Rossby Waves:
Beta-Plane
Dynamics
Zonal wavenumber k
3
Meridional wavenumber l
2
Beta parameter β
1.00
Mean wind U₀
0.50
Show:
Streamfunction ψ
Vorticity ζ
Potential vorticity q
Velocity field
Phase speed c_x
—
Group velocity c_gx
—
Period T
—
Stationary if U₀ = β/K²
—
Pause
Rossby dispersion:
ω = U₀k − βk/(k²+l²)
Phase speed c_x = U₀ − β/(k²+l²) — always less than mean flow, always westward relative to U₀.
Group velocity c_gx = U₀ + β(k²−l²)/(k²+l²)² — can be eastward!
Stationary waves:
c_x = 0 when U₀ = β/K². Blocking events in atmosphere.