Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite reynolds number

Renwei Mei, Ronald J. Adrian

Research output: Contribution to journalArticlepeer-review

207 Scopus citations


Unsteady flow over a stationary sphere with a small fluctuation in the free-stream velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency,ω, under the restriction St <<Re <1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St ~ ωinstead of the ω12 dependence predicted by Stokes solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finite-difference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t-2, instead of t-1/2, at large time for both small and finite Reynolds numbers.

Original languageEnglish (US)
Pages (from-to)323-341
Number of pages19
Journaljournal of fluid mechanics
Issue number323
StatePublished - Mar 1992
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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