Mathematical derivation of Coriolis force
The geostrophic bias force is actually Coriolis force. The expression of Coriolis force in non-inertial system is 2v across w, and the way to push it is to decompose the velocity in any direction into radial direction and normal direction. It is proved that the radial velocity changes vw, the direction is tangential, and the change of velocity direction leads to the velocity variable vw, so the radial velocity is 2ww, and the direction is tangential. However, the tangential speed increases the centrifugal force of 2wv+v 2/r, and the object that is always tangent to the disk speed needs the centripetal force of v 2/r, so the variable of force is 2wv and the direction is radial. It's a little hard to understand. Generally, college textbooks only have the deduction of the first case, and it is made by displacement, so I won't explain it here. Then decompose the tangential velocity on the earth, multiply it by w, and use the determinant. If you can't write it here, don't push it down. The result is f=2mvωsinφ. Then, let's talk about tidal force and tidal force. The acceleration at different positions is different because of the imbalance of gravitational field. If the mass of one element is much less than the mass of another element (such as the water on the earth and the surface), the tidal force is the difference of the gravitational field between the two positions multiplied by the mass of the small element; If the two elements are similar in mass, similar to a binary star system, then the tidal force of the sun is the difference between the gravitational field of the center of mass and that of a star multiplied by the mass of the planet. If the distance between two prime elements is much smaller than the distance between the planet and the sun, according to the approximate principle of differential, the gravitational field here can be regarded as uniform change, and its rate of change is the derivative of the gravitational field about the distance here. This can greatly simplify the calculation. I don't know if I made it clear. Do you have any questions to ask? . .