Upper bound on angular momentum transport in Taylor-Couette flow.

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Computational Physics

Background:

• Taylor-Couette flow involves fluid between rotating inner and fixed outer cylinders.
• Understanding angular momentum transport is crucial for predicting turbulent flow behavior.
• Previous theoretical upper bounds existed but lacked precise numerical validation.

Purpose of the Study:

• To theoretically and numerically investigate the upper bound of angular momentum transport in Taylor-Couette flow.
• To refine existing upper bounds using a novel one-dimensional background field method.
• To determine the dependence of this bound on the radius ratio.

Main Methods:

• Utilized a one-dimensional background field method for theoretical analysis.
• Employed a pseudo-time-stepping method to solve a variational problem numerically.
• Investigated three specific radius ratios: 0.5, 0.714, and 0.909.
• Conducted inductive bifurcation analysis to assess the impact of three-dimensional fields.

Main Results:

• Established an upper bound for angular momentum transport as Nu ≤ cTa^(1/2).
• Calculated specific prefactor values (c) for different radius ratios (η).
• Achieved improvements (lower bounds) of at least one order of magnitude compared to prior work.
• Demonstrated that a three-dimensional background velocity field does not further reduce the established bound.

Conclusions:

• The study provides significantly improved upper bounds for angular momentum transport in Taylor-Couette flow.
• The findings offer more accurate predictions for turbulent transport phenomena in confined geometries.
• The theoretical framework and numerical results are robust, even when considering more complex flow fields.