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Hilfe!!! - Horizontale Euler Gleichung
geschrieben von: gatzlphi (IP-Adresse bekannt)
Datum: 16. Januar 2018 16:05

Hallo zusammen,

Ich hab mal wieder ein paar Fragen um Metrologie ein bisschen besser zu verstehen. Zwinkern
Ich schreib einfach mal meine Aufgabenstellung rein. Dazu habe ich eine Dropbox erstellt, wo die Dokumente auch nochmal als .pdf Datein hinterlegt sind.

Da es mir das letzte mal super geholfen hat, hier meine Aufgabenstellungen:

1.1 Components and terms of the Euler equation.
1.1.1. Give the terms Fc,i,j of the Coriolis force Fc of the zonal Euler equation (i=1) for an arbitrary position on earth.

1.1.2. Give the terms of the zonal Euler equation for an arbitrary position on earth.

1.1.3. Give the zonal component of the geostrophic balance equation for an arbitrary position on earth.

1.1.4. Give the terms Fc,i,j of the Coriolis force Fc of the meridional Euler equation (i=2) for an arbitrary position on earth.

1.1.5. Give the terms of the meridional Euler equation for an arbitrary position on earth.

1.1.6. Give the meridional component of the geostrophic balance equation for an arbitrary position on earth.


1.2. Target position TP = (i,j,k) at which the Euler equation is evaluated.

In the following the target position TP=(λi,ϕj,k) of the ERAinterim grid, which is nearest to Honiara, 1000 m over ground, shall be identified. The results shall be given for this ERA interim grid position.

1.2.1. Give the geographical coordinates (λi,ϕj)(λi,ϕj) of Honiara.

1.2.2. Give the grid point numbers (i,j) and the horizontal position (λi,ϕj) of the ERA interim grid point, which is the nearest neighbor of Honiara.

1.2.3. Give the ERA interim full-level k which is nearest to the height 1000 m over ground of the target position Honiara.

1.2.4. Give the height of your target position (λi,ϕj,zf,k) above sea level zf,k,abs

2. Uncertainty of the Euler equation
Give the absolute uncertainty for zonal velocity u, meridional velocity v, pressure p, temperature T, latitude ϕ and earths angular velocity Ω at your target position (i,j,k).

Note: The uncertainty of the terms shall be given in an as simple form as possible, e.g. Δ(auT)=(a(δu)2+(δT)2)1/2 with δΨ=(ΔΨZwinkern/Ψ. In the formulas small terms ( smaller than one order of magnitude than the leading term) can be neglected, e.g. Δ(u+v/10)=((Δu)2+0.1(Δu)2)1/2=Δu.
The uncertainty of the coefficients ak and bk can be assumed to be zero.

Use the provided equations for uncertainty measurement [siehe Dokument in der Dropbox].

2.1. Formulas for absolute uncertainty of terms and derived quantities

Give formulas for absolute uncertainty of terms and derived quantities relevant for calculation of uncertainty of the Euler equation in standard form as matrix fij. The components of matrix fij are defined as:

2.1.1 Coriolis force 2(Ω×v)x in the equation for zonal velocity u :

ΔFc,1=f11Δu+f12Δw+f13Δp+f14ΔT+f15ΔFIS+f16Δg+f16ΔRL+f17ΔRL+f18Δt+f19Δχ

2.1.2 Instationarity \ptu of u:

Δ∂u/∂t=f21Δu+f22Δw+f23Δps+f24ΔT+f25ΔFIS+f26Δg+f27ΔRL+f28Δt+f29Δχ

2.1.3 Pressure pk(i,j)at full level k.

Δpk(i,j)=f31Δu+f32Δw+f33Δps+f34ΔT+f35ΔFIS+f36Δg+f37ΔRL+f38Δt+f39Δχ

2.1.4 Pressure pz(i,j,k)(i+1,j) at position (i+1,j) but at height z(i,j,k) of grid point (i,j).

Δpz(i,j,k)=f41Δu+f42Δw+f43Δps+f44ΔT+f45ΔFIS+f46Δg+f47ΔRL+f48Δt+f49ΔχΔpz(i,j,k)

2.1.5 zonal pressure gradient ∂p/∂xp(i,jk)∂p/∂xp(i,jk)

Δ∂xp(i,j,k)=f51Δu+f52Δw+f53Δps+f54ΔT+f55ΔFIS+f56Δg+f57ΔRL+f58Δt+f59Δχ

2.1.6 Net horizontal transport vh⋅∇hu of u.
Δ(vh⋅∇hu)=f61Δu+f62Δw+f63Δps+f64ΔT+f65ΔFIS+f66Δg+f67ΔRL+f68Δt+f69Δχ

However, some components of fij are zero. If for a particular j=n Δn=0, all components fin can be given as fin=0. The quantity χ represents a relevant uncertainty not given explicitely in the formula.Specify f19Δχ=0Δx if no such quantity has been identfied. Give it explicitely otherwise.
The typical values introduced for k, z, u and other quantities in the document Uncertainty calculations can be used in th.

2.2. Meridional momentum equation: time derivative and net transport

The derivatives in time and in horizontal directions are to be calculated numerically using the derivative approximations suggested (midpoint rule)

2.2.1 the time derivative ∂tv of the meridional velocity v at your target position (i,j,k).

2.2.2 the levels l and l+1 located above and below your target position height z(i,j,k) at next grid point i,j+1 and i,j−1i in direction North and South.

2.2.3 the zonal advection u∂xv of the meridional velocity v at (i,j,k).

2.2.4 the meridional advection v∂yv of the meridional velocity at (i,j,k).

2.2.5 the absolute uncertainty of the time derivative ∂tv of the meridional velocity at (i,j,k).

2.2.6 the absolute uncertainty of the zonal advection u∂xv of the meridional velocity v at (i,j,k).

2.2.7 the absolute uncertainty of the meridional advection v∂yv of the meridional velocity v at (i,j,k).

2.3. Zonal momentum equation: time derivative and net transport

2.3.1. the time derivative ∂tv of the zonal velocity u at your target position (i,j,k).

2.3.2. the levels l and l+1 located below and above your target position height z(i,j,k) at next grid point i+1, j and i−1, j in direction West and East.

2.3.3. the distance Δx(i,j,k) between your target position (i,j,k) and the next grid point in direction East (i+1,j,k).

2.3.4. the zonal advection u∂xu of the zonal velocity u at (i,j,k).

2.3.5. the meridional advection v∂yu of the zonal velocity at (i,j,k).

2.3.6. the absolute uncertainty of the time derivative ∂tu of the zonal velocity at (i,j,k).

2.3.7. the absolute uncertainty of the zonal advection u∂xu of the zonal velocity u at (i,j,k).

2.3.8. the absolute uncertainty of the meridional advection v∂yu of the zonal velocity u at (i,j,k).

3. Zonal Euler equation and geostrophic equilibrium

The left hand side (LHS) of the Euler equation (1) is given by instationarity and advection, the right hand side (RHS) by the pressure gradient and the Coriolis term. In this exercise the magnitudes of the terms of the zonal component of the Euler equation at the target position (TP) are investigated.

3.1 Calculate the following terms of the zonal Euler equation

3.1.1 zonal pressure gradient term 1/ρ∂xp at your target position (i,j,k).

3.1.2 terms of the zonal Coriolis force 2(Ω×v))x at (i,j,k)

3.1.3 deviation from the zonal geostrophic equilibrium given by (RHS(1))x=∂xpρ−2(Ω×v))x at (i,j,k).

3.1.4. uncertainty of the deviation from zonal geostrophic equilibrium Δ(RHS(1))x at (i,j,k).

3.1.5 imbalance (LHS(1)−RHS(1))x of the zonal Euler equation at (i,j,k).

3.1.6 uncertainty Δ((LHS(1)−RHS(1))x) of the imbalance (LHS(1)−RHS(1))x of the zonal Euler equation at (i,j,k).

4. Meridional Euler equation and geostrophic equilibrium

The left hand side (LHS) of the Euler equation (1) is given by instationarity and advection, the right hand side (RHS) by the pressure gradient and the Coriolis term. In this exercise the magnitudes of the terms of the meridional component of the Euler equation at the target position ( TP ) are investigated.

4.1 Calculate the following terms of the meridional Euler equation:

4.1.1. meridional pressure gradient term 1/ρ∂yp at your target position (i,j,k).

4.1.2. terms of the merdional Coriolis force 2(Ω×v))x at (i,j,k).

4.1.3 deviation from the meridional geostrophic equilibrium given by (RHS(1))y=∂ypρ−2(Ω×v))y at (i,j,k).

4.1.4. uncertainty of the deviation from meridional geostrophic equilibrium Δ(RHS(1))y at (i,j,k).

4.1.5 imbalance (LHS(1)−RHS(1))y of the meridional Euler equation at (i,j,k).

4.1.6 uncertainty Δ((LHS(1)−RHS(1))y) of the imbalance (LHS(1)−RHS(1))y of the meridional Euler equation at (i,j,k).



An alle die soweit gelesen haben, Danke!!!

Ich weiß es fordert sehr sehr viel, aber wie in meinem vorherigen Post schon einmal beschrieben:
Der Dozent, der das Fach hält erklärt so gut wie garnichts und das kleine bisschen, was er erklärt versteh ich absolut nicht. (Wir haben keinerlei Physikkurse im vorherigen Studium)

Wie gesagt, jede Hilfestellung ist herzlich angenommen!!!!

Ich freue mich auf Antworten, aber sehe auch ein, wenn keine kommen. Es ist sehr viel gefragt!


Bis dahin
gatzlphi



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  Hilfe!!! - Horizontale Euler Gleichung 646 gatzlphi 16.01.18 16:05


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