“…In order to investigate the dynamics of the gyre flow field in more detail, the effects of the different terms in the momentum equation are considered. For this, the vertically averaged horizontal momentum equation over the depth layers influenced by the gyre velocity field (i.e., the thermocline layer and epilimnion) is expressed as (Brett,
2018; Brett et al.,
2020; Cimatoribus et al.,
2018; Vallis,
2017):
where U h = ( u , v ) is the horizontal velocity field,
is the acceleration induced by the barotropic and baroclinic pressure gradients,
is the acceleration caused by the nonlinear (advection) terms, C = ( fv , − fu ) is the acceleration caused by the Coriolis effect, F = ( F x , F y ) is the acceleration induced by external forces, and D = (− ν ∇ 2 u ,− ν ∇ 2 v ) is the deceleration due to dissipation (i.e., bulk, lateral, and bottom friction).
is the three‐dimensional velocity vector, ν is viscosity, 𝜌 is density, and t is time.…”