Evolutions of a Laminar Jet in a Homogeneous Rotating Fluid : A Linear Theory

Abstract

Evolutions of a laminar jet produced by an axial body force in a rotating fluid, which is inviscid, homogeneous and incompressible, are investigated by means of a linear theory. The body force is assumed to be axisymmetric and confined to a certain limited region. The forcing is suddenly initiated. As for the subsequent behavior of the forcing with time, the following are considered: 1) Continuous forcing. 2) Forcing of a finite duration.
For continuous forcing the flow fields become uniform in the axial direction as time passes with the exception of the azimuthal velocity and pressure fields within the forcing region, where the Taylor-Proudman theorem can not be applied. In the forcing region an axial pressure-gradient is gradually built up which acts to oppose the forcing. It is found that the pressure-gradient becomes nearly steady after t*=10.90/f, where t* is the ellapsed time from the initiation of the forcing and f is the Coriolis parameter. The resulting pres- sure-gradient force balances the forcing in the axial direction, and the Coriolis force in the radial direction (geostrophic balance).
For forcing of a finite duration it is found that the response of the fluid in the forcing region when the forcing ceases does not depend on the duration of the forcing T* if T* is larger than 10.90/f. For such a large value of T*, a reverse flow appears in the forcing region between t*'=3.4/f and 6.5/f after the forcing is stopped. Here, t*'=t*-T*. This phenomenon is caused by the reverse pressure-gradient force which has been maintaining a balance with the forcing. After the reverse flow weakens, continuous damped oscillations remain near the forcing region. The period of the oscillations is about 2π/f.
The present model is considered to be a refined form of a linear theory (Niino, 1978), which was developed to explain the reverse flow found in the laboratory experiment on turbulent jets in a rotating fluid.