paint-brush
Our Oceanography Study's YBJ Upper Boundary Condition: How We Found It by@oceanography
108 reads

Our Oceanography Study's YBJ Upper Boundary Condition: How We Found It

tldt arrow

Too Long; Didn't Read

This paper is available on arxiv.org/pdf/2308.00889.pdf under CC 4.0 license. The no-normal flow condition is imposed by requiring 𝑀 = 0 at 𝓉 = 0 (Young and Ben Jelloul 1997) We then horizontally average (denoted by ·) equation (B1)
featured image - Our Oceanography Study's YBJ Upper Boundary Condition: How We Found It
Oceanography: Everything You Need to Study the Ocean HackerNoon profile picture

Authors:

(1) Scott Conn, California Institute of Technology, Pasadena, California;

(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;

(3) Jorn Callies, California Institute of Technology, Pasadena, California.

Abstract and Intro

Observations

Models

Results

Discussion

Conclusion

APPENDIX A

APPENDIX B

APPENDIX C

References

APPENDIX B

YBJ Upper Boundary Condition

Beginning from (A3) with the choice C = 0, we can vertically integrate from 𝑧 = −𝐻 to 𝑧 = 0 and use 𝑀 = 0 at 𝑧 = −𝐻 to arrive at



The no-normal flow condition is imposed by requiring ∇𝑀 = 0 at 𝑧 = 0 (Young and Ben Jelloul 1997), which eliminates the advection and dissipation terms. We then horizontally average (denoted by ·) equation (B1). Because 𝑀(𝑥, 𝑦,0,𝑡) has no horizontal structure, it is equal to its horizontal average. On a horizontally periodic domain, all but two terms vanish in the averaged equation:



Because the forcing is horizontally uniform in all of our simulations, this reduces to (13). Note that subtracting (B2) from (B1) yields a condition on the integral of 𝐴:



This paper is available on arxiv under CC 4.0 license.