TY - JOUR

T1 - On the opposing roles of the Boussinesq and non-Boussinesq baroclinic torques in surface gravity wave propagation

AU - Heifetz, Eyal

AU - Maor, Ron

AU - Guha, Anirban

N1 - Publisher Copyright:
© 2019 Royal Meteorological Society

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Here we suggest an alternative understanding of the surface gravity wave propagation mechanism based on the baroclinic torque, which operates to translate the interfacial vorticity anomalies at the air–water interface. We demonstrate how the non-Boussinesq term of the baroclinic torque acts against the Boussinesq one to hinder wave propagation. By standard vorticity inversion and mirror imaging, we then show how the existence of the bottom boundary affects the two types of torque. Since the opposing non-Boussinesq torque results solely from the mirror image, it vanishes in the deep-water limit and its magnitude is half of the Boussinesq torque in the shallow-water limit. This reveals that the Boussinesq approximation is valid in the deep-water limit, even though the density contrast between air and water is large. The mechanistic roles played by the Boussinesq and non-Boussinesq parts of the baroclinic torque remain obscured in the standard derivation where the time-dependent Bernoulli equation is implemented instead of the interfacial vorticity equation. Finally, we note on passing that the Virial theorem for surface gravity waves can be obtained solely from considerations of the dynamics at the air–water interface.

AB - Here we suggest an alternative understanding of the surface gravity wave propagation mechanism based on the baroclinic torque, which operates to translate the interfacial vorticity anomalies at the air–water interface. We demonstrate how the non-Boussinesq term of the baroclinic torque acts against the Boussinesq one to hinder wave propagation. By standard vorticity inversion and mirror imaging, we then show how the existence of the bottom boundary affects the two types of torque. Since the opposing non-Boussinesq torque results solely from the mirror image, it vanishes in the deep-water limit and its magnitude is half of the Boussinesq torque in the shallow-water limit. This reveals that the Boussinesq approximation is valid in the deep-water limit, even though the density contrast between air and water is large. The mechanistic roles played by the Boussinesq and non-Boussinesq parts of the baroclinic torque remain obscured in the standard derivation where the time-dependent Bernoulli equation is implemented instead of the interfacial vorticity equation. Finally, we note on passing that the Virial theorem for surface gravity waves can be obtained solely from considerations of the dynamics at the air–water interface.

KW - baroclinic torque

KW - non-Boussinesq flows

KW - surface gravity waves

UR - http://www.scopus.com/inward/record.url?scp=85078608676&partnerID=8YFLogxK

U2 - 10.1002/qj.3719

DO - 10.1002/qj.3719

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AN - SCOPUS:85078608676

SN - 0035-9009

VL - 146

SP - 1056

EP - 1064

JO - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

IS - 727

ER -