Characteristics of Wakes in the Ocean wake hydrodynamics in the ocean

Characteristics of Wakes in the Ocean

Class	Speed, m/s (ONR)	Speed, m/s (Jane's)	Diameter (m)
Los Angeles	10	16	10
Ohio	10	12	13

These quantities imply typical Reynolds number values in the range of

Ocean shear values tend to be in the range Ri=(N/U_z)²={1,4}, although I can not find any references that claim this is true throughout the ocean. In other words, it's possible that these values are typical where people tend to measure ocean shear, and that might be biased toward regions of unusually high shear (and turbulence). It's possible that typical Ri values are smaller, e.g., under the ice in the northern polar region. I will update this when I learn more.

Simulation parameters

• Reynolds number: Re=10^5 (10k)

  Re=UL/nu={10^7, 10^8} is hopeless for DNS at this time. O(10^5) is the best we can feasibly do.

• Wake Froude number: Fr=100 (i.e., Ri_sim=0.0001, N_sim=0.01)

  We can simulate anywhere in the range subs operate, but lower Fr have wakes last longer, so interest us more. We will use Fr=100.

      Fr = U/NL ->
      N  = U/LFr
  

  Fr=100 implies N_sim=1/100=0.01. Note that this N_sim is in the non-dimensional units of the simulation, not cycles per second. This accounts for why this value of N appears to be larger than the maximum found in the ocean (N=0.001 Hz)... different units.

• Shear gradient Richardson number: 1 (i.e. U_z=0.01)

  For us Ri sets the value of U_z since Fr effectively sets the value of N.

  Ri	=	(N/Uz)2	->
  Ri1/2	=	N/Uz	->
  Uz	=	N/Ri1/2

  Choosing the strongest shear, Ri=1, yields U_z=N/1. Using N=0.01 implies U_z=0.01

  I would bet that gradient Ri is probably not the important parameter; I suspect U_z/omega or non-dimensional vortex stretching determine the outcome.