Overall depth of the flow \[h(x, y, t) = \underbrace{H}_{\text{mean depth}} + \underbrace{\eta(x,y,t)}_{\text{sea surface height}}\] Zonal Momentum Equation \[\underbrace{\frac{\partial u}{\partial t}}_{\text{local acceleration}} + \overbrace{u \frac{\partial u}{\partial x}}^{\text{nonlinear advection}} + \overbrace{v \frac{\partial u}{\partial y}}^{\text{nonlinear advection}} - \underbrace{f v}_{\text{Coriolis (with } f = f_0 + \beta y \text{)}} = -\underbrace{g \frac{\partial \eta}{\partial x}}_{\text{pressure gradient force from } \eta(x,y,t)}\] Meridional Momentum Equation \[\underbrace{\frac{\partial v}{\partial t}}_{\text{local acceleration}} + \overbrace{u \frac{\partial v}{\partial x}}^{\text{nonlinear advection}} + \overbrace{v \frac{\partial v}{\partial y}}^{\text{nonlinear advection}} + \underbrace{f u}_{\text{Coriolis (with } f = f_0 + \beta y \text{)}} = -\underbrace{g \frac{\partial \eta}{\partial y}}_{\text{pressure gradient force from } \eta(x,y,t)}\] Continuity Equation \[\underbrace{\frac{\partial h}{\partial t}}_{\text{rate of change of depth}} + \underbrace{\frac{\partial (u h)}{\partial x}}_{\text{zonal transport divergence}} + \underbrace{\frac{\partial (v h)}{\partial y}}_{\text{meridional transport divergence}} = 0\] Here, all the \(\overbrace{\text{nonlinear terms}}^{u \partial u/\partial x, \, v \partial u/\partial y, \ldots}\) have been retained