University:
Widener University
Course:
ESSC 103 | Intriduction To Earth Science
Academic year:

2023
Views:

439

Pages:

1
Author:

milkstetrastyle

Waves on a PV Front — Numerical Model Purpose: Study the properties of waves on one or more fronts separating regions of constant potential vorticity. Numerical Model: Select the frontal waves, num (1 and 2 fronts) link This programs are intended to solve the inversion problem � ∇2 ψ = q0 + ∆i H(y − [Yi + ηi (x, t)]) (1) with H being the step-function and calculate the movement of the fronts ∂ ∂ψ ∂η ∂ψ ηi = + ∂t ∂y ∂x ∂x Periodicity in x is assumed, with period 2π. This is equivalent to moving the points on the front as Lagrangian particles: ẋj = −ψy (xj , yj ) , ẏj = ψx (xj , yj ) (2) The inversion of (1) is accomplished using a Green’s function integral, approximated by a sum. To Use: You need to set the values for: Y Vector of average y position of the interfaces (e.g., -0.3;0.3) ∆ Vector of PV steps across interfaces (e.g., -1;1) u0 Zonal ﬂow in southernmost region (e.g., -0.3) q0 PV in the southernmost region (e.g., 0) η1 (x, 0) Initial perturbations to the fronts (e.g., 0.1*sin(x);0.1*sin(x) Clicking on any of the Click here to run buttons will show you the background zonal ﬂow and the evolution of the frontal positions. To think about · Find the dispersion relationship for waves on a single front empirically. · How does nonlinearity aﬀect the waves? · What eﬀect does q0 have? · Consider a wave on an atmospheric/ oceanic front from some data. Estimate the speed of travel you would expect to ﬁnd and compare it to the actual evolution. · Estimate the wavelength/width ratio required for the instability of a shear layer. · What is the eﬀect of additional large scale shear (q0 )? · Unequal magnitude of PV jumps? Same sign? · Multiple waves in initial conditions? · Triangular jet (three fronts)? · Modify the code to look at two vortices or a vortex and a front and try some experiments with that.