Abstract
Unsteady nonlinear shallow-water flows typically emit inertia-gravity waves through a process called “spontaneous adjustment-emission.” This process has been studied extensively within the rotating shallow-water model, the simplest geophysical model having the required capability. Here, we consider what happens when the hydrostatic assumption underpinning the shallow-water model is dropped. This assumption is in fact not necessary for the derivation of a two-dimensional or single-layer flow model. All one needs is that the horizontal flow field be independent of height in the fluid layer. Then, vertical averaging yields a single-layer flow model with the full range of expected conservation laws, similar to the shallow-water model yet allowing for non-hydrostatic effects. These effects become important for horizontal scales comparable to or less than the depth of the fluid layer. In a rotating flow, such scales may be activated if the Rossby deformation length (the ratio of the characteristic gravity-wave speed to the Coriolis frequency) is comparable to the depth of the fluid layer. Then, the range of frequencies supporting inertia-gravity waves is compressed, and the group velocity of these waves is reduced. We find that this change in wave properties has the effect of strongly suppressing spontaneous adjustment-emission and trapping inertia-gravity waves near regions of relatively strong circulation.
Highlights
In the atmosphere and oceans, dynamical and thermodynamical fields often closely satisfy certain relations, called balance relations, the simplest of which are hydrostatic and geostrophic
We focus on the inertia–gravity waves (IGWs) generated from initially balanced, turbulent, rotating shallow-water flows, comparing and contrasting the SW and VA models
A new feature not seen for kD = 6 is found in the right panel for H = 0.4: here the IGWs are widely distributed across the domain
Summary
In the atmosphere and oceans, dynamical and thermodynamical fields often closely satisfy certain relations, called balance relations, the simplest of which are hydrostatic and geostrophic. We focus on single-layer rotating shallow-water (SW) flows, possibly the most widelystudied model in this context due to its relative simplicity: there are just three scalar evolution equations, one of which can be taken to express material conservation of PV, while the other two allow for inertia–gravity waves (IGWs), the imbalance[3] Replacing the latter by balance relations results in a balanced model with no IGWs. The novelty in this paper is to relax the hydrostatic approximation which forms the basis of the traditional SW model. We focus on the IGWs generated from initially balanced, turbulent, rotating shallow-water flows, comparing and contrasting the SW and VA models These flows develop small scale features, in PV, and in vorticity and (horizontal) divergence.
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