A review of material frame-indifference in mechanics

Applied Mechanics Reviews

Volumn 51, Issue 8, 1998, Pages 489-504

  Speziale, Charles G ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; LAMINAR FLOW; MATERIALS SCIENCE; MATHEMATICAL MODELS; NON NEWTONIAN LIQUIDS; STATISTICAL MECHANICS; TENSORS; TURBULENCE;

CONSTITUTIVE EQUATIONS; MATERIAL FRAME INDIFFERENCE;

CONTINUUM MECHANICS;

EID: 0032139380     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3099017     Document Type: Article

References (51)

1. Bardina J, Ferziger JH, and Reynolds WC (1983), Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows, Stanford Univ Tech Report No TF-19.
2. Batchelor GK (1970), Stress system in a suspension of force-free particles, J Fluid Mech 41,545-570.
3. Bergmann PG (1976), Introduction to the Theory of Relativity, Dover, New York.
4. Bird R, Curtiss CF, Armstrong RC, and Hassager O (1987), Dynamics of Polymeric Liquids, Vol 2: Kinetic Theory. Wiley-Interscience, New York.
5. Chapman S and Cowling TG (1970), Mathematical Theory of Non-Uniform Gases, Cambridge liniv Press, Slew York.
6. Edelen DGB and McLennan JA (1973), Material indifference: a principle or a convenience, IntJEngSci 11, 813-817.
7. Eringen AC (1967), Mechanics of Continua, Wiley, New York.
8. Ferziger JH and Kaper HG (1972), Mathematical Theory of Transport Processes in Gases, N Holland, Amsterdam.
9. Green AE (1982), Axioms of continuum mechanics, Bulletin Inst Math Appl 18, 7-9.
10. Haworth DC and Pope SB (1986), Generalized Langevin model for turbulent flows, Phys Fluids 29, 387-405.
11. Heckl M and Müller I (1983), Frame dependence, entropy, entropy flux and wave speeds in mixtures of gases, Acta Mechanica 50,71-95.
12. Hinze JO (1975), Turbulence, McGraw-Hill, New York.
13. Huang YN (1996), Comment on the principle of material ffarne-indifference in the limit of two-dimensional turbulence, Private Communication.
14. Launder BE, Reece GJ, and Rodi W (1975), Progress in the development of a Reynolds stress turbulence closure, J Fluid Mech 68, 537-566.
15. Lumley JL (1970), Toward a turbulent constitutive equation, J Fluid Mech 41,413-434.
16. Müller I (1972), Frame dependence of stress and heat flux, Arch Rat Mech Anal 45,241-249.
17. Müller I (1976), Frame dependence of electric current and heat flux in a metal, Acta Mechanica 24, 117-128.
18. Murdoch AI (1983), Material ffame-indifference, intrinsic spin, and certain constitutive equations motivated by the kinetic theory of gases, Arch Rat Mech Anal 83, 185-194.
19. Oldroyd JG (1950), Formulation of rheological equations of state, Proc Royal Soc London A 200, 523-541.
20. Reynolds WC (1990), Potential and limitations of direct and large-eddy simulations, Lecture Notes in Phys 357, 313-343.
21. Ristorcelli JR, Lumley JL, and Abid R (1995), Rapid-pressure correlation representation consistent with the Taylor-Proudman theorem and materially frame-indifferent in the 2D limit, J Fluid Mech 292, 111-152.
22. Rivlin RS (1957), Relation between the flow of a non-newtonian fluid and turbulent newtonian fluid, Q Appl Math 15, 212-215.
23. Rivlin RS (1987), Material ffame-indifference, IntJ Solids Struct 23, 1639-1643.
24. Rivlin RS (1992), Frame-indifference, Rend Math Acad Lincei 3,51-59.
25. Roberts PH and Donnelly RJ (1974), Superfluid mechanics, Annual Rev Fluid Mech 6, 179-225.
26. Rogallo RS (1981), Numerical experiments in homogeneous turbulence, NASA TM-81315.
27. Rosen G (1980), Restricted invariance of the Navier-Stokes equation, Phys. Rev A 22,313-314.
28. Rosenau P (1989), Extending hydrodynamics via the regularization of the Chapman-Enskog expansion, Phys Rev A 40,7193-7196.
29. Ryskin G (1985), Misconception which led to the material ffame-indifference controversy, Phys Rev A 32, 1239-1240.
30. Ryskin G (1988), Brownian motion in a rotating fluid: Diffusivity is a function of the rotation rate; Phys Rev Let 61,1442-1445.
31. Sõderholm LH (1976), Principle of material ffame-indifference and material equations of gases, IntJ Eng Sci 14,523-528.
32. Speziale CG (1979), Invariance of turbulent closure models, Phys Fluids 22, 1033-1037.
33. Speziale CG (1981a), Some interesting properties of two-dimensional turbulence, Phys Fluids 24, 1425-1427.
34. Speziale CG (1981b), On ffame-indifference and iterative procedures in the kinetic theory of gases, IntJ Eng Sci 19,63-73.
35. Speziale CG (1983), Closure models for rotating two-dimensional turbulence, Geophys Astrophys Fluid Dyn 23, 69-84.
36. Speziale CG (1984), Invariance of constitutive equations according to the kinetic theory of gases, J Stat Phys 35,457-470.
37. Speziale CG (1986), Effect of the reference ffame on the thermophysical properties of an ideal gas, Int J Thermophys 7,99-110.
38. Speziale CG (1987), Comments on the material ffame-indifference controversy, Phys Rev A 36,4522-4525.
39. Speziale CG (1988), On the Einstein equivalence principle, intrinsic spin, and the invariance of constitutive equations in continuum mechanics, Int J Eng Sci 26,211-220.
40. Speziale CG (1989), Turbulence modeling in non-inertial ffames of reference, Theor Comput Fluid Dyn 1,3-19.
41. Speziale CG (1991), Analytical methods for the development of Reynolds stress closures in turbulence, Ann Rev Fluid Mech 23, 107-157.
42. Speziale CG and Mac Giolla Mhuiris N (1989), Scaling laws for homogeneous turbulent shear flows in a rotating ffame, Phys Fluids A 1,294-301.
43. Speziale CG, Mansour NN, and Rogallo RS (1987), Decay of isotropic turbulence in a rapidly rotating frame, in Studying Turbulence Using Numerical Simulation Databases, P Moin, WC Reynolds, and J Kim (eds), 205-211, NASA Ames, Stanford Center for Turbulence Res.
44. Tritton DJ (1977), Physical Fluid Dynamics, Van Nostrand, New York.
45. Truesdell C (1976), Correction of two errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material ffame-indifference, Meccanica 11, 196-199.
46. Truesdell C and Toupin (1960), Classical field theories, Handbuch der Physik 111/1, Springer-Verlag, New York.
47. Truesdell C and Noll W (1965), NonLinear field theories of mechanics, Handbuch der Physik 111/3, Springer-Verlag, New York.
48. Truesdell C and Muncaster R (1980), Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas, Academic Press, New York.
49. Wallin S and Johansson AV (1998), New explicit algebraic stress model for incompressible and compressible turbulent flows, J Fluid Mech, Submitted for publication.
50. Wang CC (1975), Concept of ffame-indifference in continuum mechanics and in the kinetic theory of gases, Arch Rat Mech Anal 58, 381 -392.
51. Woods LC (1981), Bogus axioms of continuum mechanics, Bulletin Inst Math Appl 17, 98-102.