Shelf water entrainment by gulf stream warm core rings
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Shelf Water Entrainment by Gulf Stream Warm Core Rings. By Ayan Chaudhuri. Agenda. Overview Data Quasi-geostrophic Potential Vorticity Model Ring Entrainment Model Results Future Work. Overview.

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Agenda
Agenda

  • Overview

  • Data

  • Quasi-geostrophic Potential Vorticity Model

  • Ring Entrainment Model

  • Results

  • Future Work


Overview
Overview

  • Common Occurrence of Gulf Stream warm-core rings (WCRs) within the western North Atlantic’s Slope Sea (SS) and their role in causing seaward entrainment of outer continental shelf water is well documented.

  • Most reports concerning WCRs and their associated shelf water entrainments have been based upon single surveys or time-series from individual WCRs. Long term impacts not known.

  • AIM: Estimate annual shelf water volume entrained into the SS by WCRs and study its interannual variability.

Source: John Hopkins Remote Sensing Lab

05/02/98


Data

  • Sea Surface Temperature (SST) observations of WCRs within the Slope Sea from 1978-1999.

  • Domain 75oW and 50oW

  • Satellite data were digitized at Bedford Institute of Oceanography (BIO), provided by Ken Drinkwater

  • Data only has positions of rings

  • Shelf Slope Front (SSF) and Gulf Stream North Wall (GSNW) also available


Quasi geostrophic potential vorticity model qgpv
Quasi-geostrophic Potential Vorticity Model (QGPV)

  • Proposed by Melvin E. Stern, “Large-Scale Lateral Entrainment and Detrainment at the Edge of a Geostrophic Shear Layer”, JPO, Vol.17, No. 10, 1987

  • “The evolution of large-amplitude disturbances at the outer edge of a quasi-geostrophic shear layer depends on the sign of the outward gradient of potential vorticity. Entrainment of ambient water can occur when the gradient of relative vorticity dominates in the potential vorticity, and detrainment from the current can occur when the gradient of isopycnal thickness dominates.”


QGPV

  • Derivation (International Geophysics Series, Vol. 19, M.E. Stern)

    Geostrophic Equation:

    fv = 1/r dp/dx; fu = -1/r dp/dy …. (1)

    Substituting dp = rg dH in (1) we get

    v = (g/f) dH/dx ; u = -(g/f) dH/dy or V = (g/f) kdH….(2)

    Integrate (2) over time on a length scale L

    |V|L = (g/f)[h - Hm] where Hm = mean thickness and h varies over time

    H-Hm = |V|L f/g …. (3)

    Dividing both sides of (3) by Hm we get

    (H-Hm)/Hm = |V|L f/gHm ….. (4)

    Multiply and divide RHS (4) by fL we get

    (h-Hm)/Hm = |V|/fL * f2L2/gHm … (5)


QGPV

(h-Hm)/Hm = |V|/fL * f2L2/gHm … (5)

Now |V|/fL= Rossby No. (R) and f2L2/gHm = Burger No.

Quasi-geostrophy assumes that Burger No. ~ 1, thus (5) becomes

h’/Hm = |V|/fL …. (6) where h’(x,y,t) = h-Hm

Now |V|/L = dv/dx - du/dy= z ,thus

PV = z/f - h’/Hm …. (7)

Quasi-geostrophic equation for Potential Vorticity

where z = relative vorticity

f = Coriolis parameter

h’ (x,y,t) = deviation of thickness from Hm in time

Hm = mean thickness


QGPV

PV = z/f - h’/Hm

  • PV is dimensionless

    dPV = dz/df – dh’/Hm … (8) (where d is in space or time)

  • Ideally df /dx ~ constant b hence important factors are

    Dz and dh’

  • Conservation of PV suggests that dPV =0, thus

    if z increases, h’ should increase or vice versa

    if z decreases, h’ should decrease or vice versa (As observed with WCRs, rings decrease in size and slow down with time)


QGPV

  • In reality ideal case does not hold true. Large scale amplitude disturbances cause PV anomalies with predominant effect on dh’

    dPV = dz/df – dh’/Hm (8)

  • Positive anomaly occurs when dz dominates (8) and negative anomaly occurs when dh’ dominates (8)

  • The shear layer however would want to reach its equilibrium stage (PV=0), hence

    Positive anomaly caused by dz domination will cause dh’ to increase, leading to ambient water entrainment.

    Negative anomaly caused by dh’ domination will cause dh’ to decrease, leading to detrainment


Ring entrainment model
Ring Entrainment Model

PV = z/f - h’/Hm …. (7)

  • Since no depth data is available for WCRs, thickness at the surface is taken in consideration. Thickness at the surface is governed by radius (R) of the ring.

    Thus (7) becomes

    PV = z/f - r’/Rm …. (9)

    where r’ is deviation from the mean radius Rm of a ring

    z = V/R + dV/dR …. (10) [Csanady, 1979] for WCRs

    f = 2W sinf …. (11)

  • How do we get V and R from WCR dataset ????????


REM

  • Best fit Ellipse Model

  • Ellipse provides Ring Center, Orientation, and Radius = sqrt(a*b),

    where a and b are length of semi-major and semi-minor axis lengths

  • Finite difference scheme was used to calculate swirl velocity as

    V = f2- f1/(t2-t1)

Taylor and Gangopadhyay, 1997



REM

PV = z/f - r’/Rm …. (9)

  • Taking the mean radius (Rm) of all observations of a single ring and consequently calculating radius anomalies to the mean (r’) would invoke a biased estimate in (9)

  • Finite differencing chosen to be better estimate, thus

    PV = z/f – ri’/Ri where ri’ = Ri – Ri-1 …. (12)

  • Temporal Gradient of PV is calculated using finite differencing assuming that the first observation is in steady state or dPV =0;



REM

  • All observations with positive PV anomalies are taken to entrain ambient water based on

    dPV = dz/df – d ri’/ Ri

  • The amount of water entrained depends on ri’

    Suppose dPV > 0 at somed ri’ = Zobs

    Ideally dPV ~ 0 , thus d ri’ would want increase to

    dz/df X Ri= Zcalc

    Entrained Area (A) = p (Zcalc– Zobs)2

    Entrained Area (A) = Streamer Area (Length X Width)

    Streamer Length = A/ Streamer Width

    Streamer Width = 12km (Bisagni, 1983)


REM

  • If streamer Length > Observed Distance (Ring Edge and SSF), shelf water entrainment is assumed.





Future work
Future Work

  • SHORT TERM

    - Assign Uncertainties

    - Verification ?????

    - Regional correlation with NAO

  • LONG TERM

    - Nutrient Fluxes

    - Why NAO strongly correlates to WCR activity ? Model Results


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