Lesson 13 Hydrodynamic Instability Baroclinic and Barotropic Instability A flow field is said to be unstable if a small – Be able to define each disturbances introduced to the flow grows – Understand the applications Basic example – Parcel instability - convection The role of the growing disturbance is to bring the system back to a stable state Most of the instability we want to work with is due to wave propagation – Therefore, the parcel method is not a good measure of stability Barotropic Fluid Barotropic Fluid An atmosphere or ocean in which the density depends only on the pressure so Geostrophic wind constant with height that isobaric surfaces are also surfaces Thermal wind is zero of constant density (isopycnals) ρ = ρ(P) Advection of temperature by the Temperature does not vary on a constant geostrophic wind is zero since the pressure surface temperature gradient is zero In a barotropic fluid: ∇T = 0 ∂V and g = 0 ∂z 1 Barotropic Instability Barotropic Instability In terms of potential vorticity (PV) Wave instability associated with the – Begin with a gradient of PV horizontal shear in a jet-like current – Include a mass sink – Over time circulations will develop Growth is due to obtaining kinetic Theoretical: energy from the mean flow Example Real atmosphere: Example 2 African Easterly Jet (AEJ) 600 hPa Monsoon winds African Easterly Wave (AEW) 2 Baroclinic Fluid Baroclinic Fluid An ocean or atmosphere in which density The geostrophic wind has vertical shear is a function of other parameters Thermal wind is not zero ρ = ρ ρ = ρ (S,T, P) or (T, P) There is temperature advection by the Isobaric and isopycnal surfaces do not geostrophic wind coincide In a baroclinic fluid: Baroclinicity is of primary importance in ∇T ≠ 0 dynamic meteorology and oceanography ∂V g ≠ 0 ∂z Baroclinic Instability Baroclinic Instability Occurs at long wavelengths Wave instability associated with the vertical shear of the mean flow Implies that longwave flows (i.e. Rossby waves) are prone to spontaneous Growth is due to the conversion of PE formation of disturbances associated with the mean horizontal – i.e. intensification of small perturbations via temperature gradient that must exist to energy conversion - the fluid trying to get to provide thermal wind balance for the the lowest PE state vertical shear in the mean flow 3 African Easterly Jet (AEJ) (Burpee 1972) 4.