|
|
Mathematical modelling of selected problems in cryogenic fluid mechanics
Hodic, Jan ; La Mantia, Marco (advisor) ; Kreml, Ondřej (referee)
The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak ort he strong solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate properties of the solution.
|
|
| |
|
|
Mathematical modelling of selected problems in cryogenic fluid mechanics
Hodic, Jan ; La Mantia, Marco (advisor) ; Schmoranzer, David (referee)
The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate numerical schemes to solve these equations.
|
|
|
Quantum turbulence in superfluid helium studied by particle tracking velocimetry visualization technique
Duda, Daniel ; Skrbek, Ladislav (advisor) ; Chára, Zdeněk (referee) ; Skyba, Peter (referee)
❚✐t❧❡✿ ◗✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡ ✐♥ s✉♣❡r✢✉✐❞ ❤❡❧✐✉♠ st✉❞✐❡❞ ❜② ♣❛rt✐❝❧❡ tr❛❝❦✐♥❣ ✈❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❆✉t❤♦r✿ ❘◆❉r✳ ❉❛♥✐❡❧ ❉✉❞❛ ❉❡♣❛rt♠❡♥t✿ ❉❡♣❛rt♠❡♥t ♦❢ ▲♦✇ ❚❡♠♣❡r❛t✉r❡ P❤②s✐❝s ❙✉♣❡r✈✐s♦r✿ ♣r♦❢✳ ❘◆❉r✳ ▲❛❞✐s❧❛✈ ❙❦r❜❡❦✱ ❉r❙❝✳ ❆❜str❛❝t✿ ❚❤❡ P❛rt✐❝❧❡ ❚r❛❝❦✐♥❣ ❱❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ✉s✐♥❣ ♠✐❝✲ r♦♠❡t❡r s✐③❡ s♦❧✐❞ ❞❡✉t❡r✐✉♠ ♣❛rt✐❝❧❡s ❛s tr❛❝❡rs ❤❛s ❜❡❡♥ ❛♣♣❧✐❡❞ t♦ st✉❞② ♦s❝✐❧✲ ❧❛t♦r② ✢♦✇s ♦❢ ❍❡ ■■✱ ✇❤✐❝❤ ✐s ❛ q✉❛♥t✉♠ ✢✉✐❞ ✇✐t❤ q✉❛♥t✐③❡❞ ✈♦rt✐❝✐t②✱ ❛s ✇❡❧❧ ❛s ✢♦✇s ♦❢ ❍❡ ■✱ ✇❤✐❝❤ ✐s ❛ ❝❧❛ss✐❝❛❧ ✈✐s❝♦✉s ❧✐q✉✐❞✱ ❢♦❝✉s✐♥❣ ♦♥ t❤❡ s✐♠✐❧❛r✐t✐❡s ❛♥❞ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ q✉❛♥t✉♠ ❛♥❞ ❝❧❛ss✐❝❛❧ ✢♦✇s✳ ❚❤r❡❡ ❡①♣❡r✐♠❡♥ts ❛r❡ ❞❡s❝r✐❜❡❞✿ t❤❡ ✢♦✇ ♣❛st ❛ ❧❛r❣❡✲❛♠♣❧✐t✉❞❡ ❧♦✇✲❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ ♦❜st❛❝❧❡ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛ ♣r✐s♠❀ t❤❡ st❡❛❞② str❡❛♠✐♥❣ ✢♦✇ ❞✉❡ t♦ ❛ s♠❛❧❧✲❛♠♣❧✐t✉❞❡ ❧❛r❣❡✲ ❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ q✉❛rt③ t✉♥✐♥❣ ❢♦r❦ ✲ ❛ ✇✐❞❡❧② ✉s❡❞ t♦♦❧ t♦ st✉❞② q✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡❀ ❛♥❞ t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❝❛✈✐t❛t✐♦♥ ✐♥ t❤❡ ✈✐❝✐♥✐t② ♦❢ ❛ ❢❛st✲♦s❝✐❧❧❛t✐♥❣ t✉♥✐♥❣ ❢♦r❦✳ ❚❤❡ ♠❛✐♥ ♦✉t❝♦♠❡ ✐s t❤❡ ♦❜s❡r✈❛t✐♦♥ t❤❛t t❤❡s❡ ✢♦✇s ❛r❡ s✐♠✐❧❛r ✐♥ ❍❡ ■ ❛♥❞ ✐♥ ❍❡ ■■ ❛t ❧❛r❣❡ ❧❡♥❣t❤✲s❝❛❧❡s✱ ✇❤❡r❡❛s ❛t s♠❛❧❧ s❝❛❧❡s✱ t❤❡② ❡①❤✐❜✐t t♦t❛❧❧② ❞✐✛❡r❡♥t st❛t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s✳ ▼♦r❡♦✈❡r✱ ✐♥ ❍❡ ■■✱ t❤❡s❡ s♠❛❧❧ s❝❛❧❡ st❛✲ t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s ❛r❡ ✉♥✐✈❡rs❛❧ ✐♥ t❤❛t t❤❡② ❞♦ ♥♦t ❞❡♣❡♥❞ ♦♥ t❤❡ t②♣❡ ♦❢ t❤❡ ✐♠♣♦s❡❞ ♠❡❛♥ ✢♦✇ ♦❢ t❤❡ s✉♣❡r✢✉✐❞ ❛♥❞ ♥♦r♠❛❧...
|
|
|
Visualization of particle motions in superfluid helium flows
Švančara, Patrik ; La Mantia, Marco (advisor)
Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.
|
|
|
Visualization of particle motions in superfluid helium flows
Švančara, Patrik ; La Mantia, Marco (advisor)
Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.
|
|
|
Visualization of superfluid helium flows in the proximity of boundaries
Hrubcová, Petra ; La Mantia, Marco (advisor) ; Jackson, Martin James (referee)
The investigation of superfluid helium (He II) flows is an active and challenging research field. Progress in our phenomenological understanding of the underlying physics has been achieved in recent years by employing flow visualization techniques that allow following the motion of relatively small particles suspended in the fluid. The flow-induced particle behaviour is studied in the case of thermal counterflow - the most common type of He II flow - close to the flow source, where a significant vorticity enhancement is observed. The work aim is therefore to give a significant contribution to the emerging line of scientific enquiry dedicated to the study of wall-bounded quantum flows.
|
|
|
Mathematical modelling of selected problems in cryogenic fluid mechanics
Hodic, Jan ; La Mantia, Marco (advisor) ; Kreml, Ondřej (referee)
The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak ort he strong solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate properties of the solution.
|
|
|
Quantum turbulence in superfluid helium studied by particle tracking velocimetry visualization technique
Duda, Daniel ; Skrbek, Ladislav (advisor) ; Chára, Zdeněk (referee) ; Skyba, Peter (referee)
❚✐t❧❡✿ ◗✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡ ✐♥ s✉♣❡r✢✉✐❞ ❤❡❧✐✉♠ st✉❞✐❡❞ ❜② ♣❛rt✐❝❧❡ tr❛❝❦✐♥❣ ✈❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❆✉t❤♦r✿ ❘◆❉r✳ ❉❛♥✐❡❧ ❉✉❞❛ ❉❡♣❛rt♠❡♥t✿ ❉❡♣❛rt♠❡♥t ♦❢ ▲♦✇ ❚❡♠♣❡r❛t✉r❡ P❤②s✐❝s ❙✉♣❡r✈✐s♦r✿ ♣r♦❢✳ ❘◆❉r✳ ▲❛❞✐s❧❛✈ ❙❦r❜❡❦✱ ❉r❙❝✳ ❆❜str❛❝t✿ ❚❤❡ P❛rt✐❝❧❡ ❚r❛❝❦✐♥❣ ❱❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ✉s✐♥❣ ♠✐❝✲ r♦♠❡t❡r s✐③❡ s♦❧✐❞ ❞❡✉t❡r✐✉♠ ♣❛rt✐❝❧❡s ❛s tr❛❝❡rs ❤❛s ❜❡❡♥ ❛♣♣❧✐❡❞ t♦ st✉❞② ♦s❝✐❧✲ ❧❛t♦r② ✢♦✇s ♦❢ ❍❡ ■■✱ ✇❤✐❝❤ ✐s ❛ q✉❛♥t✉♠ ✢✉✐❞ ✇✐t❤ q✉❛♥t✐③❡❞ ✈♦rt✐❝✐t②✱ ❛s ✇❡❧❧ ❛s ✢♦✇s ♦❢ ❍❡ ■✱ ✇❤✐❝❤ ✐s ❛ ❝❧❛ss✐❝❛❧ ✈✐s❝♦✉s ❧✐q✉✐❞✱ ❢♦❝✉s✐♥❣ ♦♥ t❤❡ s✐♠✐❧❛r✐t✐❡s ❛♥❞ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ q✉❛♥t✉♠ ❛♥❞ ❝❧❛ss✐❝❛❧ ✢♦✇s✳ ❚❤r❡❡ ❡①♣❡r✐♠❡♥ts ❛r❡ ❞❡s❝r✐❜❡❞✿ t❤❡ ✢♦✇ ♣❛st ❛ ❧❛r❣❡✲❛♠♣❧✐t✉❞❡ ❧♦✇✲❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ ♦❜st❛❝❧❡ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛ ♣r✐s♠❀ t❤❡ st❡❛❞② str❡❛♠✐♥❣ ✢♦✇ ❞✉❡ t♦ ❛ s♠❛❧❧✲❛♠♣❧✐t✉❞❡ ❧❛r❣❡✲ ❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ q✉❛rt③ t✉♥✐♥❣ ❢♦r❦ ✲ ❛ ✇✐❞❡❧② ✉s❡❞ t♦♦❧ t♦ st✉❞② q✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡❀ ❛♥❞ t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❝❛✈✐t❛t✐♦♥ ✐♥ t❤❡ ✈✐❝✐♥✐t② ♦❢ ❛ ❢❛st✲♦s❝✐❧❧❛t✐♥❣ t✉♥✐♥❣ ❢♦r❦✳ ❚❤❡ ♠❛✐♥ ♦✉t❝♦♠❡ ✐s t❤❡ ♦❜s❡r✈❛t✐♦♥ t❤❛t t❤❡s❡ ✢♦✇s ❛r❡ s✐♠✐❧❛r ✐♥ ❍❡ ■ ❛♥❞ ✐♥ ❍❡ ■■ ❛t ❧❛r❣❡ ❧❡♥❣t❤✲s❝❛❧❡s✱ ✇❤❡r❡❛s ❛t s♠❛❧❧ s❝❛❧❡s✱ t❤❡② ❡①❤✐❜✐t t♦t❛❧❧② ❞✐✛❡r❡♥t st❛t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s✳ ▼♦r❡♦✈❡r✱ ✐♥ ❍❡ ■■✱ t❤❡s❡ s♠❛❧❧ s❝❛❧❡ st❛✲ t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s ❛r❡ ✉♥✐✈❡rs❛❧ ✐♥ t❤❛t t❤❡② ❞♦ ♥♦t ❞❡♣❡♥❞ ♦♥ t❤❡ t②♣❡ ♦❢ t❤❡ ✐♠♣♦s❡❞ ♠❡❛♥ ✢♦✇ ♦❢ t❤❡ s✉♣❡r✢✉✐❞ ❛♥❞ ♥♦r♠❛❧...
|
|
|
Visualization of particle motions in superfluid helium flows
Švančara, Patrik ; La Mantia, Marco (advisor) ; Chagovets, Tim (referee)
Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.
|
guest ::
