# Fluids Dynamics – Math Problem Example

(i)20* 1000= 200010/100*2000 = 200200/60 = 3.3So the answer is 3.3m/s(ii)dV/dt = −V 2/LFLF = 3m/s * 1 hour and L = 50 km50 * 1000 = 50,000.SodV/dt = 50, 000/3 = 16, 666.7m/s (iii)Dθ / Dt = kH ∂2θ/ ∂x2 Estimate of kH16, 666.7m/s = kH ∂2θ/ ∂x2 So16, 666.7 = kH * 580Hence kH = 16,666.7/580 = 28.This is how the extent of real sea breeze is determined. No 3Quasi-Geostrophic (QG) equationsBasically, planetary scale fluid motions within the earth’s atmosphere as well as oceans are as a result of strong stable stratification in addition to rapid planetary rotation.

The suitable equations of motion for the asymptotic regime are known as Quasi-Geostrophic (QG) equations. At the momentum level and making use of the pseudo height coordinate z = [1 − (p/p0)κ]cpθ0/g the equations are They are used in large scale atmospheric floe in addition to some oceanic flows. However, at times the Rossy number is small and hence at times the inertial accelerations can be neglected (Masaki 2004). Planetary geostrophic equations Planetary geostrophic equations are a standard model of thermohaline circulation. They are obtained from equations such as the Froude number Fr, the Rossby number, as well as the Burger number Bu go to 0.These equations are of tremendous diagnostic value.

Pressure field allied to geostrophic velocities is an applicable solution as long as boundary requirements have been satisfied. However, these equations do not give any information regarding how the flow evolves (Chelton 2006). B(i)Where the potential vorticity q is(Chelton 2006). (ii)At first, we begin with disturbing a flow that with only a time and spatially invariant zonal flow U without meridional component.

1We assume the perturbation to be a lot smaller than the mean zonal flow. Supposing non-divergent flow which stream function entirely describes the flow, 2 3Which, and plug to get: 4A traveling wave solution having wave numbers k and l, in addition to frequency omega: 5Dispersion relation of the below equation is obtained: 6Both zonal phase speed together with group speed are given by the following equations respectively: (Chelton 2006). (iii)c is the phase speed, cg is the group speed, u is the mean westerly flow, β is the Rossby parameter, k is the zonal wave number.

The above indicates that phase speed is at all times westward relative to mean flow. The meaning of large and small is entirely dependant on the value of l, if l = k, subsequently the group speed is equivalent to the mean zonal flow. Vertical in-uniformity within the stratification is given by: And the β plane approximation is used to take in the end product of the variation in f with latitude, . The dissipation operator shows the effects of each and every scale of motion smaller than those unambiguously resolved in the numerical calculation; characteristically this equation is used which is hyper-viscous diffusion: , where is a small hyperviscosity. Therefore there are only two major variables in the QG code: and q. (Chelton 2006). BibliographyChelton, G., 2006, Global observations of oceanic Rossby waves, Science.

Vol. 5/4.Masaki, S., 2004, Atmospheric circulation dynamics and general circulation models, Chicago, Springer.