite well. Also considered is scalar mixing jointly conditioned on the scalar and scalar dissipation. Terms appearing in the balance equation for the pdf of &fgr; are examined. From a solution of the scalar pdf equation two sufficient conditions arise for the scalar pdf to be Gaussian. These are shown to be well satisfied for moderate values of the scalar, and approximately so for large fluctuations. Many correlations are also presented, including &rgr;(v,&fgr;), which changes during the evolution of the scalar from a value of unity when initialized to the stationary value of 0.5–0.6. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869099

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This work concerns the interaction between a mean flow and large‐scale coherent structures in a wall jet at low Reynolds numbers in the case of single and multiple modes. The Navier–Stokes equations have been used to study the evolution of the wall jet and, in particular, its kinetic energy. The nonlinear interaction problem has been solved by means of the integral method taking into account the shape assumptions and local linear theory to obtain characteristics of coherent modes in the wall jet. It has been observed that the fundamental wave in case of a single mode, extracts its energy from the mean flow. When considering the fundamental mode superposed to its first subharmonic one with a phase difference &thgr;=0, it can be observed that there are interactions between the mean flow and these waves. Energy is extracted from the mean flow to the fundamental wave and then to its first subharmonic mode. The evolution of the thickness of the jet &dgr; and the maximum velocityUfor each dimensionless downstream coordinate is also shown with a growth of increasing of &dgr; and decreasing ofU. Initial conditions play an important role. In this work, fine‐grained turbulence quantities have been neglected. Some comparisons with experimental results have been performed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869088

出版商:AIP    

年代:1996

数据来源: AIP