Residual streaming flows in buoyancy-driven cross-shore exchange Articles uri icon

publication date

  • June 2021

start page

  • A1-1

end page

  • A1-26

issue

  • A1

volume

  • 920

International Standard Serial Number (ISSN)

  • 0022-1120

Electronic International Standard Serial Number (EISSN)

  • 1469-7645

abstract

  • We present an analytical study of two-dimensional flow in a wedge driven by a time-dependent surface heat flux as a model problem to understand buoyancy-induced cross-shore flow. Besides the turbulent Prandtl number and the relevant Rayleigh number, both assumed to be of order unity, the solution is seen to depend on the geometry through a parameter β
    , representing the bottom slope. An analytic solution is sought in the asymptotic limit β≪1
    for a water layer bounded by an adiabatic bottom surface subject to a harmonic heat flux on the upper surface. The analysis reveals that the motion at leading order can be expressed as the sum of a harmonic component and a steady component, the latter driven by nonlinear advection. This steady-streaming motion includes a near-shore vortex with associated recirculating motion that can affect cross-shore transport and dispersion in coastal environments. The analytical solution is compared with numerical solutions of the complete conservation equations for small values of β
    . Excellent quantitative agreement is found for values of the Rayleigh number below a critical value at which the periodic solution undergoes a period-doubling bifurcation, leading to the establishment of thermal-instability cells that dominate the offshore flow dynamics, while the near-shore dynamics remains well described by the analytical solution. The analysis illustrates that a periodic heat input that leads to a vertically inhomogeneous temperature distribution can result in residual motion, net heat fluxes and persistent temperature structure in the cross-shore direction.

subjects

  • Industrial Engineering
  • Materials science and engineering
  • Mechanical Engineering

keywords

  • baroclinic flows; ocean processes