Forces of Nature
The gravity force is the vector sum of the true gravitation vector (g*) and this force
A unit vector dot multiplied with itself is equal to this
What is '1'?
Hydrostatic balance arises from the balance of these two forces
What is gravity and the vertical pressure gradient force?
The conservation of momentum is represented by these equations
What are the equations of motion?
A flow balance is achieved by neglecting accelerations and friction
What is geostrophic balance?
The name for the "real" force that causes acceleration of a spinning ball.
What is the centripetal acceleration/force?
The del operator multiplied by a scalar variable is called this
What is the gradient?
The equation of state (or ideal gas law) relates these three variables
What is temperature, pressure, and density?
The mass divergence form of this conservation equation can be used to predict changes in density over time
What is the continuity equation (del pho/dt = ...)?
The meridional (v) component of the geostrophic wind depends on the change of pressure in this direction
What is the x (zonal) direction?
The horizontal equations of motion contain these three forces
What is the pressure gradient, Coriolis, and Friction force?
The mathematical representation of the divergence of the horizontal wind
What is del dot V?
This form of the continuity equation is commonly applied because it does not contain a density term
What is the pressure coordinate (or "isobaric") form (du/dx + dv/dy + d(omega)/dp = 0)?
The fundamental law from which the thermodynamic equation is derived
What is the conservation of energy (1st law of thermodynamics)?
This dimensionless number is used to determine the validity of geostrophic flow. It is the ratio of the wind acceleration to the Coriolis acceleration
What is the Rossby number?
Of the horizontal or vertical pressure gradient forces, this one is always much greater in magnitude
What is the vertical pressure gradient force?
The name for situations when the del operator is dot multiplied with a second del operator
What is the Laplacian?
A scale analysis on the equations of motion reveal that this term can be safely neglected in most situations.
What is the friction term?
This variable is the vertical velocity in all of the equations of motion expressed in isobaric coordinates.
What is omega?
In geostrophic balance, we eliminate the acceleration terms in the equations of motion because this technique shows they are one order of magnitude smaller than the PGF and CF terms
What is scale analysis?
An eastward travelling zonal wave that oscillates north and south across the equator due to the change in sign of the Coriolis Force in each hemisphere
This relation shows how a total derivative can be broken down into a local rate change plus advection terms
What is Euler's Relation?
The thermodynamic energy equation is derived from the sum of these two other equations
What is the thermal energy equation (how internal energy changes with time) and the mechanical energy equation (energy change through movement)?
The static stability parameter comes out of the isobaric form of this conservation equation
What is the thermodynamic equation?
This thickness equation is derived from the Equation of state and the hydrostatic approximation
What is the hypsometric equation?