Transverse-velocity fluctuations in a liquid under steady shear
José M Ortiz de Zárate1, Jan V Sengers
1Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain. jmortizz@fis.ucm.es
Summary
We analyzed transverse-velocity fluctuations in a sheared liquid layer. Results show a wave number dependent maximum, influenced by boundary conditions and increasing with Reynolds number squared.
Area of Science:
- Fluid dynamics
- Non-equilibrium statistical mechanics
Background:
- Understanding fluid behavior under shear is crucial for various industrial processes.
- Transverse-velocity fluctuations in sheared liquids are complex and influenced by boundary conditions.
Purpose of the Study:
- To analyze transverse-velocity fluctuations in an isothermal liquid layer with uniform shear.
- To investigate the dependence of these fluctuations on wave number and Reynolds number.
Main Methods:
- Solving a stochastic version of the Orr-Sommerfeld equation.
- Applying no-slip boundary conditions within a second-order Galerkin approximation.
Main Results:
- A maximum in transverse-velocity fluctuations was observed as a function of wave number.
- A crossover from q(-4) to q(2) dependence was identified, with boundary conditions significantly impacting small wave numbers.
- The intensity of fluctuations remains finite but increases with the square of the Reynolds number.
Conclusions:
- Boundary conditions play a critical role in the behavior of transverse-velocity fluctuations at small wave numbers.
- The findings provide insights into non-equilibrium fluid dynamics and enhance understanding of sheared liquid layers.
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