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4.1 Results of the tests on the convergence on grid for P r = 1, Γ = 1. . . . 46

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List of Tables

3.1 Finite-difference schemes Ref. [30]. . . . 31

4.1 Results of the tests on the convergence on grid for P r = 1, Γ = 1. . . . 46

4.2 Comparison with linear stability analysis for P r = 1, 3 and 4, Γ = 1. . . . 47

4.3 Influence of R

ν

on Re

cr

and on the critical frequency for medium Prandtl number liquids. . . . 58

4.4 . The rate of decreasing of Re

cr

with Prandtl number due to variable viscosity. . 58

4.5 Properties of tetradecamethylhexasiloxane. . . . . 65

4.6 . Comparison of simulations with experimental observations. (f.f. means funda- mental frequency). . . . 66

4.7 . Critical Reynolds number, when P r = 35, Gr = 0. . . . 70

4.8 . Critical Reynolds number, when P r = 35, Gr = 0. . . . 70

4.9 . Comparison of critical Reynolds and wave numbers. . . . . 72

5.1 Effect of the grid resolution on the parameters of supercritical flow, Re ≈ 5Re

cr

. 77 5.2 Study of the final flow symmetry on different grids, Re ≈ 10Re

cr1

. . . . . 80

5.3 Spatial disorganization of the flow δ

Φ

, eq.( 5.3), as a function of the Re, 3300 ≤ Re ≤ 5000, m = 3. . . . . 99

6.1 Effect of the grid resolution on the parameters of supercritical flow, Re = 3.06Re

cr

, while ∆T is increased. . . . 103

6.2 Effect of the grid resolution on the parameters of supercritical flow, Re = 5.8Re

cr

, while the system is cooled. . . 103

6.3 The change of flow regimes with the increase of ∆T . . . 120

7.1 Physical properties of the silicone oil 10 cSt . . . 125

8.1 Critical Reynolds number for unit aspect ratio when P r = 0.01. . . 143

8.2 Critical Reynolds number for the aspect ratio Γ = 1.2 when P r = 0.01. . . 143

8.3 Critical Reynolds number for deformed liquid bridge and low Prantdl numbers. . 143

10.1 Physical properties of a mixture of Ethylene-glycol and water . . . 152

10.2 The values of |ψ

max

| P r = 0.71, Γ

x

= 1, Γ

y

= 1 . . . 153

10.3 Velocity and the temperature on the free surface at x = y = 0.5, z = 1. Results of 3D calculation: P r = 1, Γ

x

= 1, Γ

y

= 1 . . . 153

10.4 Numerical results for pure buoyancy induced flow . . . 155

10.5 Numerical results for buoyancy induced velocities in future space experiments. |g

∗

| = 10

−5

g

0

, ∆T = 60 K, . . . 157

10.6 Numerical results for combined Rayleigh and Marangoni convection. Pr = 20, Γ

x

= 2.5, Γ

y

= 1, V = 0.0468 [V] mm/s. . . . 162

xi

(2)

10.7 Comparison of the results for combined convection with different Rayleigh num-

bers. Ma = 74 000, ∆T = 60

o

C. . . 163

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