TY - JOUR

T1 - Instability in stratified shear flow

T2 - Review of a physical interpretation based on interacting waves

AU - Carpenter, Jeffrey R.

AU - Tedford, Edmund W.

AU - Heifetz, Eyal

AU - Lawrence, Gregory A.

PY - 2011/11

Y1 - 2011/11

N2 - Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other (“phase-locking”), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjortoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary.

AB - Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other (“phase-locking”), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjortoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary.

UR - http://www.scopus.com/inward/record.url?scp=85017106162&partnerID=8YFLogxK

U2 - 10.1115/1.4007909

DO - 10.1115/1.4007909

M3 - מאמר

AN - SCOPUS:85017106162

VL - 64

SP - 60801-1-60801-17

JO - Applied Mechanics Reviews

JF - Applied Mechanics Reviews

SN - 0003-6900

IS - 6

ER -