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Mach-like capillary-gravity wakes.

Frédéric Moisy1, Marc Rabaud1

  • 1Université Paris-Sud, CNRS, Laboratoire FAST, Bâtiment 502, 91405 Orsay, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
PubMed
Summary
This summary is machine-generated.

The wake angle behind a cylinder follows a Mach-like law, transitioning between capillary-gravity and gravity-dominated regimes based on the Bond number (Bo(D)). This transition is explained by a new model involving a capillary cusp angle.

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Area of Science:

  • Fluid dynamics
  • Wave phenomena
  • Surface tension effects

Background:

  • The wake angle behind moving objects is a fundamental aspect of fluid dynamics.
  • Previous studies focused on gravity-dominated wakes, particularly for ship wakes.
  • The role of surface tension (capillary effects) in wake formation at smaller scales was less understood.

Purpose of the Study:

  • To experimentally determine the wake angle behind a translating cylinder across a range of Bond numbers (Bo(D)).
  • To investigate the transition between capillary-gravity and gravity-dominated wake regimes.
  • To develop a model explaining the observed wake angle behavior and the influence of capillary effects.

Main Methods:

  • Experimental measurements of wake angle behind a vertical surface-piercing cylinder.
  • Systematic variation of cylinder diameter and fluid properties to control the Bond number (Bo(D)).
  • Numerical simulations of surface elevation for a moving pressure disturbance.

Main Results:

  • The wake angle (α) follows a Mach-like law (α∼U⁻¹) at high velocities, with prefactors dependent on Bo(D).
  • For low Bo(D) (strong capillary effects), α≃c(g,min)/U, where c(g,min) is the minimum group velocity.
  • For high Bo(D) (weak capillary effects), α∼√[gD]/U, consistent with ship wakes.
  • A model was proposed explaining the transition and the origin of the capillary law from a capillary cusp angle.

Conclusions:

  • The wake angle dynamics are significantly influenced by capillary effects, especially at smaller scales or lower velocities.
  • A unified model successfully describes the transition between different wake regimes based on the Bond number.
  • The concept of a capillary cusp angle is introduced as a key factor in energy accumulation and wake formation under capillary-gravity wave dominance.