Specifically in relation to meteorology. I was wondering if the angular momentum an object, lets say a parcel of air has due to the roation about the earths axis. Is it conserved if moved to a different lattitude.
According to my understanding the conservation of angular momentum applies as long as there is no torque on it. Is moving an object in latitudinal direction a torque in this case?
Let me first introduce a name.
The physics of the motions of the atmosphere and the oceans is referred to as 'geophysical fluid dynamics'. (The physics of the motions of the atmosphere's air can to a good approximation be treated as fluid dynamics.)
For the assessment of what happens to momentum we must distinguish between air mass being pushed by pressure gradient, and change of velocity in the absence of pressure gradient.
The latter, air mass changing velocity without a pressure gradient present, is very rare. (It's somewhat less rare in oceanography - I will return to that.)
I will first discuss a simpler case: planar circumnavigating motion.
The animated GIF below shows two views of a rotating platform. The view on the left is from a non-rotating point of view, the view on the right shows the same platform, as seen from a co-rotating point of view.
The black dot represents an object that is subject to a centripetal force. The arrow represents that centripetal force. The force is such that it increases linear in proportion to the distance to the center of rotation. This proportional force is tuned to match the rate of rotation.
As we know: in the case of circumnavigating motion due to a centripetal force: angular momentum is conserved.
I divided the perimeter ring in 4 quadrants, to assist in discerning the motion of the object relative to the platform.
About the motion of the object:
When the object is at its closest to the perimeter the angular velocity of the object is slower than the angular velocity of the platform. At that point in its motion there is a surplus of centripetal force acting on the object. (As pointed out earlier: at every distance to the center: the amount of centripetal force is just the right amount for an object that is co-rotating with the platform.) The centripetal force pulls the object closer to the center of rotation.
When the object is at its closest to the center of rotation it has gained so much velocity that subsequently its distance to the center of rotation increases again.
And so the cycle goes on and on.
We have: in all of that cycling: while there is change of (angular) velocity: since the force that causes that change of velocity is a central force: angular momentum is conserved.
Now to the more complicated case of motion along the surface of the rotating Earth
The following is an animated GIF consisting of three frames.
(In this diagram the amount of equatorial bulge is exaggerated. In the case of the actual Earth the ratio is about 1:300)
The blue arrow represents the Earth's gravity, pulling towards the center of the Earth. The red arrow represents what I will refer to as buoyancy force.
We can think of air mass as buoyant. Every layer of air mass is carried by the layer(s) beneath it. The buoyancy force is perpendicular to the local level surface.
Because of its rotation the Earth has an equatorial bulge. As a consequence: the gravity and the buoyancy force are not completely aligned. The resultant force (green arrow) provides required centripetal force to remain co-rotating with the Earth.
(To get an idea: at 45 degrees latitude the amount of required centripetal force for an object, in the direction parallel to the local level surface, is given by dividing the mass of that object by 580. So, for a hovercraft with a weight of ten thousand units of weight the required centripetal force comes to about 17 units of weight.)
The amount of equatorial bulge of the solid Earth is tuned to the rotation rate. (As we know from plate tectonics: over geologic time scale the solid Earth is deformable.)
With all of the above in place I can now discuss the case of air mass moving parallel to the surface of the Earth.
Let's first take the case of air mass flowing from west-to-east, along, say, 45 degrees latitude.
When air mass is flowing eastward: the air mass is circumnavigating the Earth's axis faster than the Earth itself is rotating. Then the amount of provided centripetal force (the green arrow in the animated GIF) is not enough, and the air mass will swing wide, migragitn away from the pole.
In the absence of a pressure gradient force that migration to another latitude will be with conservation of angular momentum.
Conversely:
When air mass is flowing east-to-west: then the air mass is circumnavigating the Earth's axis at a slower angular velocity than the Earth itself is rotating. For the westward flowing air there is a surplus of centripetal force, and the westward flowing air mass will tend to be pulled closer to the nearest pole.
Just as in the case of eastward flow:
In the absence of a pressure gradient force that migration to another latitude will be with conservation of angular momentum.
Now, in our atmosphere all air mass is from all sides constrained. There is almost never opportunity for air mass to change velocity without involvement of pressure gradient. That pressure gradient force is not a central force. Therefore in general: when there is involvement of pressure gradient force angular momentum will not be conserved.
Oceanography
I now return to the circumstance of mass changing velocity without presence of any pressure gradient.
In Oceanography a phenomenon is recognized that is triggered by specific circumstances. The type of triggering event: a strong wind that lasts a day or so sets a stretch of sea water into motion, and after that wind has subsided that velocity tends to continue. That moving water can then continue in a pattern similar to the motion depicted on the right hand side of the animation showing the rotating platform. In geophysical fluid dynamics this pattern of motion is called 'inertial oscillation'.
Incidentally, the reason that it is referred to as 'inertial oscillation' is very interesting. In the diagram that depicts the Earth's equatorial bulge: in that diagram the green arrow is a component of gravity.
As we know: inertial mass and gravitational mass are equivalent. As a consequence of that: the inertial oscillation is true inertial motion. An omnidirectional accelerometer that is co-moving with inertial oscillation will only register acceleration in the direction perpendicular to the local level surface; the inertial oscillation is true inertial motion.
Angular momentum conservation on the rotating earth (under the guise of potential vorticity) provides the restoring force that creates Rossby waves.
If I understand your question correctly, a parcel of air moved for example from near the equator in the direction of the north pole will indeed strive to conserve its angular momentum, subject to the fact that friction along the way will also tend to rub away some of that momentum during the move.
Direct evidence of this is furnished by the coriolis effect.
Simply translating an object along the surface of the earth -- in any direction -- does not impose a torque.
Note that this whole discussion is ignoring the rotation of the earth. Just pretend it's a motionless ball in space for now, and add in the confounding rotations later.
However, translating an object while constraining some part of its orientation to the surface of the earth somehow may well impose a torque. Imagine picking up a stick at the equator, that's lying in the north-south direction. Now without rotating it with respect to the average motion of the Milky Way, walk to the North Pole -- your stick is now vertical, but it has not rotated in an inertial reference frame, so no torques need to be applied.
Conversely, pick up the same stick in the same place at the same orientation, and walk to a pole while keeping the stick level to the ground. For every kilometer you walk, you need to rotate the stick through about 628 microradians (if I'm getting my math right). So you need to accelerate it up to whatever its rotation rate will be when you start walking, and decelerate it when you're done.
With respect to meteorology, if you have some weather system big enough to notice the motion of the earth (i.e., a jet stream, or a hurricane), then yes, inasmuch as the atmospheric mass tends to stay the same shape it will "feed" a torque as you move it in latitude. I'm not at all sure that this will be significant enough to matter, though -- that's a question best asked on a meteorology forum.
